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ANDREW LO: What I want to
talk about is option pricing.

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00:00:28,960 --> 00:00:31,860
But given that there's
the midterm coming up,

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00:00:31,860 --> 00:00:34,420
what I'd like to do
is to actually skip

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the more technical part today.

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00:00:36,766 --> 00:00:38,140
Today, what I was
going to do was

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00:00:38,140 --> 00:00:42,060
to describe a method
for pricing options,

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00:00:42,060 --> 00:00:44,350
a particular
option-pricing formula.

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00:00:44,350 --> 00:00:48,520
Now, we have a course, 15.437,
on options and futures.

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00:00:48,520 --> 00:00:51,340
And that's really what I would
recommend for those of you who

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00:00:51,340 --> 00:00:53,200
are interested in derivatives.

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00:00:53,200 --> 00:00:55,780
But we really can't
let you leave MIT

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00:00:55,780 --> 00:00:58,720
without understanding a little
bit about the basics of option

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00:00:58,720 --> 00:00:59,680
pricing.

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00:00:59,680 --> 00:01:03,500
And it's such a beautiful
argument that it's important,

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00:01:03,500 --> 00:01:06,310
I think, for all of you
to see it at least once.

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00:01:06,310 --> 00:01:09,190
But since I'd like you to focus
on it and really absorb it,

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00:01:09,190 --> 00:01:11,410
and I suspect that most
of you are thinking

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00:01:11,410 --> 00:01:15,430
about the mid-term, I'd rather
postpone that till Monday,

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00:01:15,430 --> 00:01:19,060
and then talk today about the
very basics of option payoff

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00:01:19,060 --> 00:01:22,280
diagrams, which is
relatively straightforward.

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00:01:22,280 --> 00:01:25,490
And then give you a little bit
of a history of option pricing,

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00:01:25,490 --> 00:01:28,070
and tell you a bit
about how it came about.

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00:01:28,070 --> 00:01:31,060
And ultimately,
where the literature

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00:01:31,060 --> 00:01:34,220
fits within the grand
scheme of things.

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00:01:34,220 --> 00:01:38,710
So last time, if you recall,
we talked about options

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00:01:38,710 --> 00:01:40,570
as insurance.

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00:01:40,570 --> 00:01:46,270
And we went through a very
simple set of examples,

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00:01:46,270 --> 00:01:49,150
where I described the
put option as really

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00:01:49,150 --> 00:01:52,810
being parallel to insurance in
all of these different terms.

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00:01:52,810 --> 00:01:56,920
But the differences are that
a put option, first of all,

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00:01:56,920 --> 00:01:58,810
can be used early.

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00:01:58,810 --> 00:02:01,480
So you don't have to wait
until you have an accident

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00:02:01,480 --> 00:02:02,950
or wait until it expires.

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00:02:02,950 --> 00:02:05,050
You can decide at
any point in time

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00:02:05,050 --> 00:02:07,130
that you want to exercise it.

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00:02:07,130 --> 00:02:10,539
Also, unlike
insurance contracts,

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00:02:10,539 --> 00:02:15,470
options can be bought and
sold in organized exchanges.

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00:02:15,470 --> 00:02:16,690
So you can buy a put option.

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00:02:16,690 --> 00:02:18,460
You can sell a put option.

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00:02:18,460 --> 00:02:23,590
And then finally, dividends
have an impact on options.

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00:02:23,590 --> 00:02:26,470
And so most options have
dividend protection,

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00:02:26,470 --> 00:02:28,450
in the sense that if
there's a dividend paid,

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00:02:28,450 --> 00:02:32,450
then the strike price will
be adjusted accordingly.

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00:02:32,450 --> 00:02:35,170
Now, it's important
to understand

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00:02:35,170 --> 00:02:39,220
the differences between an
option and an underlying.

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00:02:39,220 --> 00:02:43,180
Because they really have
some very, very important

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00:02:43,180 --> 00:02:45,560
distinctions, in terms
of their payoffs.

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00:02:45,560 --> 00:02:48,190
So the way that we
try to emphasize that

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00:02:48,190 --> 00:02:53,020
is by looking at a diagram
that graphs the option

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00:02:53,020 --> 00:02:57,310
value as a function of the
underlying parameters that

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00:02:57,310 --> 00:02:58,270
influence the option.

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00:02:58,270 --> 00:03:01,130
And the most important
parameter is, of course,

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00:03:01,130 --> 00:03:04,540
the underlying price
of the stock or asset

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00:03:04,540 --> 00:03:07,640
on which the option is written.

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00:03:07,640 --> 00:03:10,510
So this is an example
of a payoff diagram

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00:03:10,510 --> 00:03:16,280
that plots the value of
the option at maturity

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00:03:16,280 --> 00:03:20,060
for a call option on
an underlying stock.

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00:03:20,060 --> 00:03:23,180
And the x-axis is the
price of the stock.

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And the y-axis is
the value or price

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00:03:26,300 --> 00:03:31,850
of the option on the date
of maturity or exercise.

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00:03:31,850 --> 00:03:37,760
So let's suppose that the option
has a strike price of $20.

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00:03:37,760 --> 00:03:39,680
That gives the
holder of the option

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00:03:39,680 --> 00:03:47,030
the right to purchase the stock
for $20 at the maturity date.

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00:03:47,030 --> 00:03:49,820
So it's a call option,
meaning it gives you the right

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00:03:49,820 --> 00:03:52,670
to call away or buy the stock.

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00:03:52,670 --> 00:03:55,820
And the strike
price is set at $20.

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00:03:55,820 --> 00:03:59,720
Now, if the actual price
of the stock is below $20,

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00:03:59,720 --> 00:04:01,637
you're never going to
want to call the option.

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00:04:01,637 --> 00:04:03,844
Rather, you're never going
to want to call the stock.

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00:04:03,844 --> 00:04:06,470
You're never going to want
to exercise the call option.

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00:04:06,470 --> 00:04:09,200
Because if you did,
you'd be buying something

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00:04:09,200 --> 00:04:14,000
for $20 that would be
worth less than $20.

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00:04:14,000 --> 00:04:18,980
So if the true stock price
is anything less than $20,

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00:04:18,980 --> 00:04:24,350
this option, at expiration,
is worth nothing to you.

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00:04:24,350 --> 00:04:26,560
You would never use it.

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00:04:26,560 --> 00:04:30,700
Now, it's critical to understand
that this payoff diagram is

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00:04:30,700 --> 00:04:33,630
the value at maturity.

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00:04:33,630 --> 00:04:38,010
Prior to maturity, if the
value of the underlying stock

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00:04:38,010 --> 00:04:41,730
is less than $20, the option
could still have value.

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00:04:41,730 --> 00:04:43,020
Typically it will have value.

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00:04:43,020 --> 00:04:46,320
Because there's always a chance
that the stock price goes

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00:04:46,320 --> 00:04:50,750
above $20 at the maturity date.

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00:04:50,750 --> 00:04:53,810
So let's be clear that this
is the value of the call

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00:04:53,810 --> 00:04:56,150
option at maturity date.

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00:04:56,150 --> 00:04:57,830
And if it turns
out that the stock

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00:04:57,830 --> 00:05:03,020
price is greater than $20,
then the option has value.

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00:05:03,020 --> 00:05:07,460
And the value increases,
dollar for dollar,

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00:05:07,460 --> 00:05:12,760
with the stock price above $20.

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00:05:12,760 --> 00:05:17,020
So the slope of this
line is 45 degrees.

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00:05:17,020 --> 00:05:21,070
It literally goes up in lockstep
with the underlying stock

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00:05:21,070 --> 00:05:22,210
price.

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00:05:22,210 --> 00:05:25,900
To be clear, if the
stock price is $25

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00:05:25,900 --> 00:05:29,200
and you get to buy it
for $20, the option,

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00:05:29,200 --> 00:05:34,510
that right to buy
for $20 is worth $5.

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00:05:34,510 --> 00:05:36,730
Because the stock
is really worth $25.

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00:05:36,730 --> 00:05:39,760
So the way you can see that is
you can buy the stock for $20,

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00:05:39,760 --> 00:05:42,620
with this piece of
paper that you own.

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00:05:42,620 --> 00:05:44,620
And then you can turn
around and sell that stock

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00:05:44,620 --> 00:05:48,730
on the open market for $25.

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00:05:48,730 --> 00:05:50,200
So you've made that $5 profit.

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00:05:53,100 --> 00:05:56,610
The important thing about
this diagram, the blue line,

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00:05:56,610 --> 00:06:02,370
is that the upside is unlimited.

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00:06:02,370 --> 00:06:08,120
But the downside is
very much limited, at 0.

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00:06:08,120 --> 00:06:09,860
OK?

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00:06:09,860 --> 00:06:14,530
So this is an example
of a security that

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00:06:14,530 --> 00:06:18,760
has an asymmetric
payoff, asymmetric.

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00:06:18,760 --> 00:06:20,860
The upside is not the
same as the downside.

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00:06:20,860 --> 00:06:25,420
Remember the payoff of a stock,
or of a futures contract.

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00:06:25,420 --> 00:06:26,170
It's symmetric.

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00:06:26,170 --> 00:06:27,834
It's that straight line.

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00:06:27,834 --> 00:06:29,250
Here, this is not
a straight line.

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00:06:29,250 --> 00:06:32,920
It's kinked at the
strike price, K. That's

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00:06:32,920 --> 00:06:34,570
a very important feature.

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00:06:34,570 --> 00:06:37,570
Now, it looks like,
from this diagram,

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00:06:37,570 --> 00:06:41,650
this call option is one
of these propositions

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00:06:41,650 --> 00:06:45,190
that you hear on late-night TV,
make a $1 million with no money

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00:06:45,190 --> 00:06:45,850
down.

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00:06:45,850 --> 00:06:47,860
Like, there's no way to lose.

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00:06:47,860 --> 00:06:49,020
How could that possibly be?

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00:06:49,020 --> 00:06:51,685
How could we have come up with
a security that has no downside?

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00:06:54,780 --> 00:06:58,170
Wouldn't everybody want one?

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00:06:58,170 --> 00:06:58,670
Yeah?

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00:06:58,670 --> 00:07:01,239
AUDIENCE: Well, it
has value [INAUDIBLE].

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00:07:01,239 --> 00:07:02,030
ANDREW LO: Exactly.

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00:07:02,030 --> 00:07:03,520
Yeah, there's no free lunch.

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00:07:03,520 --> 00:07:06,090
So of course, everybody
wants it if it's free.

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00:07:06,090 --> 00:07:07,977
But of course, it's not free.

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00:07:07,977 --> 00:07:09,060
So you have to pay for it.

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00:07:09,060 --> 00:07:13,170
You have to pay something
today in order to get access

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00:07:13,170 --> 00:07:15,420
to this asymmetric payoff.

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00:07:15,420 --> 00:07:21,180
So the net payoff, that is, if
you were buying the call option

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00:07:21,180 --> 00:07:24,240
and paying a certain
amount of money,

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00:07:24,240 --> 00:07:27,210
then the net payoff
to you would be

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00:07:27,210 --> 00:07:31,530
given by the dotted line,
which is the blue line.

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00:07:31,530 --> 00:07:38,680
But you subtract from it
the value of the premium

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00:07:38,680 --> 00:07:39,520
that you pay.

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00:07:39,520 --> 00:07:41,510
It's called an option premium.

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00:07:41,510 --> 00:07:45,560
But it's just the price of the
option whenever you bought it.

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00:07:45,560 --> 00:07:47,780
And then if you want to
take into account the time

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00:07:47,780 --> 00:07:53,030
value of money, you should take
the future value of that price

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00:07:53,030 --> 00:07:55,440
that you paid when
you bought the option.

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00:07:55,440 --> 00:07:58,580
So if you bought the option
in the beginning of the month

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00:07:58,580 --> 00:08:01,034
and it expires at
the end of the month,

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00:08:01,034 --> 00:08:03,200
you've paid something at
the beginning of the month.

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00:08:03,200 --> 00:08:05,480
If you want to find
your net payoff,

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00:08:05,480 --> 00:08:09,830
you could either, at
the maturity date,

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00:08:09,830 --> 00:08:12,920
subtract from the
blue line the value

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00:08:12,920 --> 00:08:16,940
of what you paid multiplied
by the one-month interest rate

156
00:08:16,940 --> 00:08:22,680
factor, so that you subtract
time t dollars from time t

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00:08:22,680 --> 00:08:24,320
dollars.

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00:08:24,320 --> 00:08:26,870
Or you can do a present value,
where you take the payoff

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00:08:26,870 --> 00:08:28,786
and you move it back to
the beginning of time.

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00:08:28,786 --> 00:08:30,260
Typically what we
do is we actually

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00:08:30,260 --> 00:08:33,890
ignore the time value of
money, just because it's

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00:08:33,890 --> 00:08:35,059
a month's worth of interest.

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00:08:35,059 --> 00:08:37,669
And people don't really
worry about that too much.

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00:08:37,669 --> 00:08:38,784
Yeah?

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00:08:38,784 --> 00:08:41,676
AUDIENCE: Can you
make some inferences

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00:08:41,676 --> 00:08:43,604
about the future
price of the stock

167
00:08:43,604 --> 00:08:45,532
by looking at the
price of the option?

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00:08:45,532 --> 00:08:47,542
ANDREW LO: Yes,
absolutely, you can.

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00:08:47,542 --> 00:08:49,500
And we're going to show
you how to do that when

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00:08:49,500 --> 00:08:51,333
I give you the asset
pricing formula for it.

