WEBVTT 00:01.530 --> 00:07.910 Professor Robert Shiller: Today I want to 00:07.909 --> 00:10.759 talk about options. 00:10.760 --> 00:15.120 I should just say what an option is. 00:15.120 --> 00:15.980 I'll write the word. 00:15.980 --> 00:22.310 00:22.310 --> 00:28.490 It's a contract that has an owner and the owner of the 00:28.486 --> 00:35.356 option contract has rights to find in the contract either to 00:35.362 --> 00:41.772 buy or sell some thing--let's say a share of stock--at a 00:41.771 --> 00:46.551 specified price and specified date. 00:46.550 --> 00:54.360 There are two kinds; there's a put and a call. 00:54.360 --> 01:03.010 A put option is the right to sell. 01:03.009 --> 01:05.769 It's typically a hundred shares, so we'll say a hundred 01:05.766 --> 01:12.006 shares of a company; let's say it's Google. 01:12.010 --> 01:16.900 The option would have--if it was a put option and there was a 01:16.904 --> 01:21.314 price, then you would have the right up--let me see, 01:21.310 --> 01:31.410 there's the exercise price, also known as the strike, 01:31.412 --> 01:37.632 and there's the exercise date. 01:37.630 --> 01:43.510 01:43.510 --> 01:53.940 I should also emphasize that there are two kinds of options. 01:53.940 --> 02:02.780 There are American, so called, and European, 02:02.782 --> 02:05.252 so called. 02:05.250 --> 02:09.010 02:09.009 --> 02:13.249 It has nothing to with whether they are in America or Europe 02:13.253 --> 02:17.073 because in Europe they trade both American options and 02:17.066 --> 02:21.596 European options and in America they trade both American options 02:21.597 --> 02:25.657 and European options; so, it's very unfortunate 02:25.658 --> 02:29.178 terminology. The American--what this 02:29.177 --> 02:35.797 means--an American option means the right to exercise the option 02:35.799 --> 02:41.369 on any date until and including the exercise date; 02:41.370 --> 02:50.910 with European, it's only on exercise date. 02:50.910 --> 02:53.730 That's what those words mean. 02:53.729 --> 02:58.599 So, usually we're talking about American options. 02:58.599 --> 03:06.179 If you have an American option--American put option--on 03:06.181 --> 03:12.651 shares of some stock, then you have the right anytime 03:12.646 --> 03:16.926 you feel like it, until the exercise date, 03:16.927 --> 03:23.397 to sell that option at the price specified in the contract, 03:23.400 --> 03:25.450 called the exercise price. 03:25.450 --> 03:29.010 03:29.009 --> 03:32.389 If it's European, you have to wait until the 03:32.393 --> 03:37.353 exercise date and then you have one day when you can do that. 03:37.349 --> 03:44.449 A call option is the right to buy a share of stock or whatever 03:44.451 --> 03:49.691 it is--whatever is specified in the option. 03:49.690 --> 03:56.010 In a traditional option, there are two parties; 03:56.009 --> 04:01.779 there's the buy of the option and usually we present them from 04:01.776 --> 04:06.026 the perspective of the buyer of the option. 04:06.030 --> 04:10.640 The buyer of the option pays a price to buy the option--not to 04:10.641 --> 04:14.271 be confused with the exercise price--and then, 04:14.270 --> 04:20.160 depending on whether it's American or European, 04:20.157 --> 04:26.937 has until the exercise date to exercise the option; 04:26.939 --> 04:28.999 but, the buyer doesn't have to do anything. 04:29.000 --> 04:32.180 You can just do nothing; you can buy the option and if 04:32.177 --> 04:35.787 you do nothing it becomes worthless because the only way 04:35.793 --> 04:39.543 the option ever gives you value after you buy it is if you 04:39.542 --> 04:42.142 exercise it, meaning you say, 04:42.136 --> 04:45.456 I will use my right to buy or sell. 04:45.459 --> 04:53.369 The other party is the writer of the option. 04:53.370 --> 04:56.850 Because it's a contract, it has to be between two 04:56.854 --> 05:00.894 parties. Somebody is on the other side 05:00.894 --> 05:10.574 and you can do either one; you can either buy or write an 05:10.572 --> 05:16.982 option. If you--let me make this clear; 05:16.980 --> 05:22.970 if you write a call option, then what you are committing 05:22.973 --> 05:28.423 yourself to do as the writer--you sign the contract 05:28.421 --> 05:33.661 from the writer's contract, which goes along with the 05:33.660 --> 05:35.000 buyer's contract. 05:35.000 --> 05:39.000 Well, it provides rights to the buyer. 05:39.000 --> 05:42.940 If you write a call option, then you--and say it's 05:42.940 --> 05:47.770 American--then you are signing a contract --let's say it's on 05:47.765 --> 05:52.425 stock--to deliver one hundred shares to the other guy, 05:52.430 --> 05:57.720 the buyer, whenever that guy feels like it. 05:57.720 --> 06:00.580 That guy will pay you the contracted price, 06:00.584 --> 06:04.614 so it's not--it doesn't seem like much fun to be a writer of 06:04.607 --> 06:08.147 an option because you have--you're just sitting there 06:08.153 --> 06:12.453 waiting for this other person to make up his or her mind. 06:12.450 --> 06:18.240 There's a benefit; mainly, you get the money. 06:18.240 --> 06:24.630 The buyer of the option pays you up front for providing this 06:24.627 --> 06:29.607 right to the buyer, so writers of options write 06:29.608 --> 06:34.478 them hoping that they expire unexercised; 06:34.480 --> 06:36.470 that's when they make money. 06:36.470 --> 06:40.570 If you write an option and the buyer of the option pays you the 06:40.574 --> 06:44.684 money up front and then you never hear from the buyer again, 06:44.680 --> 06:48.360 then you're--that's the way you like it. 06:48.360 --> 06:56.040 So, you make money by writing options and hoping that they 06:56.044 --> 06:59.014 don't get exercised. 06:59.009 --> 07:05.089 Of course, you can write a put option and that means--if you 07:05.086 --> 07:09.756 write a put option, you are signing a contract that 07:09.763 --> 07:14.063 says that whenever this other guy on the other side, 07:14.060 --> 07:19.050 the buyer, decides to, that guy will sell you a 07:19.050 --> 07:23.390 hundred shares at the specified price. 07:23.389 --> 07:31.009 Again, you're laying yourself open to, whenever this guy wants 07:31.010 --> 07:37.630 to, you've got to receive a hundred shares and pay the 07:37.630 --> 07:42.230 money. Now, these kinds of contracts 07:42.234 --> 07:47.444 are very old and, in fact, we had a conference 07:47.440 --> 07:54.270 over the weekend at the Yale School of Management on--it was 07:54.266 --> 08:01.316 a very interesting--I've never experienced anything quite like 08:01.323 --> 08:04.563 it. Maybe I should put the website 08:04.563 --> 08:06.163 up for you to look at. 08:06.160 --> 08:13.810 There's a book; it's called The Great Mirror 08:13.811 --> 08:20.021 of Folly, written in 1720 about the stock 08:20.016 --> 08:28.756 market and the Beinecke Rare Book Library has a copy of it. 08:28.759 --> 08:36.609 They're very rare--about the stock market crash of 1720. 08:36.610 --> 08:40.410 Did you know that there was a big stock market crash in the 08:40.413 --> 08:44.283 year 1720? What was happening in New Haven 08:44.276 --> 08:47.506 in 1720? Well, I know one thing that was 08:47.505 --> 08:50.965 happening in 1720 in New Haven--I'm guessing; 08:50.970 --> 08:54.040 I'm pretty sure. You had some pretty angry 08:54.035 --> 08:57.315 investors who lost everything in the stock market, 08:57.319 --> 08:59.529 but it couldn't have been the U.S. 08:59.531 --> 09:02.481 stock market, which wasn't created yet. 09:02.480 --> 09:12.630 The crash of 1720 was primarily in Paris and London, 09:12.628 --> 09:19.798 also less so in Amsterdam; those were the financial 09:19.796 --> 09:21.256 centers of the world. 09:21.259 --> 09:25.179 So, I'm speculating there must have been someone here in New 09:25.178 --> 09:28.428 Haven; probably Yale University lost 09:28.434 --> 09:31.164 in this crash--I don't know. 09:31.159 --> 09:33.999 There must have been someone here who lost--it was a huge and 09:34.001 --> 09:35.281 devastating stock market. 09:35.280 --> 09:40.760 This is the first one actually; the first stock market crash. 09:40.759 --> 09:42.899 We had a lot of fun at this conference; 09:42.900 --> 09:44.630 it just relates to options. 09:44.629 --> 09:50.309 I'll tell you why it relates to options, because people were 09:50.310 --> 09:54.450 writing options galore in 1720 on stocks. 09:54.450 --> 10:00.290 The book--if you search on Great Mirror of Folly on 10:00.294 --> 10:06.554 the Web, it'll come up with our conference and proceedings. 10:06.549 --> 10:09.869 Since this book--copyrights expire after, 10:09.866 --> 10:14.096 well, it's a complicated formula, but in less then a 10:14.095 --> 10:16.455 century. So, this is all public domain, 10:16.456 --> 10:19.276 so Yale has it up on the Web and you can read the whole book. 10:19.279 --> 10:22.029 Unfortunately, it's written in Dutch, 10:22.030 --> 10:26.690 which might deter some of you, but it has lots of pictures. 10:26.690 --> 10:31.590 We had great--at this conference, the--it was the most 10:31.594 --> 10:36.874 interdisciplinary conference I've ever seen because we had 10:36.868 --> 10:42.538 professors from the Art History, Comparative Literature, 10:42.538 --> 10:46.198 Finance, Economics, and Psychology. 10:46.200 --> 10:51.010 We had scholars from all over the world who knew about the 10:51.009 --> 10:55.649 year 1720, including a lot of Dutchmen who were here. 10:55.649 --> 11:01.479 Anyway, the highlight of it was--one highlight for me was, 11:01.479 --> 11:07.309 it had a--we saw a picture of an option from this time--an 11:07.308 --> 11:12.318 option contract to buy stocks from Amsterdam. 11:12.320 --> 11:17.370 It showed it was a printed form; they had printed forms back 11:17.371 --> 11:18.561 then, at least in Holland they did. 11:18.559 --> 11:20.999 So, a printer had printed up with blanks to fill in. 11:21.000 --> 11:26.390 There's a place to fill in the exercise price and the exercise 11:26.391 --> 11:28.251 date. I don't know whether it was 11:28.252 --> 11:30.782 American or European at the time, but I'm sure if it was 11:30.784 --> 11:33.504 American they didn't call it an American option in 1720. 11:33.500 --> 11:34.610 They didn't even call them options. 11:34.610 --> 11:36.720 Of course, it's all in Dutch, so I don't know; 11:36.720 --> 11:41.710 it was some other word--not options. 11:41.710 --> 11:45.250 I'm just saying this because the-- The other interesting 11:45.248 --> 11:49.168 thing about 1720 is that they didn't make the same distinction 11:49.173 --> 11:52.393 between investing and gambling that we do now. 11:52.389 --> 11:58.039 Right now, anyone on Wall Street is very loathe to have 11:58.037 --> 12:02.427 any suggestion of connection with gambling, 12:02.429 --> 12:06.089 but back then they didn't care. 12:06.090 --> 12:09.750 So, lots of stocks would have lotteries attached or there 12:09.750 --> 12:13.150 would be all kinds of--something called a tontine, 12:13.149 --> 12:17.029 where a group of investors would invest in something and 12:17.025 --> 12:20.755 then all the money would go to the last one to die, 12:20.760 --> 12:22.690 after all of them died but one. 12:22.690 --> 12:27.220 That's a sort of gambling; I don't know what sense it 12:27.215 --> 12:29.885 makes, but they did that. 12:29.889 --> 12:37.489 I remember an old story on--I just heard this somewhere--from 12:37.490 --> 12:40.350 the 1920s. Two brokers on the New York 12:40.350 --> 12:43.180 Stock Exchange floor were talking to each other and one of 12:43.181 --> 12:46.361 them says, "I'll be you $5 that the market's going to go up." 12:46.360 --> 12:52.950 Then the senior man scolded him and said, "are you betting? 12:52.950 --> 12:56.870 You will be thrown off this floor permanently if I hear that 12:56.869 --> 12:59.289 word again." So, that attitude has 12:59.287 --> 13:03.887 persisted--that investing should be distinguished from gambling. 13:03.889 --> 13:08.519 I suppose there's good reason for that because gambling 13:08.523 --> 13:13.073 instincts can take hold of us and investing has a good 13:13.070 --> 13:15.250 purpose. Unfortunately, 13:15.247 --> 13:19.747 our emotions can carry us away from the good purpose and 13:19.753 --> 13:22.133 gambling is not investing. 13:22.129 --> 13:25.409 Back in 1720, the distinction was not so 13:25.406 --> 13:30.616 clear and this event was so--it got--the reason they called the 13:30.616 --> 13:35.486 book The Great Mirror of Folly is that the event got 13:35.489 --> 13:38.669 totally crazy. People were squandering their 13:38.672 --> 13:43.322 life fortunes. I'll tell you one more story. 13:43.320 --> 13:46.000 We had a great time at this conference because this book, 13:46.002 --> 13:48.902 Mirror of Folly, includes plays that were 13:48.898 --> 13:53.428 written in 1720 and performed in Amsterdam about the crash--about 13:53.429 --> 13:55.269 the stock market crash. 13:55.269 --> 13:59.239 The organizers of this conference got some students 13:59.244 --> 14:04.174 from Saybrook College to perform one of the plays from Great 14:04.172 --> 14:06.082 Mirror of Folly. 14:06.080 --> 14:07.630 Is anyone here from Saybrook? 14:07.629 --> 14:11.759 Okay, you weren't in the--I didn't see you there though. 14:11.759 --> 14:17.269 There was a scene in the play where the young woman was being 14:17.266 --> 14:22.496 told by her father that he intends for her to marry a very 14:22.497 --> 14:27.637 promising young man who is speculating in stocks and will 14:27.636 --> 14:31.346 soon be rich. She is very skeptical about 14:31.351 --> 14:36.271 being forced to marry; she has somebody else in mind. 14:36.269 --> 14:40.319 The father says that the other young man is worthless; 14:40.320 --> 14:42.250 he'll never amount to anything. 14:42.250 --> 14:46.570 But, she stuck by her guns and insisted that I will never marry 14:46.566 --> 14:49.626 a man who's in love with the stock market. 14:49.629 --> 14:52.989 We don't know what happened because it's all fictional, 14:52.993 --> 14:55.863 but as we know, the whole stock market crashed, 14:55.859 --> 14:58.599 so she was right on two counts probably. 14:58.600 --> 15:03.250 Anyway, that's all about--options are very old, 15:03.250 --> 15:08.300 but they've emerged more recently as very important 15:08.304 --> 15:11.434 contracts. In particular, 15:11.431 --> 15:16.081 what they didn't have in 1720--in fact, 15:16.076 --> 15:22.676 they didn't have anywhere until recently--is an options 15:22.678 --> 15:26.618 exchange. The problem with a traditional 15:26.618 --> 15:30.478 option is that it's a contract between two parties. 15:30.480 --> 15:34.010 15:34.009 --> 15:36.669 If you write--if you buy an option, you're at the mercy of 15:36.674 --> 15:37.614 this other person. 15:37.610 --> 15:41.670 So, if you buy an option that was written by a broker, 15:41.670 --> 15:44.890 as they were in 1720, what if the other guy 15:44.888 --> 15:48.618 doesn't--he just skips town; he's gone. 15:48.620 --> 15:52.540 You bought this option to either buy or sell and then when 15:52.540 --> 15:55.360 the date comes you can't find this guy. 15:55.360 --> 15:56.680 So, what do you do? 15:56.679 --> 16:02.009 You obviously were cheated out of your money. 16:02.009 --> 16:08.599 So, we created--that was a problem until 1973, 16:08.603 --> 16:14.613 when the first options exchange opened. 16:14.610 --> 16:18.070 16:18.070 --> 16:20.570 Well, I think there may have been ways of dealing with the 16:20.572 --> 16:21.892 problem, but not before '73. 16:21.889 --> 16:28.869 But, this is the first options exchange--Chicago Board Options 16:28.870 --> 16:36.080 Exchange--which was a spin off of the Chicago Board of Trade. 16:36.080 --> 16:40.800 Now, what they did was they organized a central marketplace 16:40.795 --> 16:42.985 for standardized options. 16:42.990 --> 16:46.620 Options used to be written for whatever exercise date anybody 16:46.624 --> 16:52.264 wanted; there was no standardization. 