171
00:08:51,333 --> 00:08:52,770
But you're absolutely right.

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00:08:52,770 --> 00:08:54,984
By looking at the
option, that gives you

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00:08:54,984 --> 00:08:56,400
information about
what's going on.

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00:08:56,400 --> 00:09:00,780
Just like when I tell you
for crisis management,

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00:09:00,780 --> 00:09:02,820
if you look at
T-bills today, you

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00:09:02,820 --> 00:09:06,420
get a sense of how much demand
there is for cash, putting

177
00:09:06,420 --> 00:09:07,650
money in your mattress.

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00:09:07,650 --> 00:09:09,750
By looking at
options, you actually

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00:09:09,750 --> 00:09:12,690
get a sense of where markets
are going to be going.

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00:09:12,690 --> 00:09:14,420
So after I give you
a pricing formula,

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00:09:14,420 --> 00:09:16,940
next time, I'm going to show
you the prices of options.

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00:09:16,940 --> 00:09:18,356
In particular,
we're going to look

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00:09:18,356 --> 00:09:24,600
at the price of a put option on
the S&P 500 for the next month

184
00:09:24,600 --> 00:09:26,070
and for the next two months.

185
00:09:26,070 --> 00:09:29,370
And you're going to find a
very, very big difference

186
00:09:29,370 --> 00:09:30,450
in those two.

187
00:09:30,450 --> 00:09:33,060
That's telling you something
about where the market thinks

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00:09:33,060 --> 00:09:36,759
volatility is going
in the S&P 500

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00:09:36,759 --> 00:09:38,050
over the next couple of months.

190
00:09:38,050 --> 00:09:40,091
So yes, there'll be all
sorts of wonderful things

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00:09:40,091 --> 00:09:42,910
you'll be able to tell
by looking at the prices.

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00:09:42,910 --> 00:09:44,460
But in order to do
that, we do have

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00:09:44,460 --> 00:09:47,250
to understand how
these payoffs work.

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00:09:47,250 --> 00:09:49,330
So getting back
to this diagram--

195
00:09:49,330 --> 00:09:51,690
I want to make sure
everybody is with me now--

196
00:09:51,690 --> 00:09:55,080
this dotted line shows
you your net payoff

197
00:09:55,080 --> 00:09:59,310
and a net of the price you
paid for this particular call

198
00:09:59,310 --> 00:10:00,360
option.

199
00:10:00,360 --> 00:10:03,120
And the neat thing
about this net payoff

200
00:10:03,120 --> 00:10:06,650
is that it then describes to
you the fact that this is not

201
00:10:06,650 --> 00:10:09,690
a surefire way to make
money and not lose any.

202
00:10:09,690 --> 00:10:12,600
You might lose money, because
you paid something upfront

203
00:10:12,600 --> 00:10:14,600
for the call option.

204
00:10:14,600 --> 00:10:18,380
And so the only way you're
going to come out ahead

205
00:10:18,380 --> 00:10:22,600
is if the stock price
actually exceeds--

206
00:10:22,600 --> 00:10:28,460
not this point, but actually
something like this point.

207
00:10:28,460 --> 00:10:33,560
So the stock price has to go up
by a little bit more than $20

208
00:10:33,560 --> 00:10:35,540
in order for you to
make money, net of what

209
00:10:35,540 --> 00:10:39,140
it cost you to buy that option.

210
00:10:39,140 --> 00:10:40,880
Now, I want you to
go back and think

211
00:10:40,880 --> 00:10:43,790
about the difference between an
option and a futures contract.

212
00:10:43,790 --> 00:10:48,230
Remember a futures contract
we said was no money down,

213
00:10:48,230 --> 00:10:51,530
0 NPV when you get
into the futures.

214
00:10:51,530 --> 00:10:53,090
That's not true
with a call option.

215
00:10:53,090 --> 00:10:57,800
A call option is actually worth
a positive amount of money

216
00:10:57,800 --> 00:10:59,330
on day one.

217
00:10:59,330 --> 00:11:01,910
So if you want a
call option, you've

218
00:11:01,910 --> 00:11:03,440
actually got to pay for it.

219
00:11:03,440 --> 00:11:06,290
And then there's an issue about
whether you'll make money.

220
00:11:06,290 --> 00:11:08,720
Because it depends on
whether the stock price

221
00:11:08,720 --> 00:11:10,310
exceeds this point.

222
00:11:10,310 --> 00:11:13,190
It's got to exceed not only the
strike price, but the amount

223
00:11:13,190 --> 00:11:16,810
that you paid for that option.

224
00:11:16,810 --> 00:11:17,980
Any questions about that?

225
00:11:17,980 --> 00:11:20,200
Or is that pretty clear?

226
00:11:20,200 --> 00:11:21,100
So this is important.

227
00:11:21,100 --> 00:11:23,279
So ask now if you
don't quite get it.

228
00:11:23,279 --> 00:11:24,820
Because if you don't
get this, you're

229
00:11:24,820 --> 00:11:26,194
going to get
confused by what I'm

230
00:11:26,194 --> 00:11:28,860
going to say in a few minutes.

231
00:11:28,860 --> 00:11:31,530
Let me give you another example,
just to really fix ideas.

232
00:11:31,530 --> 00:11:33,890
Let's do the put option case.

233
00:11:33,890 --> 00:11:38,720
Now, the put option allows me to
sell the stock for, let's say,

234
00:11:38,720 --> 00:11:43,740
$20, or before
the exercise date.

235
00:11:43,740 --> 00:11:50,130
So with a put option, am I
going to hope if I buy a put--

236
00:11:50,130 --> 00:11:55,680
so I buy the right to
sell the stock at $20.

237
00:11:55,680 --> 00:11:58,620
That's a little bit
hard to keep track of.

238
00:11:58,620 --> 00:12:01,440
I'm buying a piece of paper
that gives me the right

239
00:12:01,440 --> 00:12:03,510
to sell the stock for $20.

240
00:12:03,510 --> 00:12:06,210
If I own that piece of
paper, this put option,

241
00:12:06,210 --> 00:12:08,555
am I going to wish that the
stock price goes up or down?

242
00:12:08,555 --> 00:12:09,180
AUDIENCE: Down.

243
00:12:09,180 --> 00:12:09,805
AUDIENCE: Down.

244
00:12:09,805 --> 00:12:11,050
ANDREW LO: Down.

245
00:12:11,050 --> 00:12:13,480
I'm only going to get
paid on the put option

246
00:12:13,480 --> 00:12:16,990
if the stock price
goes below $20.

247
00:12:16,990 --> 00:12:19,630
Because then I have
something valuable, right?

248
00:12:19,630 --> 00:12:22,720
If it goes below $20, I get
to sell the stock for $20.

249
00:12:22,720 --> 00:12:27,460
So I make the difference
between what it's worth and $20.

250
00:12:27,460 --> 00:12:30,200
If the stock price
is at $20 or above,

251
00:12:30,200 --> 00:12:32,530
then my put option
expires, worthless.

252
00:12:32,530 --> 00:12:33,730
I'm not going to use it.

253
00:12:33,730 --> 00:12:35,896
Because it would be foolish
for me to sell something

254
00:12:35,896 --> 00:12:39,070
for $20, when I can sell
on the open market for $25.

255
00:12:39,070 --> 00:12:43,630
So the payoff diagram is
exactly the opposite of this.

256
00:12:43,630 --> 00:12:47,610
In fact, it looks like this.

257
00:12:47,610 --> 00:12:53,120
So now the blue line is
the payoff of the option

258
00:12:53,120 --> 00:12:56,390
itself, the gross payoff.

259
00:12:56,390 --> 00:12:59,330
$20 and above, it's worthless.

260
00:12:59,330 --> 00:13:03,860
But $20 and below, this
is the 45-degree line.

261
00:13:03,860 --> 00:13:09,650
But unlike the call option,
my upside for the put option

262
00:13:09,650 --> 00:13:11,030
is limited.

263
00:13:11,030 --> 00:13:12,464
Is limited to what?

264
00:13:12,464 --> 00:13:14,120
AUDIENCE: 0.

265
00:13:14,120 --> 00:13:18,880
ANDREW LO: Right, 0 or whatever
that is, $10, in this case.

266
00:13:18,880 --> 00:13:21,530
If the stock price goes
to $0, then my put option

267
00:13:21,530 --> 00:13:24,290
is worth a maximum of $10.

268
00:13:24,290 --> 00:13:28,700
So the upside is bounded
by that $10 limit.

269
00:13:28,700 --> 00:13:30,860
And that's the gross upside.

270
00:13:30,860 --> 00:13:34,699
If I look at the net, I
subtract how much I pay.

271
00:13:34,699 --> 00:13:35,990
And then I get the dotted line.

272
00:13:39,739 --> 00:13:41,530
Any questions about
the put options payoff?

273
00:13:44,420 --> 00:13:47,240
Now, just to fix ideas, let
me go back to the call option

274
00:13:47,240 --> 00:13:50,720
and show the difference
between the stock return

275
00:13:50,720 --> 00:13:53,490
versus the call option return.

276
00:13:53,490 --> 00:13:56,470
If you take a look at
the call option, again,

277
00:13:56,470 --> 00:13:58,420
it's going to look
like this when

278
00:13:58,420 --> 00:14:00,490
you subtract from it the price.

279
00:14:00,490 --> 00:14:04,390
But the stock is going to
look like that line there.

280
00:14:04,390 --> 00:14:08,060
Meaning that the stock
return is linear.

281
00:14:08,060 --> 00:14:10,750
But the option
return is non-linear.

282
00:14:10,750 --> 00:14:14,470
And this is one of the most
important and subtle ideas

283
00:14:14,470 --> 00:14:15,430
with this instrument.

284
00:14:15,430 --> 00:14:17,500
Up until now, all
of the instruments

285
00:14:17,500 --> 00:14:22,150
that we've looked at stocks,
bonds, futures, and forwards,

286
00:14:22,150 --> 00:14:24,790
their payoffs have
been relatively simple,

287
00:14:24,790 --> 00:14:27,490
in the sense that they're
straight lines if you

288
00:14:27,490 --> 00:14:31,960
plot the underlying
price and their payoffs.

289
00:14:31,960 --> 00:14:36,370
This is the first time we have
analyzed the security that has

290
00:14:36,370 --> 00:14:38,980
a bizarre structure like this.

291
00:14:38,980 --> 00:14:40,840
And you might think
it's straightforward

292
00:14:40,840 --> 00:14:45,910
because well, you understand the
contractual terms of an option.

293
00:14:45,910 --> 00:14:47,980
But from a risk-and-return
perspective,

294
00:14:47,980 --> 00:14:50,110
it's actually quite a
bit more complicated

295
00:14:50,110 --> 00:14:52,540
than most people
would appreciate.

296
00:14:52,540 --> 00:14:56,140
One of the reasons that we are
in a current financial crisis

297
00:14:56,140 --> 00:14:59,860
today is because of the
complexity of the securities

298
00:14:59,860 --> 00:15:01,180
that have been created.

299
00:15:01,180 --> 00:15:03,610
And the complexities are
really along the lines

300
00:15:03,610 --> 00:15:05,380
of these non-linearities.

301
00:15:05,380 --> 00:15:09,130
As I mentioned to you,
insurance is a put option.

302
00:15:09,130 --> 00:15:13,210
So you can actually use the
theory of option pricing

303
00:15:13,210 --> 00:15:17,437
to value insurance contracts,
like credit default swaps.

304
00:15:17,437 --> 00:15:19,270
In fact, the payoff of
a credit default swap

305
00:15:19,270 --> 00:15:22,740
is not that different from
something that looks like this.

306
00:15:22,740 --> 00:15:26,390
And what that means is that
a portfolio of credit default

307
00:15:26,390 --> 00:15:30,440
swaps does not behave
like a portfolio of stocks

308
00:15:30,440 --> 00:15:31,940
or a portfolio of bonds.

309
00:15:31,940 --> 00:15:34,970
They have very
important differences,

310
00:15:34,970 --> 00:15:38,660
both in terms of their risk,
and in terms of their return.

311
00:15:38,660 --> 00:15:42,590
In this case, you can see
the risk of a put option

312
00:15:42,590 --> 00:15:44,420
is bounded above.

313
00:15:44,420 --> 00:15:46,130
The upside is bounded above.

314
00:15:46,130 --> 00:15:48,170
The downside is bounded.

315
00:15:48,170 --> 00:15:53,340
But the call option is unbounded
above, in terms of its upside.

316
00:15:53,340 --> 00:15:56,760
Bounded below, in
terms of its risk.

317
00:15:56,760 --> 00:15:59,340
What if, now, you
decided you were going

318
00:15:59,340 --> 00:16:02,640
to sell somebody a call option?

319
00:16:02,640 --> 00:16:06,210
Or you were going to
short a call option?

320
00:16:06,210 --> 00:16:09,201
Can anybody guess what the
payoff would look like?

321
00:16:09,201 --> 00:16:10,175
Yeah?

322
00:16:10,175 --> 00:16:12,610
AUDIENCE: If you're going
to sell a call [INAUDIBLE]

323
00:16:12,610 --> 00:16:14,071
agreement that's your payoff.

324
00:16:14,071 --> 00:16:14,937
ANDREW LO: Yeah.

325
00:16:14,937 --> 00:16:16,520
AUDIENCE: As long
as the stock doesn't

326
00:16:16,520 --> 00:16:19,460
go above the [INAUDIBLE] so
someone can call you out.