16:52.259 --> 16:55.889 An options exchange is like creating a futures market when 16:55.894 --> 16:58.704 you only had a forward market in the past. 16:58.700 --> 17:04.390 They started trading options on U.S. 17:04.391 --> 17:14.471 stocks in 1973 and they require that the writer of a naked call 17:14.474 --> 17:18.544 has to put up margin. 17:18.540 --> 17:21.030 What is a naked call? 17:21.029 --> 17:25.659 If you write a call, you are standing ready to sell 17:25.664 --> 17:31.324 a hundred shares to the buyer, whenever that buyer decides--if 17:31.319 --> 17:34.099 it's American--to do that. 17:34.099 --> 17:40.769 But you're naked if you don't own the hundred shares. 17:40.769 --> 17:45.239 One way you can do it is, you can show that you own a 17:45.244 --> 17:48.774 hundred shares, so there's no way that you 17:48.772 --> 17:51.012 could fail to deliver. 17:51.009 --> 17:55.669 If you're naked, then you are required to put up 17:55.674 --> 18:01.334 margin and the margin is an amount that was enough so that 18:01.330 --> 18:06.450 if you fail to deliver, the CBOE could access your 18:06.452 --> 18:11.812 margin account and buy the shares on the market to sell to 18:11.808 --> 18:15.798 the buyer; there'd be enough money to do 18:15.797 --> 18:19.317 that. The margin requirement for the 18:19.323 --> 18:25.033 writer makes the contract secure so that there is really no 18:25.033 --> 18:30.253 counterparty risk with options purchased on an options 18:30.251 --> 18:33.501 exchange. Now, there are many options 18:33.498 --> 18:37.718 exchanges, but the CBOE--I'm just listing it--was the first. 18:37.720 --> 18:46.780 Now, futures exchanges sell options on futures; 18:46.780 --> 18:49.960 18:49.960 --> 18:52.740 that's the same thing as an option on a stock, 18:52.742 --> 18:55.592 but instead of a stock contract, it's a futures 18:55.586 --> 19:01.136 contract. That would be done at the CME 19:01.141 --> 19:07.041 Group, which is a futures exchange. 19:07.039 --> 19:12.919 That's just--we're just talking about where you can do these 19:12.922 --> 19:18.222 things. Did I explain the concept of 19:18.224 --> 19:25.324 options? Maybe I should go through 19:25.318 --> 19:37.128 the--I have here a plot illustrating a call option. 19:37.130 --> 19:43.010 On the vertical--on the horizontal axis, 19:43.006 --> 19:46.166 I have stock price; 19:46.170 --> 19:49.650 19:49.650 --> 19:54.760 that's $0 a share, $5 a share, $10 a share. 19:54.759 --> 19:58.439 I'm showing it up to $45 a share. 19:58.440 --> 20:06.100 Now, I'm going to illustrate the intrinsic value of an option 20:06.100 --> 20:09.420 with a $20 strike price. 20:09.420 --> 20:12.250 Now, the option would be typically for 100 shares, 20:12.254 --> 20:15.844 but I'm going to describe it as if it were an option to buy one 20:15.841 --> 20:18.931 share; so, it would be 1/100th of a 20:18.933 --> 20:23.263 typical option. This broken straight line is 20:23.258 --> 20:27.998 what we call the intrinsic value of the option, 20:28.002 --> 20:33.882 which is the money you could get if you exercised it right 20:33.881 --> 20:37.061 now. If you decided--we'll never 20:37.055 --> 20:42.125 have intrinsic value negative because you wouldn't exercise. 20:42.130 --> 20:46.040 So, let me explain what this means. 20:46.039 --> 20:51.959 Suppose you own an option with an exercise price of $20 and the 20:51.958 --> 20:54.438 price of a share is $15. 20:54.440 --> 20:58.500 What is the value of that option today--the intrinsic 20:58.504 --> 21:02.614 value? Well, it's nothing because the 21:02.613 --> 21:08.073 option gives me a right to buy a share at $20, 21:08.069 --> 21:10.729 but hey, I can buy it under the stock market for $15, 21:10.728 --> 21:13.028 so I would never exercise the option today. 21:13.030 --> 21:16.250 It would be worthless; it would be worth minus $5 if I 21:16.253 --> 21:19.573 exercised it today because I would be paying $20 for 21:19.566 --> 21:23.146 something I could get for $15, but I'm not going to call it 21:23.147 --> 21:25.357 minus 5; I'm going to call it 0 because 21:25.359 --> 21:27.109 you just--you won't exercise. 21:27.109 --> 21:31.179 If the stock price is below the exercised price, 21:31.178 --> 21:35.168 I have a value. On the vertical axis is the 21:35.166 --> 21:38.736 intrinsic of the call; I have to distinguish it 21:38.739 --> 21:40.049 between actual value. 21:40.049 --> 21:49.009 This isn't the price that is quoted for the option; 21:49.009 --> 21:52.779 this is what it would be worth if you exercised it today if it 21:52.778 --> 21:55.988 were--the option has value beyond its intrinsic value 21:55.990 --> 21:58.770 because even though it's worthless today, 21:58.769 --> 22:02.069 it might be worth something in the future. 22:02.069 --> 22:05.249 I'll come back to that but this is just--I'm just talking about 22:05.247 --> 22:08.457 intrinsic value. Now, what if the stock price is 22:08.458 --> 22:11.878 $30 today. What is the value of the 22:11.882 --> 22:15.042 option--the intrinsic value? 22:15.039 --> 22:18.449 Well, it's going to be $10, obviously, because if you 22:18.446 --> 22:21.656 exercise it today, you're buying the stock for $20 22:21.656 --> 22:25.386 and you can sell it today for 30 on the stock market; 22:25.390 --> 22:27.550 so, the difference is 10. 22:30.732 --> 22:33.972 angle here--doesn't look like it, but that's what it is. 22:33.970 --> 22:35.240 It has a slope of one. 22:35.240 --> 22:38.920 It's very simple; the intrinsic value for a call 22:38.919 --> 22:43.259 is just a broken straight line; it breaks at the exercised 22:43.257 --> 22:46.857 price. To give you a little bit more 22:46.862 --> 22:52.452 jargon, in this region we say the option is "out of the 22:52.454 --> 22:56.144 money." That means, exercised today, 22:56.141 --> 22:58.321 it would be worthless. 22:58.319 --> 23:03.869 This one right here is called "at the money." 23:03.869 --> 23:08.519 If the stock price is equal to the exercised price, 23:08.523 --> 23:13.083 then the stock--we'd call the option at the money, 23:13.083 --> 23:17.143 for a call. Here, if the stock price is 23:17.136 --> 23:22.446 above the exercise price, we say it's "in the money." 23:22.450 --> 23:23.970 This line goes off into infinity; 23:23.970 --> 23:26.250 I just stopped it there. 23:26.250 --> 23:32.060 That's straightforward, right? 23:32.059 --> 23:35.099 Anyway, this does illustrate something about options that is 23:35.097 --> 23:37.617 different from anything we've discussed before. 23:37.619 --> 23:42.019 This is a broken straight line, not a straight line. 23:42.019 --> 23:48.769 All of our talk about portfolios to date has been 23:48.773 --> 23:51.423 linear. When you combine stocks, 23:51.423 --> 23:54.833 you are making your portfolio respond linearly to the return 23:54.825 --> 23:57.415 of any one of the stocks in the portfolio, 23:57.420 --> 24:01.250 but this is non-linear because we have a break; 24:01.250 --> 24:10.240 that's what options do, so it's non-linear finance. 24:10.240 --> 24:13.770 Some people are confused about what options really are. 24:13.769 --> 24:17.139 Often people say, well if I buy a stock option 24:17.143 --> 24:21.873 that means I can make up my mind later whether I want to buy and 24:21.865 --> 24:24.405 sell. So hey, I'm just getting the 24:24.406 --> 24:27.806 right to be indecisive or to--well, think of it this 24:27.805 --> 24:31.865 way--I haven't made up my mind whether I really want to invest 24:31.870 --> 24:34.870 in options or not--in stocks or not--so, 24:34.869 --> 24:37.839 I'll buy an option and that gives me the right to buy. 24:37.839 --> 24:42.099 You could say that and a lot of people think that way. 24:42.099 --> 24:46.769 Like, a company will think, we're trying to decide whether 24:46.765 --> 24:50.035 we want to build this shopping center. 24:50.039 --> 24:53.339 So, we'll buy an option on the land underlying where we would 24:53.344 --> 24:56.544 build the shopping center and we'll think more about it and 24:56.539 --> 25:00.009 decide whether it's a good idea to build a shopping center. 