327
00:16:19,460 --> 00:16:20,940
Then it's [INAUDIBLE].

328
00:16:20,940 --> 00:16:21,960
ANDREW LO: So what is
it going to look like,

329
00:16:21,960 --> 00:16:23,010
in terms of the diagram?

330
00:16:23,010 --> 00:16:24,360
How would I have to change this?

331
00:16:24,360 --> 00:16:26,220
AUDIENCE: It would
be flat, say, $2.

332
00:16:26,220 --> 00:16:27,615
And then it would go down.

333
00:16:27,615 --> 00:16:28,890
ANDREW LO: That's right.

334
00:16:28,890 --> 00:16:32,430
It would be a mirror image
of the blue line, where

335
00:16:32,430 --> 00:16:36,540
you reflect it along the
x-axis, it would go this way.

336
00:16:36,540 --> 00:16:41,560
And what that means is that
your downside is unlimited.

337
00:16:41,560 --> 00:16:44,915
But your upside is very limited.

338
00:16:44,915 --> 00:16:46,540
Now, why would anybody
want to do that?

339
00:16:46,540 --> 00:16:48,550
That seems like a terrible deal.

340
00:16:48,550 --> 00:16:50,260
Well, the difference
is that you are now

341
00:16:50,260 --> 00:16:52,700
getting paid to do that.

342
00:16:52,700 --> 00:16:55,930
In other words, if
you flip this image--

343
00:16:55,930 --> 00:16:57,520
let me draw it here.

344
00:17:01,470 --> 00:17:06,270
If you now have a call
option that you've shorted,

345
00:17:06,270 --> 00:17:08,900
you go down here.

346
00:17:08,900 --> 00:17:10,599
This is $20.

347
00:17:10,599 --> 00:17:12,440
You will get paid
for doing this.

348
00:17:12,440 --> 00:17:15,252
Meaning if you look
at your net return,

349
00:17:15,252 --> 00:17:16,460
it's going to look like this.

350
00:17:22,210 --> 00:17:25,200
So that means that as long
as the stock price stays

351
00:17:25,200 --> 00:17:31,230
below a little bit
extra than $20,

352
00:17:31,230 --> 00:17:33,810
you will actually get
to keep that premium.

353
00:17:33,810 --> 00:17:38,682
But if the stock price goes
up, your losses are unbounded.

354
00:17:38,682 --> 00:17:39,390
That's different.

355
00:17:39,390 --> 00:17:41,700
That's a different
payoff structure

356
00:17:41,700 --> 00:17:47,190
than what we're used to with
traditional instruments.

357
00:17:47,190 --> 00:17:50,550
You can do all sorts
of calculations.

358
00:17:50,550 --> 00:17:52,410
Long Call looks like that.

359
00:17:52,410 --> 00:17:53,880
Long Put looks like that.

360
00:17:53,880 --> 00:17:55,740
Shorter Call looks like this.

361
00:17:55,740 --> 00:17:58,370
And Shorting a Put
looks like that.

362
00:18:00,990 --> 00:18:06,050
And once you take all of these
things and put them together,

363
00:18:06,050 --> 00:18:10,850
you can mix and match and get
some really interesting payoff

364
00:18:10,850 --> 00:18:13,860
types of structures.

365
00:18:13,860 --> 00:18:15,630
So let me give you an example.

366
00:18:15,630 --> 00:18:18,320
This is just payoff
tables that will show you

367
00:18:18,320 --> 00:18:19,430
when you get paid what.

368
00:18:19,430 --> 00:18:21,500
So this is a very
helpful exercise for you

369
00:18:21,500 --> 00:18:25,160
to go through, just to
verify that these graphs are,

370
00:18:25,160 --> 00:18:27,560
in fact, what they should be.

371
00:18:27,560 --> 00:18:30,080
So I would ask you to go
through this on your own.

372
00:18:30,080 --> 00:18:33,440
And there are all
sorts of trade-offs

373
00:18:33,440 --> 00:18:36,740
that you can
implement by looking

374
00:18:36,740 --> 00:18:39,110
at these various
different payoffs

375
00:18:39,110 --> 00:18:40,290
and putting them together.

376
00:18:40,290 --> 00:18:43,640
For example, you can
buy a stock and a put,

377
00:18:43,640 --> 00:18:46,160
or buying a call with one
strike and selling a call

378
00:18:46,160 --> 00:18:49,730
with another, or buying a call
and a put with the same strike.

379
00:18:49,730 --> 00:18:53,360
Each of these
portfolios of options

380
00:18:53,360 --> 00:18:56,510
gives you a different
kind of a payoff diagram.

381
00:18:56,510 --> 00:19:01,970
And as a result, it allows you
to make bets on market events

382
00:19:01,970 --> 00:19:05,730
that you otherwise wouldn't
be able to make a bet on.

383
00:19:05,730 --> 00:19:08,230
So let me give you
an example of this.

384
00:19:08,230 --> 00:19:09,270
Let's see.

385
00:19:09,270 --> 00:19:13,680
Let's do something
like, oh, I don't know.

386
00:19:13,680 --> 00:19:16,320
How about a call and a put?

387
00:19:16,320 --> 00:19:18,840
Suppose you decide
to buy a call,

388
00:19:18,840 --> 00:19:22,150
and you buy a put with the
exact same strike price.

389
00:19:22,150 --> 00:19:24,000
So buying a call at
a strike price of $50

390
00:19:24,000 --> 00:19:26,280
will give you that left diagram.

391
00:19:26,280 --> 00:19:29,070
And then buying a put with
the strike price of $50

392
00:19:29,070 --> 00:19:31,980
will give you the right diagram.

393
00:19:31,980 --> 00:19:36,000
And your payoff for
those two, at maturity,

394
00:19:36,000 --> 00:19:37,710
is going to look like a V.

395
00:19:37,710 --> 00:19:40,290
Now, in fact, you have
to subtract how much you

396
00:19:40,290 --> 00:19:42,690
paid in order to do this.

397
00:19:42,690 --> 00:19:50,690
So your net payoff will
be this V, shifted down.

398
00:19:50,690 --> 00:19:54,210
Sorry, I didn't do the
interactive graphics here.

399
00:19:54,210 --> 00:19:58,900
But it's going to look like
this, where what I've done

400
00:19:58,900 --> 00:20:02,230
is I've subtracted the
amount of money it cost you

401
00:20:02,230 --> 00:20:05,760
to buy the put and the call.

402
00:20:05,760 --> 00:20:06,430
Yeah, question.

403
00:20:06,430 --> 00:20:10,275
AUDIENCE: In this particular
example, really all

404
00:20:10,275 --> 00:20:13,690
you're saying is, except for a
short range in the stock price

405
00:20:13,690 --> 00:20:16,441
around the strike price,
you will always make money.

406
00:20:16,441 --> 00:20:17,440
ANDREW LO: That's right.

407
00:20:17,440 --> 00:20:19,144
AUDIENCE: So is
there a reason why

408
00:20:19,144 --> 00:20:20,884
you wouldn't do a
lot of this, if you

409
00:20:20,884 --> 00:20:22,509
know that there is
some movement that's

410
00:20:22,509 --> 00:20:23,845
going to happen in the stock?

411
00:20:23,845 --> 00:20:26,440
ANDREW LO: So the question
is, how much does it

412
00:20:26,440 --> 00:20:28,460
cost you to do that?

413
00:20:28,460 --> 00:20:31,240
When you say small,
it's all relative.

414
00:20:31,240 --> 00:20:33,700
You've got to find out
exactly what that is.

415
00:20:33,700 --> 00:20:37,570
The smaller the range
is, the more expensive

416
00:20:37,570 --> 00:20:40,120
it'll be for you
to actually buy it.

417
00:20:40,120 --> 00:20:42,310
So there's a trade-off.

418
00:20:42,310 --> 00:20:44,450
It's all a matter of
how much you pay for it.

419
00:20:44,450 --> 00:20:46,210
But before I go
there, let me just

420
00:20:46,210 --> 00:20:47,950
make sure everybody
understands what

421
00:20:47,950 --> 00:20:50,110
this payoff is accomplishing.

422
00:20:50,110 --> 00:20:52,690
What are you doing
when you are buying

423
00:20:52,690 --> 00:20:56,920
a portfolio with a payoff
diagram that looks like this?

424
00:20:56,920 --> 00:20:59,440
What you're doing is
saying that you're

425
00:20:59,440 --> 00:21:02,800
going to make lots
of money if the stock

426
00:21:02,800 --> 00:21:06,160
price goes way up or way down.

427
00:21:06,160 --> 00:21:09,280
The only way you're not
going to make money,

428
00:21:09,280 --> 00:21:11,830
if the stock is not
doing a whole lot,

429
00:21:11,830 --> 00:21:13,540
if it's staying around here.

430
00:21:13,540 --> 00:21:14,650
OK.

431
00:21:14,650 --> 00:21:18,430
So this is an example
where you are making a bet.

432
00:21:18,430 --> 00:21:20,260
Not that markets
are going to go up,

433
00:21:20,260 --> 00:21:22,040
not that markets are
going to go down,

434
00:21:22,040 --> 00:21:24,790
but that markets are
going to be wild.

435
00:21:24,790 --> 00:21:27,940
That is, you're making
a bet on volatility.

436
00:21:27,940 --> 00:21:32,530
Which may seem like a
pretty good bet nowadays.

437
00:21:32,530 --> 00:21:35,470
But the problem is that
there's a difference

438
00:21:35,470 --> 00:21:40,526
between this diagram
and this diagram.

439
00:21:40,526 --> 00:21:41,650
And what is the difference?

440
00:21:41,650 --> 00:21:45,340
What determines how big or
small this little tiny area is,

441
00:21:45,340 --> 00:21:47,140
where you don't make any money?

442
00:21:47,140 --> 00:21:50,470
What determines that is how
much you have to subtract

443
00:21:50,470 --> 00:21:53,590
and how far this V
gets shifted down.

444
00:21:53,590 --> 00:21:54,340
And you know what?

445
00:21:54,340 --> 00:21:57,440
Right now, it's
shifted down a lot.

446
00:21:57,440 --> 00:22:01,030
In other words, it costs a
lot to buy a put and a call.

447
00:22:01,030 --> 00:22:02,080
Why does it cost a lot?

448
00:22:02,080 --> 00:22:04,180
Because volatility is very high.

449
00:22:04,180 --> 00:22:07,120
And when you're buying a
put, you're buying insurance.

450
00:22:07,120 --> 00:22:10,390
It's very, very expensive
now to buy insurance.

451
00:22:10,390 --> 00:22:13,471
Because we're in the
middle of a hurricane.

452
00:22:13,471 --> 00:22:15,220
And that's probably
the worst time for you

453
00:22:15,220 --> 00:22:17,345
to buy hurricane insurance,
is when you're actually

454
00:22:17,345 --> 00:22:19,420
in the middle of a hurricane.

455
00:22:19,420 --> 00:22:22,460
So what that means is, that this
thing has shifted down a lot.

456
00:22:22,460 --> 00:22:26,020
So that means that you have to
have really, really volatile

457
00:22:26,020 --> 00:22:28,720
markets in order to make money.

458
00:22:28,720 --> 00:22:33,940
So it's shifted down enough
so that supply equals demand,

459
00:22:33,940 --> 00:22:35,057
as you would expect.

460
00:22:35,057 --> 00:22:36,890
So there's no free lunch
going on out there.

461
00:22:36,890 --> 00:22:38,230
It's priced fairly.

462
00:22:38,230 --> 00:22:39,730
Now, even though
it's priced fairly,

463
00:22:39,730 --> 00:22:42,146
if it turns out that you're
the kind of person that really

464
00:22:42,146 --> 00:22:44,260
doesn't like a lot of
risk and you believe

465
00:22:44,260 --> 00:22:46,210
there's going to be
tons more volatility

466
00:22:46,210 --> 00:22:49,060
coming, then for you,
it's worth it to do it.

467
00:22:49,060 --> 00:22:52,600
For somebody else who
doesn't believe that there's

468
00:22:52,600 --> 00:22:55,470
going to be a lot more
volatility coming,

469
00:22:55,470 --> 00:22:58,200
it's worth it to be on the
other side of that trade.

470
00:22:58,200 --> 00:23:01,090
By the way, if I'm on the
other side of the trade,

471
00:23:01,090 --> 00:23:04,020
what does my payoff
diagram look like then?

472
00:23:04,020 --> 00:23:07,450
If I'm selling a put and a
call, what will it look like?

473
00:23:07,450 --> 00:23:08,450
AUDIENCE: The opposite.

474
00:23:08,450 --> 00:23:10,180
ANDREW LO: Yeah,
exactly, the opposite.

475
00:23:10,180 --> 00:23:13,880
We're going to flip it, flip
this thing against the x-axis.

476
00:23:13,880 --> 00:23:19,030
So it'll be an upside-down
V. But because we're

477
00:23:19,030 --> 00:23:22,600
shorting puts and calls,
we get money upfront.

478
00:23:22,600 --> 00:23:28,910
So the upside-down V is going
to be pushed up over the x-axis.

479
00:23:28,910 --> 00:23:33,600
So it's going to look like
the mirror image of this.

480
00:23:33,600 --> 00:23:36,960
And as long as
stock prices are not

481
00:23:36,960 --> 00:23:42,950
more volatile than this
range, we will make money.

482
00:23:42,950 --> 00:23:48,370
But our downside is
unlimited in both directions.

483
00:23:48,370 --> 00:23:50,370
So you got to be
really confident

484
00:23:50,370 --> 00:23:52,890
that you know that markets
aren't going to be any more

485
00:23:52,890 --> 00:23:54,870
volatile than they are now.

486
00:23:54,870 --> 00:23:58,230
Now, if you were Warren Buffett,
and you bought Goldman Sachs

487
00:23:58,230 --> 00:24:00,210
three, four weeks
ago, and you thought

488
00:24:00,210 --> 00:24:02,842
it was a great deal
then, well, you

489
00:24:02,842 --> 00:24:04,050
would have lost money by now.

490
00:24:04,050 --> 00:24:05,910
Warren Buffett has lost money.

491
00:24:05,910 --> 00:24:07,560
On the other hand,
as you all know,

492
00:24:07,560 --> 00:24:10,200
Warren Buffett doesn't it make
investments for the short term.

493
00:24:10,200 --> 00:24:11,658
He's thinking about
this investment

494
00:24:11,658 --> 00:24:14,230
as a 10, 20-year investment.

495
00:24:14,230 --> 00:24:16,230
And over 10 or 20
years, I suspect

496
00:24:16,230 --> 00:24:18,044
it will be a very good deal.

497
00:24:18,044 --> 00:24:19,710
But if you're looking
at what's going on

498
00:24:19,710 --> 00:24:21,595
over the next few
weeks, the question

499
00:24:21,595 --> 00:24:23,220
is, do you believe
that markets will be

500
00:24:23,220 --> 00:24:24,962
less volatile or more volatile?

501
00:24:24,962 --> 00:24:26,670
If you do, you're
going to be on one side

502
00:24:26,670 --> 00:24:28,170
or the other of that trade.

503
00:24:28,170 --> 00:24:29,880
The point is that
this now allows

504
00:24:29,880 --> 00:24:33,080
us to make bets on volatility.

505
00:24:33,080 --> 00:24:35,540
Whereas before, with
a futures or a forward

506
00:24:35,540 --> 00:24:37,640
or a stock or a
bond, you only could

507
00:24:37,640 --> 00:24:40,580
bet on it going
up or going down,

508
00:24:40,580 --> 00:24:42,710
or mispricings
because certain kinds

509
00:24:42,710 --> 00:24:44,960
of arbitrage relationships
have been violated.

510
00:24:44,960 --> 00:24:46,820
This is the first
time that we've

511
00:24:46,820 --> 00:24:52,010
been able to make a
bet on wild swings.

512
00:24:52,010 --> 00:24:53,750
And that's a really
amazing thing.

513
00:24:53,750 --> 00:24:57,380
It's an extraordinary innovation
to be able to do that.

514
00:24:57,380 --> 00:25:02,254
It allows individuals to
engage in kinds of side bets

515
00:25:02,254 --> 00:25:03,920
that they otherwise
wouldn't be able to.

516
00:25:03,920 --> 00:25:06,170
And more importantly, it
allows other individuals

517
00:25:06,170 --> 00:25:10,027
to insure against certain
kinds of eventualities

518
00:25:10,027 --> 00:25:11,360
that they'd never be able to do.

519
00:25:11,360 --> 00:25:14,880
Now you can buy insurance
against volatility,

520
00:25:14,880 --> 00:25:17,620
which is a pretty remarkable
thing to be able to do.

521
00:25:17,620 --> 00:25:20,555
OK, so that's just one
example of an option strategy,

522
00:25:20,555 --> 00:25:21,950
a very simple one.

523
00:25:21,950 --> 00:25:25,670
There are other examples
that I've given you here.

524
00:25:25,670 --> 00:25:28,740
For example, this is
kind of a fun one.

525
00:25:28,740 --> 00:25:31,262
This is two calls.

526
00:25:31,262 --> 00:25:32,720
That should be a
minus sign, sorry.

527
00:25:32,720 --> 00:25:35,180
Call1 minus Call2.

528
00:25:35,180 --> 00:25:37,820
So you basically
buy a call option,

529
00:25:37,820 --> 00:25:41,210
and you short another one
at different strike prices.

530
00:25:41,210 --> 00:25:44,600
And so what this allows you to
do, this is really interesting.

531
00:25:44,600 --> 00:25:49,850
This gives you upside
from 50 up until 60.

532
00:25:49,850 --> 00:25:51,980
So you buy a call at 50.

533
00:25:51,980 --> 00:25:55,880
You're short a call at 60.

534
00:25:55,880 --> 00:25:59,150
So that means you're going to
get upside between 50 and 60.

535
00:25:59,150 --> 00:26:03,340
And then nothing after that
and nothing before that.

536
00:26:03,340 --> 00:26:05,770
Now, this seems like a
really ridiculous strategy

537
00:26:05,770 --> 00:26:06,520
to engage in.

538
00:26:06,520 --> 00:26:09,840
Why would you want to
cut off your upside?

539
00:26:09,840 --> 00:26:13,350
Because with a call, if
you just bought a call,

540
00:26:13,350 --> 00:26:15,240
you'd basically get
all of the upside.

541
00:26:15,240 --> 00:26:16,470
Right?

542
00:26:16,470 --> 00:26:18,030
Why would you ever
want to do this?

543
00:26:18,030 --> 00:26:19,680
Anybody tell me what
the logic for that is?

544
00:26:19,680 --> 00:26:19,890
Yeah.

545
00:26:19,890 --> 00:26:20,355
AUDIENCE: Because it's cheaper.

546
00:26:20,355 --> 00:26:21,330
ANDREW LO: Exactly.

547
00:26:21,330 --> 00:26:22,090
It's cheaper.

548
00:26:22,090 --> 00:26:25,110
It's cheaper because when
you short the call at 60,

549
00:26:25,110 --> 00:26:26,640
you're getting money today.

550
00:26:26,640 --> 00:26:29,580
So that helps you
finance the call at 50.

551
00:26:29,580 --> 00:26:32,030
It's cheaper, but
it's not a free lunch.

552
00:26:32,030 --> 00:26:35,130
What you're getting in
exchange for that extra premium

553
00:26:35,130 --> 00:26:39,180
is you're giving up any profits
above and beyond the stock

554
00:26:39,180 --> 00:26:41,010
price going above 60.

555
00:26:41,010 --> 00:26:44,070
So you're giving up
the unbounded upside.

556
00:26:44,070 --> 00:26:46,590
And you're bounding it at 60.

557
00:26:46,590 --> 00:26:48,420
But the benefit of
giving up that upside

558
00:26:48,420 --> 00:26:52,680
is that you now have some money
to reduce the cost of getting

559
00:26:52,680 --> 00:26:54,510
that call at 50.

560
00:26:54,510 --> 00:26:55,680
OK?

561
00:26:55,680 --> 00:26:58,380
And so you might use
this if you think,

562
00:26:58,380 --> 00:27:03,700
well, I suspect that the stock
has got some room to grow.

563
00:27:03,700 --> 00:27:07,420
I think it will bounce
around between 50 and 60.

564
00:27:07,420 --> 00:27:09,120
But I can't possibly
see the stock

565
00:27:09,120 --> 00:27:10,960
ever being worth more than 60.

566
00:27:10,960 --> 00:27:14,130
So I'm happy to give up that
upside to other people who

567
00:27:14,130 --> 00:27:17,370
are more optimistic than me,
and get some money for it

568
00:27:17,370 --> 00:27:22,530
and help me to finance my
purchase of the stock at 50.

569
00:27:22,530 --> 00:27:24,720
So it's cheaper.

570
00:27:24,720 --> 00:27:25,830
That's the bottom line.

571
00:27:25,830 --> 00:27:27,750
Another way of
looking at it is, you

572
00:27:27,750 --> 00:27:31,770
have to move this whole diagram
down by how much it costs.

573
00:27:31,770 --> 00:27:35,200
It turns out you move it down
by less than if it were just

574
00:27:35,200 --> 00:27:37,600
the pure call option by itself.

575
00:27:37,600 --> 00:27:41,040
So the way you can think of
it is you buy the call option.

576
00:27:41,040 --> 00:27:43,090
You move it down by that much.

577
00:27:43,090 --> 00:27:46,290
And then you sell the other
call and you move it up

578
00:27:46,290 --> 00:27:48,780
by the amount of that 60 call.

579
00:27:52,190 --> 00:27:53,000
So you can do this.

580
00:27:53,000 --> 00:27:54,200
You can do this in reverse.

581
00:27:54,200 --> 00:27:56,324
You can bet on the
downside, in that way.

582
00:27:56,324 --> 00:27:57,740
You can do something
that's called

583
00:27:57,740 --> 00:28:04,040
a butterfly spread, where
basically it looks like this.

584
00:28:07,770 --> 00:28:13,400
So the payoff if it stays
within a range, you get paid.

585
00:28:13,400 --> 00:28:17,450
But if it's really volatile,
then you don't get paid.

586
00:28:17,450 --> 00:28:20,584
So you're willing to give
up the upside on both ends

587
00:28:20,584 --> 00:28:23,000
because you think the stock
is going to be self-contained.

588
00:28:23,000 --> 00:28:26,360
You're betting against
volatility increasing,

589
00:28:26,360 --> 00:28:28,760
and you're using
the ability to get

590
00:28:28,760 --> 00:28:35,010
rid of those unbounded gains
to finance the positions.

591
00:28:35,010 --> 00:28:39,680
And it turns out that with
these kinds of payoffs,

592
00:28:39,680 --> 00:28:44,030
you can prove mathematically
that it's possible to generate

593
00:28:44,030 --> 00:28:46,910
any other payoff in the world.

594
00:28:46,910 --> 00:28:48,680
There is a mathematical
result that's

595
00:28:48,680 --> 00:28:53,600
actually related to this Taylor
approximation and Fourier

596
00:28:53,600 --> 00:28:57,350
expansion that says that any
possible security that you can

597
00:28:57,350 --> 00:29:01,730
come up with can be approximated
by a sequence of calls

598
00:29:01,730 --> 00:29:02,900
and puts.

599
00:29:02,900 --> 00:29:05,450
That's a really powerful idea.

600
00:29:05,450 --> 00:29:07,092
But in fact, from a
practical purpose,

601
00:29:07,092 --> 00:29:09,050
you don't even need to
use anything that fancy.

602
00:29:09,050 --> 00:29:12,620
If you have just a very small
number of calls and puts,

603
00:29:12,620 --> 00:29:15,470
you can put together
extraordinarily complex payoff

604
00:29:15,470 --> 00:29:20,240
diagrams that will get you
whatever kind of a risk profile

605
00:29:20,240 --> 00:29:21,310
you're looking for.

606
00:29:21,310 --> 00:29:24,670
That's the power
of option pricing.

607
00:29:24,670 --> 00:29:27,700
OK, any questions about
these payoff diagrams?

608
00:29:27,700 --> 00:29:30,190
I would urge you to work
through a few examples just

609
00:29:30,190 --> 00:29:31,980
to make sure you
really understand them.

610
00:29:31,980 --> 00:29:36,316
Because it's a easy thing to
think that you understand.

611
00:29:36,316 --> 00:29:38,440
But unless you're forced
to go through the exercise

612
00:29:38,440 --> 00:29:40,210
and draw these
diagrams, you won't

613
00:29:40,210 --> 00:29:43,090
have an appreciation
for how to do them

614
00:29:43,090 --> 00:29:45,630
and how important they are.

615
00:29:45,630 --> 00:29:46,774
Yeah, question.

616
00:29:46,774 --> 00:29:48,662
AUDIENCE: I'm
curious for a while,

617
00:29:48,662 --> 00:29:54,616
is there any
implicit volatility,

618
00:29:54,616 --> 00:30:00,028
I mean implicit in the price of
an option and a call and a put,

619
00:30:00,028 --> 00:30:01,996
is respective volatility
of the market.

620
00:30:01,996 --> 00:30:05,440
But how much inside that
price is it actually

621
00:30:05,440 --> 00:30:06,916
generating volatility itself?

622
00:30:06,916 --> 00:30:08,392
Do you see what I'm saying?

623
00:30:08,392 --> 00:30:11,162
The price, the call
could also be a motor

624
00:30:11,162 --> 00:30:12,328
of volatility in the market.

625
00:30:12,328 --> 00:30:13,780
ANDREW LO: Yes. .

626
00:30:13,780 --> 00:30:14,790
That's a great question.

627
00:30:14,790 --> 00:30:15,730
Let me repeat it.

628
00:30:15,730 --> 00:30:18,360
In fact, that question
was asked shortly

629
00:30:18,360 --> 00:30:20,485
after Black and Scholes
came up with their formula.

630
00:30:23,590 --> 00:30:26,560
It created the whole
literature, which

631
00:30:26,560 --> 00:30:30,610
was started by our very own
former Dean, Dick Schmalensee.

632
00:30:30,610 --> 00:30:34,050
He wrote a paper
with a fellow named--

633
00:30:34,050 --> 00:30:37,100
I think it's Robert Trippi,
small Schmalensee and Trippi.

634
00:30:37,100 --> 00:30:40,450
They wrote a paper on implied
volatilities of options.

635
00:30:40,450 --> 00:30:43,960
So the ideal is that
options are actually

636
00:30:43,960 --> 00:30:46,700
dependent on volatility.

637
00:30:46,700 --> 00:30:48,924
And I'll show you that not
this time, but next time.

638
00:30:48,924 --> 00:30:50,590
I'm going to go through
a pricing model.

639
00:30:50,590 --> 00:30:52,548
And you're going to see
how volatility actually

640
00:30:52,548 --> 00:30:54,250
plays a very concrete role.