25:00.009 --> 25:03.549 You could do that, but there's something a little 25:03.553 --> 25:07.763 bit misleading about that reasoning because whether or not 25:07.761 --> 25:11.011 you decide to build the shopping center, 25:11.009 --> 25:14.009 if you buy an option on the land you will always exercise it 25:14.012 --> 25:17.012 if it's in the money on the exercise date--whether you build 25:17.014 --> 25:18.494 a shopping center or not. 25:18.490 --> 25:22.180 Suppose you couldn't decide whether to build a shopping 25:22.175 --> 25:26.335 center and you bought an option on land and then someone comes 25:26.338 --> 25:28.678 in and says, well we have to make up our 25:28.676 --> 25:31.416 mind today; the option is exercising--is 25:31.423 --> 25:35.813 expiring--if we don't exercise it today it's worthless. 25:35.809 --> 25:37.569 What do you discuss at your meeting? 25:37.569 --> 25:40.189 You don't discuss whether we're going to build the shopping 25:40.187 --> 25:42.487 center or not; that's irrelevant. 25:42.490 --> 25:44.950 You discuss, what can we sell the land for 25:44.950 --> 25:48.190 and if we can sell it for more than the exercise price, 25:48.190 --> 25:50.050 we will always exercise it. 25:50.049 --> 25:56.839 So, there's no--the assumption in finance is that all options 25:56.841 --> 26:03.521 that are in the money on the exercise date are exercised and 26:03.519 --> 26:06.009 there's no choice. 26:06.009 --> 26:09.409 The word option might be misleading because--you could 26:09.414 --> 26:13.084 choose to be dumb and not exercise it, but that's not what 26:13.076 --> 26:15.176 it's about. On the other hand, 26:15.180 --> 26:18.730 options really are central to our thinking about a lot of 26:18.726 --> 26:20.996 things. I'll give you an example of an 26:20.998 --> 26:23.508 option that you might not consider an option. 26:23.509 --> 26:26.599 This is the option to marry somebody. 26:26.599 --> 26:31.909 Sometimes people will complain that their boyfriend or 26:31.913 --> 26:34.623 girlfriend cannot commit. 26:34.619 --> 26:37.859 We've been going out for three years; 26:37.859 --> 26:43.629 it's time that we get married, but this person--the 26:43.627 --> 26:48.007 counterparty--cannot seem to decide. 26:48.009 --> 26:52.019 Actually, one view of it--of that situation--could be that 26:52.021 --> 26:55.821 this person is just better schooled in finance than the 26:55.822 --> 27:00.192 other because one principle of finance is that you should never 27:00.185 --> 27:02.855 exercise an American call early. 27:02.859 --> 27:05.879 I'm not this cynical about relationships; 27:05.880 --> 27:09.130 I'm just telling you a story that comes to mind. 27:09.130 --> 27:12.190 You'd never want to--I'll come back to that--you never want to 27:12.186 --> 27:16.006 exercise an American call early, so that's why there isn't an 27:16.009 --> 27:20.019 important distinction between European and American. 27:20.019 --> 27:23.079 Just in the case of relationships, 27:23.075 --> 27:28.345 suppose your girlfriend or boyfriend really wants to marry 27:28.353 --> 27:31.783 you and is still giving you time, 27:31.779 --> 27:34.629 then you instinctively know you should wait as long--I'm saying 27:34.632 --> 27:37.232 not really, but I'm saying in terms of 27:37.233 --> 27:39.663 theory; you should wait until the last 27:39.656 --> 27:43.026 day when this other person says it's now or never because 27:43.028 --> 27:46.398 there's always exercise--there's always option value. 27:46.400 --> 27:50.240 There's always a chance--maybe that will become clearer. 27:50.240 --> 27:52.020 I don't know if you like my analogy. 27:52.019 --> 27:55.429 I'm not cynical about these things as some people are. 27:55.430 --> 28:00.190 Peter? Student: [inaudible] 28:00.190 --> 28:06.050 Professor Robert Shiller: This is a call 28:06.050 --> 28:11.020 option up here, but--this is a call. 28:11.019 --> 28:12.949 I'm going to show you a put--go ahead. 28:12.950 --> 28:17.110 What arbitrage-- Student: [inaudible] 28:17.106 --> 28:21.546 Professor Robert Shiller: The price--I'm 28:21.553 --> 28:24.553 going to come back to that. 28:24.549 --> 28:27.949 The price of the option will always be above that line, 28:27.946 --> 28:31.656 so there's no arbi--there are possible--it depends on if the 28:31.657 --> 28:34.107 price is wrong--they're arbitraged. 28:34.110 --> 28:35.150 Let me come back to that. 28:35.150 --> 28:38.060 This is a put option. 28:38.059 --> 28:42.129 This is intrinsic value for a put option because it's the 28:42.132 --> 28:43.662 opposite of a call. 28:43.660 --> 28:48.630 If the strike price is $20 and the stock price is selling for 28:48.625 --> 28:53.505 $15, then you can see that it's in the money because you can 28:53.508 --> 28:55.658 make $5 by exercising. 28:55.660 --> 28:59.670 You have the right to sell it for 20 but you can buy it in the 28:59.666 --> 29:02.486 market for 15, so you buy it for 15 and sell 29:02.490 --> 29:05.480 it for 20; you make $5. 29:05.480 --> 29:08.230 On the other hand, up here--if the stock price is 29:08.230 --> 29:10.810 $30, you have the right to sell it for $20. 29:10.810 --> 29:14.340 Well, that's worth nothing; I can sell it for 30 in the 29:14.341 --> 29:23.791 market. Then what--let me jump to this; 29:23.789 --> 29:27.389 this isn't exactly the order that I wanted to do it, 29:27.392 --> 29:31.632 but the--this has to do with arbitrage as you were saying. 29:31.630 --> 29:36.670 The price in the market should always be greater than the 29:36.670 --> 29:40.630 intrinsic value, until the exercise date--the 29:40.630 --> 29:45.760 last date for an American--even American or European, 29:45.760 --> 29:48.240 but let's talk American. 29:48.240 --> 29:55.220 This pink line is my price for the option; 29:55.220 --> 29:58.650 we'll talk about how we get that line from theory, 29:58.646 --> 30:02.836 but price--if the--let's say, if it's an American option it's 30:02.841 --> 30:06.631 got time to go. Let's say the exercise date is 30:06.631 --> 30:10.571 not for another year and it's out of the money; 30:10.569 --> 30:14.909 the price of a share is only $15 but the exercise price is 30:14.912 --> 30:16.772 $20. That option is still worth 30:16.773 --> 30:18.073 something today, right? 30:18.070 --> 30:19.730 It's not worthless. 30:19.730 --> 30:22.130 It would be worthless if you exercised it today, 30:22.128 --> 30:24.628 but hey, you're not going to exercise it today. 30:24.630 --> 30:29.480 The reason it has value is that the price might rise above $20 30:29.479 --> 30:34.089 sometime over the next year and so it--you have a chance of 30:34.091 --> 30:35.921 making money on it. 30:35.920 --> 30:40.620 That means the price of the option is always going to be 30:40.617 --> 30:44.117 worth more than the price of the stock. 30:44.119 --> 30:45.419 No, it's always going to be worth more than the intrinsic 30:45.423 --> 30:47.733 value. What about at the money? 30:47.730 --> 30:51.850 An at-the-money option--if the price of a share is 20 and the 30:51.852 --> 30:55.772 option--and the exercise is 20, exercise it today and it's 30:55.768 --> 30:58.938 worthless. It has to be valuable because 30:58.938 --> 31:03.348 fifty-fifty chance the stock price is going to go up and so 31:03.354 --> 31:07.014 you have a good chance of making money on it. 31:07.009 --> 31:11.489 So, it's going to be worth a lot more than this one was down 31:11.488 --> 31:14.068 here because we're at the money. 31:14.069 --> 31:18.729 Any little jostle upward is going to put it in the money. 31:18.730 --> 31:21.730 There's a big chance that this will become in the money, 31:21.726 --> 31:24.156 so it has real value; whereas, down here, 31:24.160 --> 31:27.700 the option doesn't have much value because it would take a 31:27.702 --> 31:30.252 big price move to put it in the money. 31:30.250 --> 31:32.000 Then what about up here? 31:32.000 --> 31:36.800 Even when they're in the money they're worth more than 31:36.799 --> 31:39.359 intrinsic value. You kind of wonder, 31:39.357 --> 31:40.527 well why would that be? 31:40.529 --> 31:48.009 Well, it's because this thing is better than owning the stock. 31:48.009 --> 31:51.939 Let's say, at this point, when the stock price is 25, 31:51.940 --> 31:56.630 I'd rather own the option than to own a share minus $20 because 31:56.627 --> 32:00.707 the option can't fail me as much as the share can. 32:00.710 --> 32:04.690 The share minus $20 could be negative in value before the 32:04.687 --> 32:07.737 exercise date, but the worst that can happen 32:07.742 --> 32:11.012 to my option is it would be worth nothing. 32:11.009 --> 32:14.089 The arbitrage, Peter, that you were referring 32:14.094 --> 32:18.444 to is the arbitrage--what if the price were below this line? 32:18.440 --> 32:20.130 Maybe that's what you were thinking. 32:20.130 --> 32:23.720 What if the option price--what if the stock price is $30 and 32:23.723 --> 32:25.553 the option is selling at $5? 32:25.549 --> 32:29.409 If it's an American option I have an immediate arbitrage. 32:29.410 --> 32:38.940 I buy--if it's a call option I would buy the option for $5. 32:38.940 --> 32:43.730 I would exercise it and sell for $30 and I'll make money 32:43.725 --> 32:46.145 instantly. That can't happen. 32:46.150 --> 32:53.220 We can't have the option price selling for less than intrinsic 32:53.218 --> 33:00.168 value, so you know just from arbitrage that that pink line is 33:00.171 --> 33:03.881 always above the solid line. 33:03.880 --> 33:08.540 Moreover, there's another arbitrage relation which I 33:12.285 --> 33:15.185 line here from the origin, that's plotting the stock price 33:15.192 --> 33:19.442 against the stock price; it has a slope of one and it 33:19.443 --> 33:22.013 comes out of the origin. 33:25.020 --> 33:25.990 line--above here. 33:25.990 --> 33:28.490 In other words, an option can never sell for 33:28.490 --> 33:29.770 more than the stock. 33:29.770 --> 33:32.190 Does that sound obvious? 33:32.190 --> 33:36.240 Why would you pay--if the share is selling for $25, 33:36.237 --> 33:40.687 why would I pay $30 for the right to buy at that $20? 33:40.690 --> 33:45.630 Obviously it's ridiculous; the stock itself is an option 33:45.630 --> 33:49.520 to buy the share at a $0 exercise price, 33:49.518 --> 33:55.398 so it has to be worse to have a positive exercise price. 33:55.400 --> 34:00.710 Now, I wanted to stress the put-call parity relation and 34:00.714 --> 34:04.004 this is another arbitrage thing. 34:04.000 --> 34:07.440 The put option price--arbitrage--the absence of 34:07.443 --> 34:12.093 arbitrage opportunities implies that the put option price minus 34:12.085 --> 34:16.495 the call option price equals the present value of the strike 34:16.501 --> 34:20.841 price--that's discounting it from this exercise date to the 34:20.843 --> 34:25.493 present--plus the present value of any dividends coming between 34:25.485 --> 34:30.685 today and the exercise date, minus the price of the stock. 34:30.690 --> 34:34.980 This has to hold because if it didn't hold, there would be an 34:34.975 --> 34:36.685 arbitrage opportunity. 34:36.690 --> 34:41.140 The put--let me just show you why. 34:41.139 --> 34:45.019 This diagram is supposed to explain that. 34:45.019 --> 34:48.479 I've got here the intrinsic value of the call, 34:48.476 --> 34:52.696 which is the yellow line, and this is an intrinsic value 34:52.701 --> 34:55.671 of a put. We've got them both at the same 34:55.665 --> 34:59.385 exercise price. Then, I've shown here the stock 34:59.385 --> 35:04.255 price on the blue line; stock price against stock price 35:08.391 --> 35:11.571 one. Well, you notice that if I were 35:11.568 --> 35:16.008 to buy a call and write a put--that's the same thing as 35:16.008 --> 35:20.778 shorting a put--I would have a combined portfolio with just 35:20.776 --> 35:23.646 those two. I would have the yellow line 35:23.651 --> 35:26.231 here and I'd have minus the pink line here. 35:26.230 --> 35:30.580 I would have a parallel straight line that looks just 35:30.580 --> 35:34.010 like the stock price just shifted down. 35:34.010 --> 35:37.930 If I buy a call and short a put--or write a put--it's the 35:37.934 --> 35:42.004 same thing as owning the stock minus the exercise price. 35:42.000 --> 35:46.300 So, that's what we have in the put-call parity relation, 35:46.300 --> 35:49.740 so that we're taking account of dividends. 35:49.739 --> 35:52.929 That diagram didn't show the fact that stocks will pay--might 35:52.930 --> 35:55.590 pay dividends between now and the exercise date. 35:55.590 --> 35:58.950 You can see what I was just saying. 35:58.950 --> 36:01.410 I've got--I said call minus put. 36:01.409 --> 36:06.929 Well, this is put minus call, minus the price of stock. 36:06.929 --> 36:10.249 I have a minus sign in front of everything here, 36:10.252 --> 36:13.082 but it's just what that diagram shows. 36:13.079 --> 36:16.809 What put-call parity means is that we only need a theory of 36:16.813 --> 36:20.683 either call prices or put prices and then the other one falls 36:20.675 --> 36:22.795 right out of put-call parity. 36:22.800 --> 36:27.860 All I need is a theory of call prices, so we will just forget 36:27.856 --> 36:32.656 about puts and we'll just talk about calls from now on. 36:32.659 --> 36:37.089 If I give you a problem to ask you--what is the put price--what 36:37.086 --> 36:38.796 is the price of a put? 36:38.800 --> 36:43.320 You would go in and calculate the price of a call and then 36:43.315 --> 36:45.925 calculate the put option price. 36:45.929 --> 36:48.289 We'll put this on right hand of the equation. 36:48.289 --> 36:51.879 The put price would equal the call price plus the present 36:51.883 --> 36:54.893 value of the strike price, plus the present value of 36:54.888 --> 36:56.868 dividends, minus the price of the stock; 36:56.870 --> 36:59.440 so, that makes it very easy. 36:59.440 --> 37:07.150 All we have to do is worry about calls. 37:07.150 --> 37:12.010 Where am I? The question for financial 37:12.012 --> 37:15.722 theory is, what determines this pink line? 37:15.719 --> 37:19.009 You agree that it should be above intrinsic value. 37:19.010 --> 37:23.290 As the option gets closer to expiration--as time moves on and 37:23.286 --> 37:27.346 the exercise date is getting closer and closer in time, 37:27.349 --> 37:30.339 this pink line is going to go down, down, down. 37:30.340 --> 37:35.570 On the last day, it hits the intrinsic value. 37:35.570 --> 37:38.670 What is it before the exercise date? 37:38.670 --> 37:45.130 I'm going to start with a theory, which illustrates how we 37:45.134 --> 37:47.974 calculate these things. 37:47.969 --> 37:54.139 This is a theory that applies to--so that we can understand it 37:54.142 --> 37:59.102 easily--that applies to a strip-down situation. 37:59.099 --> 38:03.179 I'm going to derive the price of an option under the 38:03.179 --> 38:05.979 assumption that it's very simple. 38:05.980 --> 38:09.160 There's only one period between now and exercise; 38:09.160 --> 38:11.770 it's a European option. 38:11.769 --> 38:16.239 We're going to exercise it in one--we have an exercise date of 38:16.237 --> 38:20.697 one period and also under the restrictive assumption--and this 38:20.704 --> 38:25.324 is for pedagogical purposes just to simplify option theory--that 38:25.318 --> 38:30.588 the stock price, S, is the stock price 38:30.594 --> 38:34.034 today. The stock--this stock is very 38:34.025 --> 38:38.965 special because next period it can have only two values. 38:38.969 --> 38:42.729 It's S times u if the stock goes up; 38:42.730 --> 38:44.180 u stands for up. 38:44.179 --> 38:49.859 It's S times d if the stock price goes down. 38:49.860 --> 38:52.450 What I'm saying--what's arbitrary here is, 38:52.448 --> 38:56.048 I'm saying that there are only two possible prices for the 38:56.046 --> 38:58.946 stock next period--Su or Sd. 38:58.950 --> 39:03.030 39:03.030 --> 39:05.480 That's not real world because as you know there are all kinds 39:05.478 --> 39:07.598 of infinite number of possible prices next period. 