641
00:30:54,250 --> 00:30:56,630
So they came up with
a brilliant idea.

642
00:30:56,630 --> 00:30:58,661
Let's take a look
at an option price.

643
00:30:58,661 --> 00:31:00,160
And we know what
the stock price is.

644
00:31:00,160 --> 00:31:01,300
We know what the
strike price is.

645
00:31:01,300 --> 00:31:02,883
We know what the
other parameters are.

646
00:31:02,883 --> 00:31:06,160
Let's ask the question,
given the price of an option,

647
00:31:06,160 --> 00:31:09,580
what is the volatility that
is consistent with that market

648
00:31:09,580 --> 00:31:10,960
price?

649
00:31:10,960 --> 00:31:14,650
Because allowing you
to invert the market

650
00:31:14,650 --> 00:31:17,350
price for the
volatility gives you

651
00:31:17,350 --> 00:31:18,850
information about
what's going on.

652
00:31:18,850 --> 00:31:20,350
It's exactly the
question you asked,

653
00:31:20,350 --> 00:31:23,620
about information implicit
in the market price.

654
00:31:23,620 --> 00:31:25,759
It turns out that that's
done all the time.

655
00:31:25,759 --> 00:31:27,300
And not only is it
done all the time,

656
00:31:27,300 --> 00:31:31,630
but there is now an index that's
been created by the Chicago

657
00:31:31,630 --> 00:31:35,620
Board Options Exchange
called the VIX, which

658
00:31:35,620 --> 00:31:40,120
stands for the
Volatility Implied Index.

659
00:31:40,120 --> 00:31:44,680
What they do is they look
at options on the S&P 500.

660
00:31:44,680 --> 00:31:47,440
And they ask the question,
what is the volatility that

661
00:31:47,440 --> 00:31:50,410
is consistent with the
option price on the S&P

662
00:31:50,410 --> 00:31:52,060
for at-the-money option.

663
00:31:52,060 --> 00:31:53,800
At-the-money means
the strike price

664
00:31:53,800 --> 00:31:56,890
is equal to the current price
of the stock, or the index,

665
00:31:56,890 --> 00:31:58,280
of this case.

666
00:31:58,280 --> 00:32:01,027
And that's an incredibly
important concept.

667
00:32:01,027 --> 00:32:02,860
Because that tells you
something about where

668
00:32:02,860 --> 00:32:06,580
the market sees volatility
going forward, not just looking

669
00:32:06,580 --> 00:32:07,420
backwards.

670
00:32:07,420 --> 00:32:10,750
But today, right now, what does
the market think volatility

671
00:32:10,750 --> 00:32:12,140
should be?

672
00:32:12,140 --> 00:32:14,420
And if you look at the VIX
over the last few weeks,

673
00:32:14,420 --> 00:32:17,170
you're going to be shocked.

674
00:32:17,170 --> 00:32:19,600
We're going to take a look
at it next time, next Monday.

675
00:32:19,600 --> 00:32:22,090
I'm going to do this in class,
where I'll show you what

676
00:32:22,090 --> 00:32:23,770
that volatility looks like.

677
00:32:23,770 --> 00:32:27,690
Historically, the S&P 500 has
had a volatility level of what?

678
00:32:27,690 --> 00:32:28,564
Does anybody know?

679
00:32:28,564 --> 00:32:30,355
What's the typical
stock market volatility?

680
00:32:30,355 --> 00:32:31,530
AUDIENCE: About 15%?

681
00:32:31,530 --> 00:32:32,770
ANDREW LO: 15% to 20%.

682
00:32:32,770 --> 00:32:36,520
Yeah, it's bounced around
there, on an annualized basis.

683
00:32:36,520 --> 00:32:38,500
Last week on an
intradaily basis,

684
00:32:38,500 --> 00:32:41,440
the VIX index, which is
the Implied Volatility,

685
00:32:41,440 --> 00:32:47,305
reached an interdaily high of
89% volatility, for the stock.

686
00:32:47,305 --> 00:32:48,930
And right now, I
don't know what it is.

687
00:32:48,930 --> 00:32:49,930
I haven't checked today.

688
00:32:49,930 --> 00:32:52,544
But my guess is it's
probably 60 to 70.

689
00:32:52,544 --> 00:32:53,340
AUDIENCE: 71%.

690
00:32:53,340 --> 00:32:53,820
ANDREW LO: Is it, what?

691
00:32:53,820 --> 00:32:54,570
AUDIENCE: 71%.

692
00:32:54,570 --> 00:32:55,440
ANDREW LO: 71%.

693
00:32:55,440 --> 00:32:58,680
OK, 71% annual volatility.

694
00:32:58,680 --> 00:33:01,830
Now, that's the forward-looking
implied volatility

695
00:33:01,830 --> 00:33:03,180
for S&P options.

696
00:33:03,180 --> 00:33:05,160
And what that tells
you is that we're

697
00:33:05,160 --> 00:33:07,290
in for some turbulent
times ahead.

698
00:33:07,290 --> 00:33:11,580
If you look at the implied
volatility for the one year

699
00:33:11,580 --> 00:33:14,370
contract, it's going
to be much lower.

700
00:33:14,370 --> 00:33:15,840
Because people are
going to expect

701
00:33:15,840 --> 00:33:19,320
that the volatility of the
S&P, going forward in time,

702
00:33:19,320 --> 00:33:21,960
is going to decline between
now and a year from now.

703
00:33:21,960 --> 00:33:22,890
At least, we hope so.

704
00:33:22,890 --> 00:33:24,570
Otherwise a lot of
people are going

705
00:33:24,570 --> 00:33:27,350
to be needing zan--
zan-- what is it?

706
00:33:27,350 --> 00:33:32,500
Zantac and other kinds
of pharmaceuticals.

707
00:33:32,500 --> 00:33:33,780
OK.

708
00:33:33,780 --> 00:33:35,970
So those are option diagrams.

709
00:33:35,970 --> 00:33:38,340
And I want to mention
one last thing

710
00:33:38,340 --> 00:33:43,260
before we go to the history
of option pricing theory.

711
00:33:43,260 --> 00:33:46,860
I want to mention that one
of the reasons option pricing

712
00:33:46,860 --> 00:33:50,180
theory has been so
important in finance

713
00:33:50,180 --> 00:33:55,260
is because soon after the papers
by Black and Scholes and Merton

714
00:33:55,260 --> 00:34:02,140
were published, it became clear
that everywhere you looked,

715
00:34:02,140 --> 00:34:04,890
there were options to be found.

716
00:34:04,890 --> 00:34:08,370
That is, all other kinds of
financial securities, when

717
00:34:08,370 --> 00:34:14,630
you looked more closely, they
were actually options as well.

718
00:34:14,630 --> 00:34:16,880
So let me give you an example
I said before that stock

719
00:34:16,880 --> 00:34:20,120
prices were not like options.

720
00:34:20,120 --> 00:34:23,780
Well, as an approximation,
that's true.

721
00:34:23,780 --> 00:34:28,310
But in reality, if you look
carefully at what a stock is,

722
00:34:28,310 --> 00:34:32,760
in fact, a stock is an option.

723
00:34:32,760 --> 00:34:35,400
So let me see how that is.

724
00:34:35,400 --> 00:34:40,870
Well, equity, the
equity of a corporation

725
00:34:40,870 --> 00:34:45,010
is a claim on the
corporation's assets.

726
00:34:45,010 --> 00:34:50,050
But if that corporation has any
kind of debt financing, then

727
00:34:50,050 --> 00:34:53,409
actually the equity
holders are second in line.

728
00:34:53,409 --> 00:34:56,380
The bondholders
are first in line.

729
00:34:56,380 --> 00:34:59,950
So the equity only gets
paid after the bondholders

730
00:34:59,950 --> 00:35:01,570
get paid off.

731
00:35:01,570 --> 00:35:05,110
So in particular, if you
think about the maturity

732
00:35:05,110 --> 00:35:08,920
date of the bonds,
then on maturity date,

733
00:35:08,920 --> 00:35:13,780
the value of the equity is
the maximum of either 0,

734
00:35:13,780 --> 00:35:16,540
or the value of
the firm's assets

735
00:35:16,540 --> 00:35:19,780
minus the face
value of the bond,

736
00:35:19,780 --> 00:35:23,110
or what the bond has
to be paid off at.

737
00:35:23,110 --> 00:35:25,090
Because if the bondholders
don't get paid,

738
00:35:25,090 --> 00:35:27,570
then the equity
holders get nothing.

739
00:35:27,570 --> 00:35:30,900
Then the bondholders
get the firm.

740
00:35:30,900 --> 00:35:34,590
All of the assets of the firm
transfer to the bondholders

741
00:35:34,590 --> 00:35:36,090
through bankruptcy proceedings.

742
00:35:36,090 --> 00:35:37,920
At least, that's the theory.

743
00:35:37,920 --> 00:35:43,110
So the value of the equity on
the maturity date for the bonds

744
00:35:43,110 --> 00:35:48,750
is actually the maximum
of 0, V minus B.

745
00:35:48,750 --> 00:35:50,700
Now, that should look
very familiar to you.

746
00:35:50,700 --> 00:35:55,550
That should look like the
payoff of a call option.

747
00:35:55,550 --> 00:36:00,050
Where the strike price
is B, and the value

748
00:36:00,050 --> 00:36:06,310
of the underlying security is V,
the value of the firm's assets.

749
00:36:06,310 --> 00:36:09,920
So what that means is
that equity holders can

750
00:36:09,920 --> 00:36:14,000
be viewed as owning an
option on the firm's assets

751
00:36:14,000 --> 00:36:20,010
with a strike price of B.
And the bondholders look

752
00:36:20,010 --> 00:36:24,210
like they have a put option.

753
00:36:24,210 --> 00:36:27,560
They've shorted a
put on the firm.

754
00:36:27,560 --> 00:36:30,970
But that's leveraged with
a certain amount of debt.

755
00:36:30,970 --> 00:36:33,980
It's a protected levered put,
is the way that people usually

756
00:36:33,980 --> 00:36:34,760
put it.

757
00:36:34,760 --> 00:36:36,860
So the debt is the
minimum of V or B.

758
00:36:36,860 --> 00:36:38,840
You either get the
assets, or you get what

759
00:36:38,840 --> 00:36:41,450
you owed, which is smaller.

760
00:36:41,450 --> 00:36:45,560
And you can show that that's
equivalent to B minus max of 0B

761
00:36:45,560 --> 00:36:49,730
minus V. That looks like
a short put position mixed

762
00:36:49,730 --> 00:36:51,250
in with some borrowing.

763
00:36:51,250 --> 00:36:53,750
And when you add the two, you
see that the value of the firm

764
00:36:53,750 --> 00:36:55,125
is equal to the
value of the debt

765
00:36:55,125 --> 00:36:56,480
and the value of the equity.

766
00:36:56,480 --> 00:37:00,350
The point of this example
is that option pricing

767
00:37:00,350 --> 00:37:05,120
can be used to value the capital
structure of a corporation

768
00:37:05,120 --> 00:37:07,650
as well.

769
00:37:07,650 --> 00:37:12,230
And within the last few
years, a very active part

770
00:37:12,230 --> 00:37:14,990
of the hedge fund
industry has been

771
00:37:14,990 --> 00:37:17,810
devoted to engaging in something
called capital structure

772
00:37:17,810 --> 00:37:18,980
arbitrage.

773
00:37:18,980 --> 00:37:23,740
Capital structure arbitrage says
that this equation has to hold.

774
00:37:23,740 --> 00:37:26,920
But in practice,
there is a discrepancy

775
00:37:26,920 --> 00:37:31,660
with what the market value for D
is, and the market value for E.

776
00:37:31,660 --> 00:37:35,380
And using option pricing theory
and models for credit risk,

777
00:37:35,380 --> 00:37:39,070
hedge funds have been able to
make a play by either buying

778
00:37:39,070 --> 00:37:41,740
a company's equity and shorting
their debt, or buying the debt

779
00:37:41,740 --> 00:37:43,948
and shorting the equity,
whichever is cheaper or more

780
00:37:43,948 --> 00:37:48,220
expensive, and engaging in
what seems like an arbitrage

781
00:37:48,220 --> 00:37:49,210
transaction.

782
00:37:49,210 --> 00:37:51,700
Now, that presupposes
that you've got the credit

783
00:37:51,700 --> 00:37:53,990
calculations done correctly.

784
00:37:53,990 --> 00:37:56,170
So in order to engage
in those kind of trades,

785
00:37:56,170 --> 00:37:58,720
you have to have
superior credit modeling

786
00:37:58,720 --> 00:38:01,060
capabilities, certainly
better than what

787
00:38:01,060 --> 00:38:02,290
rating agencies were doing.

788
00:38:02,290 --> 00:38:05,230
And actually, there were cases
where hedge funds were actively

789
00:38:05,230 --> 00:38:07,630
betting against
rating agency models.

790
00:38:07,630 --> 00:38:10,990
Because they felt that
rating agencies had mispriced

791
00:38:10,990 --> 00:38:15,490
some of their ratings based upon
the models that they'd created,

792
00:38:15,490 --> 00:38:19,800
versus the ones the rating
agencies were using.

793
00:38:19,800 --> 00:38:24,330
Now, turns out that when
you look more carefully

794
00:38:24,330 --> 00:38:31,010
at other securities, and even
other kinds of opportunities,

795
00:38:31,010 --> 00:38:33,990
options are there as well.