39:07.599 --> 39:11.289 Again, this is just--I think that we should be able to figure 39:11.293 --> 39:14.863 out what the price of a call option on this stock should be 39:14.864 --> 39:17.904 worth. It's very simple. 39:17.900 --> 39:22.180 They say it's very simple, but the people who invented 39:22.175 --> 39:25.075 this won the Nobel Prize for this, 39:25.079 --> 39:29.329 so I won't--I don't want to make it--this wasn't so simple 39:29.331 --> 39:32.241 in the history of financial thinking. 39:32.239 --> 39:37.029 Do you understand the situation that we're proposing in? 39:37.030 --> 39:39.490 It's just like--there's this very funny stock that we 39:39.489 --> 39:42.369 know--for some reason we know that S is the price today 39:42.374 --> 39:44.844 and next period, when the option exercise date 39:44.838 --> 39:48.028 is, its price is either going to be Su or it's going to 39:48.031 --> 39:51.281 be--S times u--or it's going to be S times 39:51.277 --> 39:53.657 d. Then, there's an interest rate 39:53.656 --> 39:57.166 and we can both borrow and lend at this riskless interest rate. 39:57.170 --> 40:00.100 What should the option be worth? 40:00.099 --> 40:04.449 In this case, I'm going to call C the 40:04.450 --> 40:07.890 current price of the call today. 40:07.889 --> 40:10.919 Now, this is before the exercise date, 40:10.920 --> 40:15.670 so the price of the call is going to be worth more than the 40:15.671 --> 40:18.761 intrinsic value. I'm going to call 40:18.756 --> 40:23.856 C_u the value of the call next period if the 40:23.863 --> 40:27.693 price is up and C_d the value 40:27.694 --> 40:31.954 of the call next period if the price is down. 40:31.949 --> 40:36.259 That's the thing that we read off of those broken straight 40:36.264 --> 40:38.974 lines. So, C_u would 40:38.972 --> 40:43.042 be the stock price minus--it's the stock minus the exercise 40:43.037 --> 40:45.137 price if it's in the money. 40:45.139 --> 40:50.129 We know that in advance because we already know what the two 40:50.132 --> 40:54.362 possible prices are next period; so, we already know what the 40:54.359 --> 40:56.479 two possible option values are next period. 40:56.480 --> 41:01.120 This is the intrinsic value if it's up and this is the 41:01.123 --> 41:03.843 intrinsic value if it's down. 41:03.840 --> 41:07.410 We'll call E the strike price of the exercise price of 41:07.407 --> 41:10.307 the option. Is everything clear here? 41:10.309 --> 41:13.219 It's just such a very simple world. 41:13.219 --> 41:17.809 I'm just saying there are only two possibilities; 41:17.809 --> 41:22.519 it's a very simple world and there's only period between now 41:22.517 --> 41:25.387 and exercise, so it's very simple. 41:25.389 --> 41:29.279 Now, what I'm going to say--we're going to develop an 41:29.278 --> 41:33.988 arbitrage theory of options and we're going to say that you want 41:33.988 --> 41:38.398 to--you'll take any profit opportunity that's riskless. 41:38.400 --> 41:41.890 It ought to be possible to get a riskless profit opportunity 41:41.892 --> 41:45.272 here by investing both in the stock and the option because 41:45.266 --> 41:48.696 there are only two possible values for the stock and you've 41:48.699 --> 41:50.889 got both a stock and an option. 41:50.889 --> 41:55.309 There must be a riskless portfolio because the price of 41:55.307 --> 41:59.807 the option depends only on the price of the stock on the 41:59.807 --> 42:03.977 exercise date. What I'm going to do is get an 42:03.980 --> 42:07.850 optimal hedge ratio, H, that makes my 42:07.849 --> 42:10.919 portfolio. I'm going to form a portfolio 42:10.921 --> 42:14.921 of the stock and the option and I'm going to put them together 42:14.922 --> 42:17.482 so that I have a riskless portfolio; 42:17.480 --> 42:20.600 that's what I'm going to do. 42:20.599 --> 42:24.329 Out of that is going to fall a value for the price of the 42:24.330 --> 42:26.220 option. This is what you want to do. 42:26.219 --> 42:31.029 We're looking for a riskless profit opportunity. 42:31.030 --> 42:35.350 Let's consider this, we're going to write one call 42:35.353 --> 42:40.913 and buy H shares and I'm going to pick H so that I 42:40.912 --> 42:43.032 have no risk at all. 42:43.030 --> 42:47.000 It's easy to see how you do that because we already 42:46.995 --> 42:51.435 know--before the exercise date--we know that if the price 42:51.436 --> 42:55.716 goes up it will be worth uHS--my portfolio--if I 42:55.718 --> 42:59.398 have H shares, the H shares will be 42:59.396 --> 43:00.416 worth uHS. 43:00.420 --> 43:07.470 uS is the price; H shares will be worth 43:07.472 --> 43:13.402 uHS. I've written one call so this 43:13.402 --> 43:21.012 would be worth uHS minus the price of a call. 43:21.010 --> 43:24.010 Similarly, if the price stock--if the stock price goes 43:24.011 --> 43:26.901 down, then this is the value--intrinsic value of the 43:26.900 --> 43:29.830 call, then next period on the 43:29.831 --> 43:35.831 exercise date the portfolio will be worth dHS minus 43:35.833 --> 43:38.363 C_D. 43:38.360 --> 43:43.380 Let's choose H so that the two are the same. 43:43.380 --> 43:47.560 All I have to do is set this equal to this and solve for 43:47.561 --> 43:51.591 H and that gives me the optimal hedge ratio. 43:51.590 --> 43:55.530 So, H is equal to C_u – 43:55.527 --> 43:58.777 C_d, all over (u – 43:58.784 --> 44:00.454 d) x S. 44:00.449 --> 44:06.019 Now it's very simple to get to option pricing. 44:06.019 --> 44:11.239 If I can form this portfolio where I have [short] 44:11.242 --> 44:17.012 one call and [long] H shares in a portfolio, 44:17.010 --> 44:20.030 it's a riskless portfolio, so it has to earn the riskless 44:20.026 --> 44:21.046 rate of interest. 44:21.050 --> 44:25.010 That's what no arbitrage assures. 44:25.010 --> 44:29.370 It can't be possible to get a riskless portfolio that earns 44:29.370 --> 44:33.660 either more or less than the riskless rate because if that 44:33.655 --> 44:37.935 did happen I would have a riskless opportunity--ability to 44:37.940 --> 44:41.850 earn more than the riskless rate with no risk. 44:41.850 --> 44:45.900 That's contrary to arbitrage. 44:45.900 --> 44:50.530 The return on--since you invested HS - C in the 44:50.532 --> 44:56.042 portfolio, the return on it--the total value of it--has to equal 44:56.038 --> 45:00.228 (one plus the riskless rate) times (HS – 45:00.233 --> 45:04.923 C). If you substitute in for HS 45:04.920 --> 45:09.770 – C, you find out that it equals 45:09.773 --> 45:12.573 this. Substitute for H into 45:12.566 --> 45:15.596 this and you get the price of the call today. 45:15.599 --> 45:19.969 It's simple algebra, but there it is. 45:19.969 --> 45:24.799 So, that's the arbitrage theory call option price. 45:24.800 --> 45:27.810 45:27.809 --> 45:30.559 That might be less than intuitive to you. 45:30.559 --> 45:33.779 See, that was very simple arguing that got us there. 45:33.780 --> 45:37.250 We merely said, the way to think about options 45:37.251 --> 45:41.261 is that options move with the stock price and they're 45:41.262 --> 45:45.812 perfectly correlated with the stock price over this interval 45:45.814 --> 45:49.904 because if the stock price goes up you know you've got 45:49.902 --> 45:52.142 C_u. 45:52.139 --> 45:53.779 If the stock price goes down, you know you've got 45:53.776 --> 45:54.556 C_d. 45:54.559 --> 45:57.889 So, you have only one source of uncertainty but you have two 45:57.891 --> 46:01.111 assets, so you can put them together to eliminate risk. 46:01.110 --> 46:03.990 If you put them together that way they have to earn the 46:03.988 --> 46:07.238 riskless rate and you just solve for it and you get this value 46:07.240 --> 46:08.520 for the call option. 46:08.519 --> 46:14.449 This is the inherent insight that Black and Scholes came up 46:14.450 --> 46:19.870 with in their classic 1973 paper on option pricing, 46:19.869 --> 46:23.439 which I've come to, but this has to be the price of 46:23.443 --> 46:26.233 the call option in this simple world; 46:26.230 --> 46:29.250 otherwise, there would be arbitrage. 46:29.250 --> 46:32.380 The interesting thing about this is that there are no 46:32.376 --> 46:34.296 probabilities in this formula. 46:34.300 --> 46:36.780 What's in this formula? 46:36.780 --> 46:40.460 I've got the riskless rate; I've got intrinsic value; 46:40.460 --> 46:43.700 I've got the difference between the price and the two 46:43.702 --> 46:45.952 circumstances, but nothing to do with 46:45.947 --> 46:49.307 probabilities. This puzzled people. 46:49.309 --> 46:51.619 People thought, well doesn't the price of an 46:51.618 --> 46:54.838 option have to depend on the probability that it will come in 46:54.838 --> 46:56.888 the money? If it's an out of the money 46:56.886 --> 46:58.756 option, don't I weigh the probability? 46:58.760 --> 47:01.230 It's not in this formula. 47:01.230 --> 47:04.200 You might say, it's implicitly in the formula 47:04.197 --> 47:07.697 because the relationship of S to Su and 47:07.704 --> 47:10.204 Sd involves probabilities, 47:10.200 --> 47:12.150 but it's not in this formula. 47:12.150 --> 47:16.700 Black and Scholes, in their famous paper, 47:16.704 --> 47:23.084 used this kind of reasoning to get to the standard option 47:23.080 --> 47:27.180 contract, which--option formula. 47:27.179 --> 47:30.479 I'm not going to derive it because the mathematics is quite 47:30.480 --> 47:33.810 a bit more difficult, but it's exactly the same logic 47:33.811 --> 47:37.461 that I just went through with the binomial option pricing 47:37.462 --> 47:44.272 formula. This is one of the most famous 47:44.273 --> 47:49.963 formulas in all of finance. 47:49.960 --> 47:54.950 What Black-Scholes did is, under certain assumptions about 47:54.945 --> 47:59.665 the stochastic properties of stock prices and under the 47:59.668 --> 48:03.428 assumption of no arbitrage opportunity, 48:03.429 --> 48:10.519 they came up with a formula that an option price should 48:10.524 --> 48:14.864 follow if there's no arbitrage. 48:14.860 --> 48:20.380 I'm just going to present their formula and then we'll think 48:20.376 --> 48:22.336 more about options. 48:22.340 --> 48:26.940 The Black-Scholes formula--call T the time to exercise. 48:26.940 --> 48:30.640 Before, I just said it was--when we talked binomial, 48:30.642 --> 48:33.912 I just had--I said it was one period hence, 48:33.909 --> 48:37.219 but now we're allowing the exercise date to be any distance 48:37.217 --> 48:41.427 in the future. So, T is the time to the 48:41.432 --> 48:44.672 exercise date. This is for our European 48:44.669 --> 48:48.969 option, although it's often used to apply to American options as 48:48.973 --> 48:51.943 well. We'll call σ^(2) the 48:51.936 --> 48:55.896 variance of the one-period price change. 48:55.900 --> 49:02.880 N(x) is the cumulative normal distribution function, 49:02.879 --> 49:09.739 which you can find on Excel; it's called normdist, 49:09.741 --> 49:16.401 so I don't want to get into these details. 49:16.400 --> 49:22.110 This is the formula that Black-Scholes won the Nobel 49:22.107 --> 49:24.827 Prize for. Well actually, 49:24.834 --> 49:30.474 Black died at a relatively early age from throat cancer; 49:30.469 --> 49:36.319 he was a heavy smoker and people don't do that anymore, 49:36.324 --> 49:40.014 so that's one risk that is over. 49:40.010 --> 49:44.200 Scholes won the Nobel Prize for this--they don't award that 49:44.200 --> 49:47.090 posthumously--for this little formula. 49:47.090 --> 49:52.070 It says, the price of a call is equal to the stock price times 49:52.073 --> 49:56.403 N(d_1) minus the exercise price times 49:56.402 --> 50:00.112 N(d_2), where d_1 is 50:00.113 --> 50:03.063 given by this expression and d_2 is given by 50:03.057 --> 50:03.987 this expression. 50:03.990 --> 50:07.810 50:07.809 --> 50:09.589 That might not be intuitive to you. 50:09.590 --> 50:12.540 We could spend a couple of lectures making that more 50:12.537 --> 50:16.117 intuitive, but I'm just going to stop with that formula now. 50:16.119 --> 50:21.119 That's the formula that I used back here to make this pink 50:21.116 --> 50:23.856 line. I just--I had to plug in a 50:23.862 --> 50:28.292 value for σ^(2) and T, but I did that and I 50:28.291 --> 50:31.081 used the Black-Scholes formula. 50:31.079 --> 50:34.379 The Black-Scholes formula does what we sort of think it should. 50:34.380 --> 50:42.350 The price of an option should be greater than the intrinsic 50:42.345 --> 50:49.345 value everywhere, but here is the exact equation. 50:49.350 --> 50:54.610 50:54.610 --> 50:56.880 This is one of the most famous equations in finance. 50:56.880 --> 50:59.780 It might even be on your--if you have a financial calculator 50:59.783 --> 51:01.853 you might have a key that you can press. 51:01.849 --> 51:04.889 It's already on your laptop and you don't even know it 51:04.892 --> 51:08.512 probably--maybe--depending on what kind of programs you have. 51:08.510 --> 51:12.960 It's easy to compute in Excel; you just have to use this 51:12.961 --> 51:15.361 normdist. This cumulative normal 51:15.356 --> 51:19.876 distribution function is not something you can do by hand; 51:19.880 --> 51:26.270 you have to use a--it would involve an integral that doesn't 51:26.268 --> 51:32.438 have an analytic solution, but you can get it on Excel. 51:32.440 --> 51:37.840 51:37.840 --> 51:42.140 Now, the critical problem with the Black-Scholes formula, 51:42.143 --> 51:46.683 however, is getting some of these parameters that have to go 51:46.678 --> 51:50.058 into it and the tough one is σ^(2); 51:50.059 --> 51:52.369 most of the other things we know. 51:52.369 --> 51:55.969 If you're trying to actually price an option using 51:55.967 --> 51:58.827 Black-Scholes, S, we already know 51:58.830 --> 52:01.180 that's just the stock price. 52:01.180 --> 52:04.620 E is the exercise price; we know that--that's written in 52:04.621 --> 52:05.681 the option contract. 52:05.679 --> 52:09.229 T is the time to expiration date; 52:09.230 --> 52:10.870 we know that--that's written in the contract. 52:10.869 --> 52:13.029 r is the riskless interest rate; 52:13.030 --> 52:15.820 well, that's easy to tell--that's just quoted in the 52:15.818 --> 52:18.108 market. There's only one thing that 52:18.112 --> 52:21.052 remains that's tough and that's σ^(2). 52:21.050 --> 52:24.600 That's the variance of the stock price. 52:24.599 --> 52:30.429 Black-Scholes says you have to know how variable the stock 52:30.430 --> 52:36.670 price is to price an option and intuitively you can see it. 52:36.670 --> 52:41.910 Isn't it obvious that the more variable the stock price the 52:41.909 --> 52:44.619 more valuable the option is? 52:44.619 --> 52:48.859 If the variance were zero, then the option would just be 52:48.862 --> 52:53.342 the intrinsic value because there's no chance for the stock 52:53.336 --> 52:55.646 to do anything unexpected. 52:55.650 --> 52:59.340 If it's out of the money and the variance is zero, 52:59.341 --> 53:01.301 the option is worthless. 53:01.300 --> 53:03.650 If it's in the money and the variance is zero, 53:03.648 --> 53:06.208 then it's worth something, but it's only worth the 53:06.206 --> 53:08.586 intrinsic value. If σ^(2) is 0, 53:08.585 --> 53:12.375 the price can't move anywhere, so there's no problem. 53:12.380 --> 53:17.480 As σ^(2) increases, the option gets more and more 53:17.481 --> 53:20.111 valuable; if it's out of the money it's 53:20.107 --> 53:23.187 getting more and more chance to come into the money and so 53:23.188 --> 53:24.538 that's in the formula. 53:24.539 --> 53:29.729 The key variable in the Black-Scholes formula is the 53:29.729 --> 53:35.019 variance of option--of the underlying stock price; 53:35.020 --> 53:40.120 that's the kicker; that's the hard part. 53:40.119 --> 53:43.879 People who trade options use the Black-Scholes formula, 53:43.877 --> 53:48.117 but there's a problem and the problem is you've got to plug in 53:48.121 --> 53:50.071 a number for σ^(2). 