796
00:38:33,990 --> 00:38:40,350
For example, when I started
here at MIT, 20 years ago,

797
00:38:40,350 --> 00:38:44,510
I remember, distinctly,
some of my senior colleagues

798
00:38:44,510 --> 00:38:49,610
referring to Assistant
Professors as options.

799
00:38:49,610 --> 00:38:50,150
[LAUGHTER]

800
00:38:50,150 --> 00:38:52,910
Now, let me explain.

801
00:38:52,910 --> 00:38:55,700
You know that in academia,
when you start out

802
00:38:55,700 --> 00:38:57,920
as a Assistant
Professor, there's

803
00:38:57,920 --> 00:39:00,560
no guarantee for employment.

804
00:39:00,560 --> 00:39:03,500
You have, typically,
a three-year contract.

805
00:39:03,500 --> 00:39:05,720
And at the end of three
years you either get renewed

806
00:39:05,720 --> 00:39:07,520
or you get fired.

807
00:39:07,520 --> 00:39:09,260
And at the end of
the next three years,

808
00:39:09,260 --> 00:39:12,590
you come up for what's
called a tenure review.

809
00:39:12,590 --> 00:39:14,450
Tenure review means
that they send letters

810
00:39:14,450 --> 00:39:18,560
to 15 of the top people in
your field across the country.

811
00:39:18,560 --> 00:39:20,280
Across the world, actually.

812
00:39:20,280 --> 00:39:23,750
And they base their decision
on whether to give you

813
00:39:23,750 --> 00:39:28,040
lifetime guaranteed employment,
as to whether or not

814
00:39:28,040 --> 00:39:32,240
these 15 people say
that you're the greatest

815
00:39:32,240 --> 00:39:35,370
thing since whatever.

816
00:39:35,370 --> 00:39:38,960
And if you don't get
that kind of review,

817
00:39:38,960 --> 00:39:40,397
then you're asked to leave.

818
00:39:40,397 --> 00:39:41,480
I mean, you have to leave.

819
00:39:41,480 --> 00:39:43,910
There's no choice for
continued employment.

820
00:39:43,910 --> 00:39:48,500
So the idea behind hiring
Assistant Professors

821
00:39:48,500 --> 00:39:53,430
were that each one of them
was viewed as an option.

822
00:39:53,430 --> 00:39:57,220
Meaning that you could
benefit from them for a while.

823
00:39:57,220 --> 00:40:00,180
But if they didn't work out, you
could always get rid of them.

824
00:40:00,180 --> 00:40:02,470
But once you got
tenure, that was it.

825
00:40:02,470 --> 00:40:04,110
There was no longer an option.

826
00:40:04,110 --> 00:40:07,370
So what that suggested,
from a hiring perspective,

827
00:40:07,370 --> 00:40:10,080
is what kind of
Assistant Professor

828
00:40:10,080 --> 00:40:12,680
should you hire if you
believe in option pricing,

829
00:40:12,680 --> 00:40:16,730
as applied to the labor market?

830
00:40:16,730 --> 00:40:19,267
Can you can you
characterize the type of--

831
00:40:19,267 --> 00:40:20,100
Yeah, what was that?

832
00:40:20,100 --> 00:40:20,540
AUDIENCE: Take risks.

833
00:40:20,540 --> 00:40:21,670
ANDREW LO: Take risks.

834
00:40:21,670 --> 00:40:27,260
You want to hire faculty
that are extremely volatile.

835
00:40:27,260 --> 00:40:30,640
Not emotionally, hopefully,
but intellectually.

836
00:40:30,640 --> 00:40:34,330
In other words, because
you get all the upside,

837
00:40:34,330 --> 00:40:35,961
but you don't get any downside.

838
00:40:35,961 --> 00:40:37,960
So what you want to do
is you want to take risk.

839
00:40:37,960 --> 00:40:42,430
You want to take chances on
faculty that may or may not

840
00:40:42,430 --> 00:40:43,150
work out.

841
00:40:43,150 --> 00:40:45,580
And that, in fact,
has been the approach

842
00:40:45,580 --> 00:40:48,400
that we and others have
used in hiring, based

843
00:40:48,400 --> 00:40:50,500
upon this kind of
option pricing analysis.

844
00:40:50,500 --> 00:40:52,420
And it applies to
all sorts of things.

845
00:40:52,420 --> 00:40:54,310
When you think about
getting an education,

846
00:40:54,310 --> 00:40:58,030
you can argue that getting
an education is an option.

847
00:40:58,030 --> 00:40:59,720
You don't have to
use your degree.

848
00:40:59,720 --> 00:41:00,910
You don't have to
use your education.

849
00:41:00,910 --> 00:41:01,576
But you have it.

850
00:41:01,576 --> 00:41:02,800
It's an option.

851
00:41:02,800 --> 00:41:06,880
And so thinking about value in
education, you could actually

852
00:41:06,880 --> 00:41:10,550
use this framework, try
to compute the flexibility

853
00:41:10,550 --> 00:41:12,700
it gives you, in order
to take advantage

854
00:41:12,700 --> 00:41:16,150
of career opportunities.

855
00:41:16,150 --> 00:41:19,010
So there are lots of things
that look like options.

856
00:41:19,010 --> 00:41:20,502
Yeah, Megan?

857
00:41:20,502 --> 00:41:28,438
AUDIENCE: [INAUDIBLE] distressed
debt manager, [INAUDIBLE]?

858
00:41:38,854 --> 00:41:41,470
ANDREW LO: A
distressed debt manager

859
00:41:41,470 --> 00:41:43,810
if they're holding
distressed debt of a company,

860
00:41:43,810 --> 00:41:46,870
they would actually be
holding a short put position.

861
00:41:46,870 --> 00:41:48,130
They're holding the debt.

862
00:41:48,130 --> 00:41:49,642
So they have a
short put position.

863
00:41:49,642 --> 00:41:51,100
So if they wanted
to hedge it, they

864
00:41:51,100 --> 00:41:55,100
can either buy a
put on the assets,

865
00:41:55,100 --> 00:41:58,023
which would then help them
to hedge it out, Yeah, right.

866
00:42:02,330 --> 00:42:04,610
And as I was saying,
there are all sorts

867
00:42:04,610 --> 00:42:10,400
of other examples of options
and derivative securities.

868
00:42:10,400 --> 00:42:12,020
The field has exploded.

869
00:42:12,020 --> 00:42:15,380
There are literally
many, many trillions

870
00:42:15,380 --> 00:42:18,690
of dollars of notional amounts.

871
00:42:18,690 --> 00:42:21,440
Now, again, notional amounts
can be a little bit misleading.

872
00:42:21,440 --> 00:42:24,200
Because you know that
for every option seller,

873
00:42:24,200 --> 00:42:25,250
there's an option buyer.

874
00:42:25,250 --> 00:42:28,650
Options are zero net
investment side bets,

875
00:42:28,650 --> 00:42:30,910
unlike equities,
where companies that

876
00:42:30,910 --> 00:42:33,860
have real assets behind
them issue pieces of paper

877
00:42:33,860 --> 00:42:34,880
called equity.

878
00:42:34,880 --> 00:42:38,180
Options are issued by
the Options Clearing

879
00:42:38,180 --> 00:42:41,510
Corporation for the Chicago
Board Options Exchange.

880
00:42:41,510 --> 00:42:43,310
The Mercantile Exchange
also has options.

881
00:42:43,310 --> 00:42:45,060
There's options
traded everywhere.

882
00:42:45,060 --> 00:42:46,852
In fact, one of the
largest exchanges

883
00:42:46,852 --> 00:42:48,560
is the International
Securities Exchange.

884
00:42:48,560 --> 00:42:50,360
It was started up
by Bill Porter,

885
00:42:50,360 --> 00:42:52,130
the fellow who started e-trade.

886
00:42:52,130 --> 00:42:55,550
And it is the most active
options exchange in the world.

887
00:42:55,550 --> 00:42:57,290
It's all done electronically.

888
00:42:57,290 --> 00:43:00,410
And these options
are pure side bets.

889
00:43:00,410 --> 00:43:04,265
But they're not just for
purposes of gambling.

890
00:43:04,265 --> 00:43:07,760
They're for purposes of hedging
and engaging in insurance,

891
00:43:07,760 --> 00:43:10,260
of the kind that we
talked about before.

892
00:43:10,260 --> 00:43:13,250
So this has really exploded.

893
00:43:13,250 --> 00:43:16,310
And that's why we have an
entire course, 15.437, devoted

894
00:43:16,310 --> 00:43:20,780
to just the pricing of
options and futures.

895
00:43:20,780 --> 00:43:25,730
So we can't, obviously, cover
all of it in this course.

896
00:43:25,730 --> 00:43:27,770
But I want to just give
you a flavor of it.

897
00:43:27,770 --> 00:43:30,590
Let me skip, now,
this next section

898
00:43:30,590 --> 00:43:32,079
on valuation of options.

899
00:43:32,079 --> 00:43:34,370
Because as I said, this is
a little bit more technical.

900
00:43:34,370 --> 00:43:36,036
I want to spend some
time on it and make

901
00:43:36,036 --> 00:43:37,790
sure you all understand it.

902
00:43:37,790 --> 00:43:40,070
And then I will come
back to this on Monday.

903
00:43:40,070 --> 00:43:42,320
When I want to do now is
just to give you a little bit

904
00:43:42,320 --> 00:43:43,760
of a history of option pricing.

905
00:43:43,760 --> 00:43:45,710
Because it's kind of fun.

906
00:43:45,710 --> 00:43:49,910
First of all, in order to
figure out how to price options,

907
00:43:49,910 --> 00:43:53,240
we have to begin
with figuring out

908
00:43:53,240 --> 00:43:57,020
what a particular model would
be for the underlying stock.

909
00:43:57,020 --> 00:43:59,150
In order to price an
option, you actually

910
00:43:59,150 --> 00:44:02,060
have to say something
about how the underlying

911
00:44:02,060 --> 00:44:04,310
security behaves.

912
00:44:04,310 --> 00:44:05,840
So we have to start with that.

913
00:44:05,840 --> 00:44:10,910
And we're going to start in
the very early 16th century,

914
00:44:10,910 --> 00:44:15,710
with probably the first-known
model for asset prices

915
00:44:15,710 --> 00:44:18,800
that ever existed in the world.

916
00:44:18,800 --> 00:44:22,130
And that was developed by
a Italian mathematician

917
00:44:22,130 --> 00:44:24,650
by the name of your
Gerolamo Cardano.

918
00:44:24,650 --> 00:44:26,960
Now, those of you who were
on high school math team,

919
00:44:26,960 --> 00:44:28,440
I suspect you've
heard of Cardano.

920
00:44:28,440 --> 00:44:32,550
Anybody tell me who Cardano was?

921
00:44:32,550 --> 00:44:34,210
No math team geeks here?

922
00:44:36,800 --> 00:44:40,280
All right, Cardano
was, it turns out,

923
00:44:40,280 --> 00:44:42,680
the second person
to have come up

924
00:44:42,680 --> 00:44:46,266
with a solution for
the cubic equation.

925
00:44:46,266 --> 00:44:48,390
You all know what the
quadratic equation is, right?

926
00:44:48,390 --> 00:44:52,430
You know, ax squared
plus bx plus c equals 0.

927
00:44:52,430 --> 00:44:53,600
That's a quadratic equation.

928
00:44:53,600 --> 00:44:57,140
Anybody know what the
solution of that is?

929
00:44:57,140 --> 00:44:58,269
Yeah, what is that?

930
00:44:58,269 --> 00:45:02,490
AUDIENCE: [INAUDIBLE]

931
00:45:02,490 --> 00:45:03,020
Great Great.

932
00:45:03,020 --> 00:45:04,936
All right, You get the
pocket protector award.

933
00:45:04,936 --> 00:45:07,170
[LAUGHTER]

934
00:45:07,170 --> 00:45:08,750
Very good.

935
00:45:08,750 --> 00:45:10,790
It turns out that
there is exactly

936
00:45:10,790 --> 00:45:13,285
the same kind of solution
for the cubic equation.

937
00:45:13,285 --> 00:45:14,660
Of course, nobody
remembers that.

938
00:45:14,660 --> 00:45:16,243
I won't ask you
whether you know that.

939
00:45:16,243 --> 00:45:17,010
You might.

940
00:45:17,010 --> 00:45:19,270
But there is a formula
for the cubic equation.

941
00:45:19,270 --> 00:45:22,915
It turns out that there are no
more formulas beyond the cubic.

942
00:45:22,915 --> 00:45:24,290
So there's something
very special

943
00:45:24,290 --> 00:45:25,670
about the cubic equation.

944
00:45:25,670 --> 00:45:28,670
And this Italian
mathematician, Cardano,

945
00:45:28,670 --> 00:45:29,840
was the first to publish it.

946
00:45:29,840 --> 00:45:31,340
The reason I say that
he's the second person

947
00:45:31,340 --> 00:45:33,006
to come up with it,
is that it turns out

948
00:45:33,006 --> 00:45:36,200
he stole the formula from a
colleague, and a colleague who

949
00:45:36,200 --> 00:45:37,940
had actually come up
with the solution.

950
00:45:37,940 --> 00:45:40,190
And Cardano heard about
it and said, well,

951
00:45:40,190 --> 00:45:41,374
please tell me what it is.

952
00:45:41,374 --> 00:45:42,790
And the other
person said, I'm not

953
00:45:42,790 --> 00:45:43,540
going to tell you what it is.

954
00:45:43,540 --> 00:45:45,080
Because you're going to just
write it up and claim credit.

955
00:45:45,080 --> 00:45:47,210
And Cardano says no,
no, I promise I won't.

956
00:45:47,210 --> 00:45:49,710
And then the guy says,
all right, here it is.

957
00:45:49,710 --> 00:45:50,290
He told him.

958
00:45:50,290 --> 00:45:53,390
And then Cardano did,
in fact, rip him off.

959
00:45:53,390 --> 00:45:55,010
So it's known as
Cardano's formula,

960
00:45:55,010 --> 00:45:55,790
but it really shouldn't.

961
00:45:55,790 --> 00:45:57,980
And I'm embarrassed to say,
I don't remember the guy

962
00:45:57,980 --> 00:46:01,350
who actually invented it.

963
00:46:01,350 --> 00:46:03,770
But Cardano, in addition
to having come up

964
00:46:03,770 --> 00:46:07,200
with this solution, or
stolen this solution,

965
00:46:07,200 --> 00:46:10,070
Cardano also wrote
a book on gambling.

966
00:46:10,070 --> 00:46:12,920
And this book, which
is titled Liber De Ludo

967
00:46:12,920 --> 00:46:15,980
Aleae, The Laws of
Gambling, he developed

968
00:46:15,980 --> 00:46:21,470
what was the precursor to the
modern mathematical description

969
00:46:21,470 --> 00:46:22,910
of stock prices.

970
00:46:22,910 --> 00:46:24,787
And it was described
in this way.

971
00:46:24,787 --> 00:46:26,870
"The most fundamental
principle of all in gambling

972
00:46:26,870 --> 00:46:28,910
is simply equal conditions, e.g.

973
00:46:28,910 --> 00:46:32,060
of opponents, of bystanders,
of money, of situation,

974
00:46:32,060 --> 00:46:35,180
of the dice box,
and the die itself.

975
00:46:35,180 --> 00:46:38,600
To the extent to which you
depart from that equality,

976
00:46:38,600 --> 00:46:41,540
if it is in your opponent's
favor, you are a fool,

977
00:46:41,540 --> 00:46:44,630
and if in your own,
you are unjust."

978
00:46:44,630 --> 00:46:46,310
It turns out that
what he was describing

979
00:46:46,310 --> 00:46:48,860
was, essentially, a 50/50 bet.

980
00:46:48,860 --> 00:46:51,740
Or what we call a
fair game, or what

981
00:46:51,740 --> 00:46:53,980
is now known as a martingale.

982
00:46:53,980 --> 00:47:00,980
A martingale simply says that
expected winnings and losses

983
00:47:00,980 --> 00:47:01,850
is equal to 0.

984
00:47:01,850 --> 00:47:05,750
Or rather, your expected
wealth next period

985
00:47:05,750 --> 00:47:08,570
is equal to whatever
your wealth is today

986
00:47:08,570 --> 00:47:14,270
if you have a fair game
that you're betting on.

987
00:47:14,270 --> 00:47:16,100
It turns out that
that simple model

988
00:47:16,100 --> 00:47:19,250
developed into what we now
think of as the Random Walk

989
00:47:19,250 --> 00:47:20,060
Hypothesis.

990
00:47:20,060 --> 00:47:23,180
And the Random Walk was
really the fundamental driver

991
00:47:23,180 --> 00:47:26,150
behind the option pricing
model that Black and Scholes

992
00:47:26,150 --> 00:47:28,010
and Merton developed.

993
00:47:28,010 --> 00:47:30,620
Now, the reason the Random
Walk holds a very special place

994
00:47:30,620 --> 00:47:33,290
in the hearts of
financial economist

995
00:47:33,290 --> 00:47:35,630
is because most
economists suffer

996
00:47:35,630 --> 00:47:40,610
from a psychological disorder
that we call physics envy.

997
00:47:40,610 --> 00:47:43,220
We all wish that we had
these three laws that

998
00:47:43,220 --> 00:47:46,110
explains 99% of all behavior.

999
00:47:46,110 --> 00:47:48,170
In fact, economists have
99 laws that explain

1000
00:47:48,170 --> 00:47:50,910
maybe 3% of economic behavior.

1001
00:47:50,910 --> 00:47:56,870
But there's one example, only
one, in the history of finance,

1002
00:47:56,870 --> 00:48:01,520
where an economist actually
came up with an idea

1003
00:48:01,520 --> 00:48:02,930
before a physicist.

1004
00:48:02,930 --> 00:48:06,230
And that was later
adopted by a physicist.

1005
00:48:06,230 --> 00:48:09,630
And the idea I'm talking about
is the Random Walk hypothesis,

1006
00:48:09,630 --> 00:48:13,040
or in the continuous time
realm, Brownian motion.

1007
00:48:13,040 --> 00:48:17,600
In 1900, a student by the
name of Louis Bachelier

1008
00:48:17,600 --> 00:48:22,310
was writing a
dissertation in Paris.

1009
00:48:22,310 --> 00:48:23,840
He was a mathematics
PhD student.

1010
00:48:23,840 --> 00:48:26,060
But he was writing about
pricing warrants that were

1011
00:48:26,060 --> 00:48:28,220
trading on the Paris Bourse.

1012
00:48:28,220 --> 00:48:30,200
So it was a finance thesis.

1013
00:48:30,200 --> 00:48:32,959
And in order to
solve the problem,

1014
00:48:32,959 --> 00:48:35,000
he had to come up with a
mathematical description

1015
00:48:35,000 --> 00:48:36,620
for the underlying price.

1016
00:48:36,620 --> 00:48:39,530
And he came up with this
notion of what we now

1017
00:48:39,530 --> 00:48:42,350
call Brownian motion,
of Random Walk.

1018
00:48:42,350 --> 00:48:46,610
And he did it a full three years
before a well-known physicist

1019
00:48:46,610 --> 00:48:47,750
published a paper on that.

1020
00:48:47,750 --> 00:48:49,130
Anybody know who
that physicist was?

1021
00:48:49,130 --> 00:48:50,088
AUDIENCE: Was it Brown?

1022
00:48:50,088 --> 00:48:50,710
ANDREW LO: No.

1023
00:48:50,710 --> 00:48:52,927
No, Brown was many years before.

1024
00:48:52,927 --> 00:48:53,885
And he was a biologist.

1025
00:48:53,885 --> 00:48:54,230
Yeah?

1026
00:48:54,230 --> 00:48:55,021
AUDIENCE: Einstein.

1027
00:48:55,021 --> 00:48:58,610
ANDREW LO: That's right,
Albert Einstein, in 1903,

1028
00:48:58,610 --> 00:49:01,250
actually published a paper
on the photoelectric effect

1029
00:49:01,250 --> 00:49:02,970
and Brownian motion.

1030
00:49:02,970 --> 00:49:07,820
And if you take a look
at what Baschelier did,

1031
00:49:07,820 --> 00:49:10,040
he was working with the
French mathematician

1032
00:49:10,040 --> 00:49:12,200
by the name of Henri Poincare.

1033
00:49:12,200 --> 00:49:15,410
Poincare was a very
well-known mathematician

1034
00:49:15,410 --> 00:49:18,380
who was the advisor
to Baschelier,

1035
00:49:18,380 --> 00:49:20,310
and who is renowned
now for a variety

1036
00:49:20,310 --> 00:49:22,310
of different contributions,
including the theory

1037
00:49:22,310 --> 00:49:24,220
of dynamical systems.

1038
00:49:24,220 --> 00:49:27,470
Baschelier wrote this thesis
and developed the mathematics

1039
00:49:27,470 --> 00:49:29,570
of Brownian motion.

1040
00:49:29,570 --> 00:49:31,370
And when he was
looking for a job,

1041
00:49:31,370 --> 00:49:33,590
Poincare wrote a letter
of recommendation.

1042
00:49:33,590 --> 00:49:37,220
And this is what Poincare
wrote about Baschelier.

1043
00:49:37,220 --> 00:49:40,880
He said that "The manner in
which the candidate obtains

1044
00:49:40,880 --> 00:49:44,014
the law of Gauss is most
original, and all the more

1045
00:49:44,014 --> 00:49:45,680
interesting as the
same reasoning might,

1046
00:49:45,680 --> 00:49:48,830
with a few changes, be extended
to the theory of errors.

1047
00:49:48,830 --> 00:49:50,420
He develops this
in a chapter which

1048
00:49:50,420 --> 00:49:52,010
might at first seem strange.

1049
00:49:52,010 --> 00:49:57,760
For he titles it
'Radiation of Probability.'

1050
00:49:57,760 --> 00:50:01,270
In effect, the author
resorts to a comparison

1051
00:50:01,270 --> 00:50:05,110
with the analytical theory
of the propagation of heat."

1052
00:50:05,110 --> 00:50:07,040
Now, remember this is
a thesis on pricing

1053
00:50:07,040 --> 00:50:10,620
warrants on the Paris Bourse.

1054
00:50:10,620 --> 00:50:14,400
Fourier's reasoning
is applicable almost

1055
00:50:14,400 --> 00:50:17,260
without change to this problem.

1056
00:50:17,260 --> 00:50:21,836
Which is so different from that
for which it had been created."

1057
00:50:21,836 --> 00:50:23,460
And of course, his
adviser, at the end,

1058
00:50:23,460 --> 00:50:25,740
always has to complain a
little bit about his student,

1059
00:50:25,740 --> 00:50:26,760
as we all do.

1060
00:50:26,760 --> 00:50:30,812
So he said, "It is regrettable
that the author did not

1061
00:50:30,812 --> 00:50:32,520
develop this part of
his thesis further."

1062
00:50:35,550 --> 00:50:38,490
What Poincare was mentioning,
with regard to Fourier,

1063
00:50:38,490 --> 00:50:40,740
was the theory of
heat conduction.

1064
00:50:40,740 --> 00:50:43,800
In physics, there is
a very standard model

1065
00:50:43,800 --> 00:50:48,810
that everybody that goes into
advanced physics will cover.

1066
00:50:48,810 --> 00:50:51,570
And that is, how does
heat get conducted

1067
00:50:51,570 --> 00:50:53,280
through a solid medium?

1068
00:50:53,280 --> 00:50:56,370
And in deriving the
equation that ultimately

1069
00:50:56,370 --> 00:50:59,430
is known as the heat
equation, you actually

1070
00:50:59,430 --> 00:51:03,840
use the same theory that
Baschelier applied to pricing

1071
00:51:03,840 --> 00:51:05,100
warrants on the Paris Bourse.

1072
00:51:05,100 --> 00:51:09,547
He gets what's known as a
partial differential equation.

1073
00:51:09,547 --> 00:51:10,630
And that's it right there.

1074
00:51:10,630 --> 00:51:12,090
That's the equation that
he used in his thesis.

1075
00:51:12,090 --> 00:51:14,048
If you look at his thesis,
you'll see it there.

1076
00:51:14,048 --> 00:51:15,190
That's the heat equation.

1077
00:51:15,190 --> 00:51:17,648
It's the same equation that
explains the conduction of heat

1078
00:51:17,648 --> 00:51:19,380
in a solid medium.

1079
00:51:19,380 --> 00:51:21,750
But he derives it
for the purpose

1080
00:51:21,750 --> 00:51:24,270
of pricing this
financial security.

1081
00:51:24,270 --> 00:51:27,930
Now, it turns out that
there was one slight mistake

1082
00:51:27,930 --> 00:51:29,805
that Baschelier
made in his thesis.

1083
00:51:29,805 --> 00:51:33,720
It was a mathematical error
that, ultimately, didn't really

1084
00:51:33,720 --> 00:51:35,490
affect the results.

1085
00:51:35,490 --> 00:51:37,980
But it became known.

1086
00:51:37,980 --> 00:51:40,080
And when he came
up for tenure, they

1087
00:51:40,080 --> 00:51:42,600
wrote to all the various
different big names.

1088
00:51:42,600 --> 00:51:45,060
And he was ultimately
turned down for tenure,

1089
00:51:45,060 --> 00:51:47,040
because they found this mistake.

1090
00:51:47,040 --> 00:51:48,750
And he was blackballed.

1091
00:51:48,750 --> 00:51:52,110
So he couldn't get a job
except for a small teaching

1092
00:51:52,110 --> 00:51:55,204
college, a women's teaching
college in the south of France.

1093
00:51:55,204 --> 00:51:56,870
Which frankly, sounds
pretty good to me.

1094
00:51:56,870 --> 00:51:59,270
[LAUGHTER]

1095
00:51:59,270 --> 00:52:06,090
But you know, for
him, it was not

1096
00:52:06,090 --> 00:52:08,160
the way he would not
want to end his career.

1097
00:52:08,160 --> 00:52:10,080
But at the end of
his career, it was

1098
00:52:10,080 --> 00:52:12,260
discovered that this
mistake was not as serious.

1099
00:52:12,260 --> 00:52:14,010
And people wrote him
a letter saying, gee,

1100
00:52:14,010 --> 00:52:15,250
you're a great guy anyway.

1101
00:52:18,480 --> 00:52:20,400
Paul Samuelson,
actually, was the person

1102
00:52:20,400 --> 00:52:22,680
who discovered
Baschelier's thesis when

1103
00:52:22,680 --> 00:52:26,040
he was in Paris at
the Sorbonne, reading

1104
00:52:26,040 --> 00:52:27,750
through various
different archives.

1105
00:52:27,750 --> 00:52:31,100
So Paul Samuelson's
responsible for resurrecting

1106
00:52:31,100 --> 00:52:35,050
the reputation and the
work of Louis Baschelier.

1107
00:52:35,050 --> 00:52:36,720
You can see his thesis now.

1108
00:52:36,720 --> 00:52:39,630
It's been republished
and reprinted.

1109
00:52:39,630 --> 00:52:43,080
But the point of the
thesis is that by assuming

1110
00:52:43,080 --> 00:52:45,810
that the underlying stock
price was a Random Walk,

1111
00:52:45,810 --> 00:52:48,420
and by developing the
mathematics of the Random Walk,

1112
00:52:48,420 --> 00:52:50,940
he was able to figure out
what the price of an option

1113
00:52:50,940 --> 00:52:53,310
was on that stock.

1114
00:52:53,310 --> 00:52:55,140
And it turns out
that the pricing

1115
00:52:55,140 --> 00:52:57,570
of the option on
the stock reduces

1116
00:52:57,570 --> 00:52:59,850
to solving this heat equation.

1117
00:52:59,850 --> 00:53:01,890
And that explains why
there are, nowadays,

1118
00:53:01,890 --> 00:53:03,665
so many physicists and
mathematicians that

1119
00:53:03,665 --> 00:53:04,290
are in finance.

1120
00:53:04,290 --> 00:53:08,280
It's because the whole body
of knowledge that comes along

1121
00:53:08,280 --> 00:53:11,040
with the physical interpretation
for the heat equation

1122
00:53:11,040 --> 00:53:14,880
can be applied, virtually
identically and verbatim,

1123
00:53:14,880 --> 00:53:17,820
to the pricing of options and
other derivative securities.

1124
00:53:17,820 --> 00:53:21,540
And so very quickly, we can
see that the information that's

1125
00:53:21,540 --> 00:53:24,030
contained in these
market prices can

1126
00:53:24,030 --> 00:53:26,370
be understood within a
mathematical framework

1127
00:53:26,370 --> 00:53:27,900
that we know.

1128
00:53:27,900 --> 00:53:30,030
So now going back
to the history,

1129
00:53:30,030 --> 00:53:33,790
it turns out that this was
not known in the 1970s.

1130
00:53:33,790 --> 00:53:38,840
It wasn't rediscovered by
Paul Samuelson until later on.

1131
00:53:38,840 --> 00:53:41,190
The folks that actually
worked on option pricing, that

1132
00:53:41,190 --> 00:53:44,520
tried to figure out the
mathematical prices of options

1133
00:53:44,520 --> 00:53:45,960
were quite a few.

1134
00:53:45,960 --> 00:53:49,410
Kruizenga, who is an MIT PhD
student in the 1950s-- oh,

1135
00:53:49,410 --> 00:53:50,680
question?

1136
00:53:50,680 --> 00:53:51,180
No?

1137
00:53:51,180 --> 00:53:51,860
OK.

1138
00:53:51,860 --> 00:53:54,170
In the 1950s, there
was an MIT PhD student

1139
00:53:54,170 --> 00:53:56,960
of Paul Samuelson's who tried
to work on this problem.

1140
00:53:56,960 --> 00:54:00,170
And he actually has a thesis
titled "Put and Call Options--

1141
00:54:00,170 --> 00:54:01,910
A Theoretical and
Market Analysis."

1142
00:54:01,910 --> 00:54:03,560
It's actually in
the MIT archives,

1143
00:54:03,560 --> 00:54:05,120
if you want to go
take a look at it.

1144
00:54:05,120 --> 00:54:06,386
But he didn't quite get it.

1145
00:54:06,386 --> 00:54:07,760
He didn't get the
right solution,

1146
00:54:07,760 --> 00:54:10,310
because he didn't have
the mathematical machinery

1147
00:54:10,310 --> 00:54:13,760
to be able to work out
the final elements of it.

1148
00:54:13,760 --> 00:54:17,690
K. Sprenkle, a student
at Yale in 1961,

1149
00:54:17,690 --> 00:54:21,800
wrote a thesis under Jim
Tobin and Arthur Okun, titled

1150
00:54:21,800 --> 00:54:25,370
"Warrant Prices As Indicators of
Expectations and Preferences,"

1151
00:54:25,370 --> 00:54:27,320
and tried to price it as well.

1152
00:54:27,320 --> 00:54:31,490
But he wasn't able to come up
with a pricing formula either.

1153
00:54:31,490 --> 00:54:34,970
And there were a number
of other attempts

1154
00:54:34,970 --> 00:54:37,550
to try to come up with the
appropriate pricing formula,

1155
00:54:37,550 --> 00:54:40,850
including attempts
by Samuelson in '65,

1156
00:54:40,850 --> 00:54:44,450
where he had to make assumptions
on individual preferences

1157
00:54:44,450 --> 00:54:46,310
in order to get a price.

1158
00:54:46,310 --> 00:54:47,290
That didn't work out.

1159
00:54:47,290 --> 00:54:49,520
And then Samuelson and
Merton in '69, they

1160
00:54:49,520 --> 00:54:52,070
tried to come up with
a pricing formula that

1161
00:54:52,070 --> 00:54:54,230
was preference free.

1162
00:54:54,230 --> 00:54:56,910
And they still couldn't do it.

1163
00:54:56,910 --> 00:54:58,970
Along came Black and Scholes.

1164
00:54:58,970 --> 00:55:02,340
Fischer Black who, at that
time, was a consultant working

1165
00:55:02,340 --> 00:55:03,480
at Arthur D. Little.

1166
00:55:03,480 --> 00:55:07,400
He wasn't even an academic.

1167
00:55:07,400 --> 00:55:09,480
The Arthur D. Little
building, that's

1168
00:55:09,480 --> 00:55:12,510
the building that
is right over there,

1169
00:55:12,510 --> 00:55:14,220
the one that they
won't let us tear down.

1170
00:55:14,220 --> 00:55:18,355
Because it's supposed to be
an architectural gem of sorts.

1171
00:55:18,355 --> 00:55:19,980
That was the Arthur
D. Little Building.

1172
00:55:19,980 --> 00:55:21,240
Fischer had his office there.

1173
00:55:21,240 --> 00:55:25,230
Myron had his office in the next
building over, Myron Sholes.

1174
00:55:25,230 --> 00:55:28,560
And they started talking
about option pricing.

1175
00:55:28,560 --> 00:55:32,610
And Fischer came
up with an analysis

1176
00:55:32,610 --> 00:55:35,400
that was very much along
the lines of Baschelier.

1177
00:55:35,400 --> 00:55:38,200
He basically got this formula,

1178
00:55:38,200 --> 00:55:40,620
but he couldn't solve
it because he had never

1179
00:55:40,620 --> 00:55:43,710
heard of the heat equation
because his Fischer Black's

1180
00:55:43,710 --> 00:55:46,020
background was in computer
science, not in mathematics.

1181
00:55:46,020 --> 00:55:48,930
It was ironic, because Fischer
Black actually had a PhD.

1182
00:55:48,930 --> 00:55:52,170
Not in economics or finance,
but in applied math.

1183
00:55:52,170 --> 00:55:54,340
But he had never taken physics.

1184
00:55:54,340 --> 00:55:56,670
So he was doing discrete math.

1185
00:55:56,670 --> 00:55:59,040
So he started talking
to Myron Scholes

1186
00:55:59,040 --> 00:56:03,000
and as legend would
have it, Myron

1187
00:56:03,000 --> 00:56:05,760
took that heat equation, went
over to the math department

1188
00:56:05,760 --> 00:56:08,517
here, and asked one of the
mathematics professors,

1189
00:56:08,517 --> 00:56:09,600
have ever seen this thing?

1190
00:56:09,600 --> 00:56:10,785
And a math person
looked at him and said,

1191
00:56:10,785 --> 00:56:11,910
oh yeah, that's
just heat equation.

1192
00:56:11,910 --> 00:56:13,118
Here, you solve it like this.

1193
00:56:17,050 --> 00:56:21,150
And so Myron apparently took
it back to Fischer Black.

1194
00:56:21,150 --> 00:56:23,620
And Fischer said, hmm,
this is interesting.

1195
00:56:23,620 --> 00:56:25,290
We can now write a paper.

1196
00:56:25,290 --> 00:56:27,930
And they wrote a paper on this.

1197
00:56:27,930 --> 00:56:30,420
At the same time, Bob
Merton was working

1198
00:56:30,420 --> 00:56:32,670
on another direction
that was trying

1199
00:56:32,670 --> 00:56:33,870
to come up with a solution.

1200
00:56:33,870 --> 00:56:35,937
Ultimately, he came up
with the same solution.

1201
00:56:35,937 --> 00:56:38,520
They didn't know it because they
had actually not communicated

1202
00:56:38,520 --> 00:56:40,170
to each other.

1203
00:56:40,170 --> 00:56:43,194
But ultimately,
Myron and Fischer,

1204
00:56:43,194 --> 00:56:44,610
they sent their
paper to something

1205
00:56:44,610 --> 00:56:46,419
like five economics journals.

1206
00:56:46,419 --> 00:56:48,210
Every single one of
them rejected the paper

1207
00:56:48,210 --> 00:56:50,550
saying this is too specialized.

1208
00:56:50,550 --> 00:56:51,822
It's not really economics.

1209
00:56:51,822 --> 00:56:52,530
It's not finance.

1210
00:56:52,530 --> 00:56:55,230
We don't know what
it is, but go away.

1211
00:56:55,230 --> 00:56:58,050
And it was only until
they were able to change

1212
00:56:58,050 --> 00:57:01,020
the title of the paper
from option pricing

1213
00:57:01,020 --> 00:57:05,910
to the pricing of options
and corporate liabilities

1214
00:57:05,910 --> 00:57:07,590
that they finally--

1215
00:57:07,590 --> 00:57:10,530
so it was exactly this--
well, I'll show you next time.

1216
00:57:10,530 --> 00:57:13,320
They changed it to
start focusing more

1217
00:57:13,320 --> 00:57:14,580
on corporate finance.

1218
00:57:14,580 --> 00:57:16,920
They ultimately got
their paper published.

1219
00:57:16,920 --> 00:57:19,410
It turns out that Merton used
a very different approach

1220
00:57:19,410 --> 00:57:21,240
but got to the same point.

1221
00:57:21,240 --> 00:57:25,320
And so Black and
Scholes got their paper,

1222
00:57:25,320 --> 00:57:26,902
ultimately, accepted
into The JPE.

1223
00:57:26,902 --> 00:57:28,860
Merton got his paper
accepted The Bell Journal,

1224
00:57:28,860 --> 00:57:30,240
both in the same year.

1225
00:57:30,240 --> 00:57:32,550
In fact, Merton got his
paper published first.

1226
00:57:32,550 --> 00:57:34,770
But he argued that
the paper should

1227
00:57:34,770 --> 00:57:38,190
be delayed because he wanted
Fischer Black and Myron

1228
00:57:38,190 --> 00:57:40,590
Scholes have their paper
come out in the same year.

1229
00:57:40,590 --> 00:57:43,020
He felt that he derived
so much intuition

1230
00:57:43,020 --> 00:57:44,820
for what Black and
Scholes were doing,

1231
00:57:44,820 --> 00:57:46,800
that he didn't want to get
there first, because it was not

1232
00:57:46,800 --> 00:57:47,520
fair to them.

1233
00:57:47,520 --> 00:57:50,040
That was one of the
most extraordinary acts

1234
00:57:50,040 --> 00:57:52,837
of professional ethics
in the profession.

1235
00:57:52,837 --> 00:57:55,420
Because it was pretty clear to
both of them what was at stake.

1236
00:57:55,420 --> 00:57:58,140
This was a huge problem that
took an enormous amount of time

1237
00:57:58,140 --> 00:57:59,220
to solve.

1238
00:57:59,220 --> 00:58:01,860
And of course, the
rest is history.

1239
00:58:01,860 --> 00:58:07,320
They were awarded the Nobel
Prize in 1997, Myron and Bob.

1240
00:58:07,320 --> 00:58:10,350
Unfortunately, Fischer Black had
died of cancer the year before.

1241
00:58:10,350 --> 00:58:14,080
But it was very clear in
the Nobel address, both

1242
00:58:14,080 --> 00:58:16,560
on the participants' part, as
well as the Nobel Committee,

1243
00:58:16,560 --> 00:58:19,840
that Black should have
received it as well.

1244
00:58:19,840 --> 00:58:23,180
So that's the history and the
heritage of option pricing.

1245
00:58:23,180 --> 00:58:26,250
You can see why MIT is
rightly proud of it.

1246
00:58:26,250 --> 00:58:28,941
And given that we're out
of time, let me stop here.

1247
00:58:28,941 --> 00:58:30,690
And then next time,
what we're going to do

1248
00:58:30,690 --> 00:58:34,650
is to take up where we left off,
and focus on the actual pricing

1249
00:58:34,650 --> 00:58:35,249
formula.

1250
00:58:35,249 --> 00:58:36,540
I'm going to derive it for you.

1251
00:58:36,540 --> 00:58:38,910
Not the Black-Scholes formula,
but a simpler version.

1252
00:58:38,910 --> 00:58:41,340
And you'll see it, and you'll
be able to take a look at it

1253
00:58:41,340 --> 00:58:42,150
and play with it.

1254
00:58:42,150 --> 00:58:43,180
We'll go on from there.

1255
00:58:43,180 --> 00:58:46,970
OK, I'll see you on Wednesday
for the mid-term exam.