53:50.070 --> 53:53.060 So, what number should I plug in? 53:53.059 --> 53:56.049 Well, you might say, let's take historical numbers. 53:56.050 --> 53:59.600 I know pretty much what the variance of stock price changes 53:59.603 --> 54:01.583 is; let's use the historical 54:01.582 --> 54:04.682 variance. I wanted to show you the 54:04.679 --> 54:08.379 historical variance of stock prices. 54:08.380 --> 54:12.240 I have--since I like history, I go all the way back to 1871. 54:12.239 --> 54:17.549 What I did to compute this chart is I took the S&P 54:17.550 --> 54:22.160 composite or S&P 500 Index back to 1871. 54:22.159 --> 54:25.759 This is my spreadsheet, which is on the web under our 54:25.757 --> 54:27.277 classroom materials. 54:27.280 --> 54:32.210 I took a six-month moving average of six-month 54:32.211 --> 54:38.131 changes--six-month standard deviation of the percentage 54:38.128 --> 54:42.948 price change for every month from 1871, July, 54:42.949 --> 54:45.469 to April of 2008. 54:45.469 --> 54:49.359 The important thing to understand here is that the 54:49.356 --> 54:52.526 variance is not constant through time; 54:52.530 --> 54:56.250 it moves around. There are high variance periods 54:56.250 --> 54:59.290 for stock prices and low variance periods. 54:59.289 --> 55:02.339 I like to look at this picture because it's interesting. 55:02.340 --> 55:04.950 The first thing that is interesting is that, 55:04.951 --> 55:08.601 overall, the market has been remarkably consistent for over a 55:08.596 --> 55:11.626 hundred years. The variance back in the 55:11.626 --> 55:15.416 nineteenth century doesn't look any different; 55:15.420 --> 55:18.650 nothing has changed in a hundred and thirty years; 55:18.650 --> 55:20.850 the market has always been volatile. 55:20.849 --> 55:24.009 There's only one thing that jumps out at you when you look 55:24.011 --> 55:26.841 at this picture and that's these numbers in here. 55:26.840 --> 55:29.160 You notice those numbers in the middle? 55:29.159 --> 55:34.119 That was the Great Depression of the 1930s and something went 55:34.119 --> 55:39.079 really haywire in the financial markets in the Depression. 55:39.080 --> 55:41.860 This is 1929; it wasn't so much 1929, 55:41.855 --> 55:44.925 but remember this is a six-month--it's a lagging six 55:44.927 --> 55:48.027 months. So, where does it--maybe the 55:48.025 --> 55:50.695 1929 crash is here somewhere. 55:50.699 --> 55:54.979 I'm not sure exactly where it is, but something went really 55:54.977 --> 55:58.887 haywire after 1929 and the markets got extraordinarily 55:58.886 --> 56:00.726 volatile for a while. 56:00.730 --> 56:04.060 56:04.059 --> 56:08.139 That was a crisis period in American history that shows up 56:08.138 --> 56:12.358 really well on this picture, but since then nothing much has 56:12.359 --> 56:14.289 happened. It's interesting to look 56:14.292 --> 56:15.902 recently. This doesn't look very 56:15.903 --> 56:18.583 important; it shows how important our 56:18.582 --> 56:23.552 lifetimes in the broad sweep of history, but your lifetimes are 56:23.547 --> 56:26.267 from in this region right here. 56:26.269 --> 56:30.849 The thing that's interesting is that we have been recently in a 56:30.853 --> 56:34.553 very low volatility period for the stock market. 56:34.550 --> 56:36.890 This is around 2003. 56:36.889 --> 56:40.659 We were in a high volatility period in the 1990s--nothing 56:40.655 --> 56:44.715 like in the Great Depression, but high in the '90s and then 56:44.719 --> 56:48.879 volatility just collapsed and the markets were the deadest and 56:48.883 --> 56:52.573 dullest place to be in the world--the stock market. 56:52.570 --> 56:58.010 Partly, I think this is because our--we were--who knows why this 56:58.011 --> 57:00.131 was. I'm going to throw out a wild 57:00.128 --> 57:02.798 suggestion. It's because we were distracted 57:02.797 --> 57:06.417 by the housing bubble and all talk after the stock market 57:06.424 --> 57:08.964 peaked in 2000. Lots of people just lost 57:08.964 --> 57:12.464 interest in the market and all of their speculative enthusiasm 57:12.458 --> 57:15.548 was focused on housing and the stock market was kind of 57:15.550 --> 57:17.730 forgotten. There has to be at least an 57:17.733 --> 57:20.333 element of truth to that story, but something has been 57:20.329 --> 57:21.309 happening lately. 57:21.309 --> 57:23.609 Look how much volatility is shooting up now; 57:23.610 --> 57:28.140 this is because of the world financial crisis that we're in. 57:28.139 --> 57:32.699 If you look at this picture it doesn't look like the world 57:32.699 --> 57:37.179 financial crisis is very important compared to historical 57:37.179 --> 57:40.859 events so far that we've seen in the past. 57:40.860 --> 57:45.380 Now, I want to define what we call implied volatility. 57:45.380 --> 57:50.360 What the--you can do with the Black-Scholes formula is it 57:50.357 --> 57:55.247 requires that you input σ^(2) to calculate what the 57:55.246 --> 57:58.176 price of an option should be. 57:58.179 --> 58:02.119 Why don't we take what the price of the option is and work 58:02.123 --> 58:06.003 backwards to figure out what volatility is implied by the 58:05.998 --> 58:08.928 price. Do you see what I'm saying? 58:08.929 --> 58:12.199 You can solve--you can turn the Black-Scholes--the Black-Scholes 58:12.195 --> 58:15.455 formula gives the price of the option in terms of σ^(2). 58:15.460 --> 58:18.070 Well, I can turn it around because I know what the market 58:18.066 --> 58:21.446 price of the option is; they're traded on the CBOE. 58:21.449 --> 58:24.919 So, I would take the market price of an option and turn it 58:24.915 --> 58:27.895 around and get what the implied volatility is from 58:27.895 --> 58:31.735 Black-Scholes. The CBOE does this for you 58:31.736 --> 58:37.756 because they trade S&P 500 options and they have it on 58:37.758 --> 58:43.778 their website and its called VIX, so I have VIX there. 58:43.780 --> 58:46.260 That's their volatility index. 58:46.260 --> 58:50.220 The CBOE was created in 1973. 58:50.219 --> 58:53.889 Unfortunately, the series doesn't--it goes 58:53.893 --> 58:58.193 only back to 1986, but it's been going for a long 58:58.193 --> 59:00.643 time. You can't get implied 59:00.635 --> 59:04.605 volatility back to 1871 because--although there were 59:04.606 --> 59:09.196 options traded back then, there was no organized market. 59:09.199 --> 59:12.669 You can't get a consistent series of prices of options 59:12.673 --> 59:15.563 going that far back, so you can't get implied 59:15.556 --> 59:18.396 volatility. Maybe you could do it if you 59:18.402 --> 59:21.992 got some records from some broker and find some option, 59:21.993 --> 59:23.593 but it would be hard. 59:23.590 --> 59:29.100 Our implied volatility only goes back a little over twenty 59:29.099 --> 59:35.189 years, but the interesting thing is I have plotted here both the 59:35.190 --> 59:39.930 implied volatility over that period and the actual 59:39.926 --> 59:43.266 volatility. You see that they line up 59:43.265 --> 59:47.325 fairly well, but this shows the strength of the Black-Scholes 59:47.334 --> 59:50.424 formula. Black-Scholes does seem to be 59:50.419 --> 59:55.259 pricing options well enough because the implied volatility, 59:55.260 --> 1:00:00.620 while it's not perfectly exactly equal to the actual 1:00:00.622 --> 1:00:07.142 volatility, it's close and so we can see that the formula makes 1:00:07.142 --> 1:00:12.832 some sense. I just wanted to conclude this 1:00:12.831 --> 1:00:19.961 lecture by talking about the effort we've made to get 1:00:19.957 --> 1:00:28.587 single-family home price options going at the Chicago Mercantile 1:00:28.591 --> 1:00:31.531 Exchange. As I told you, 1:00:31.525 --> 1:00:35.365 I and some of my colleagues have been campaigning with 1:00:35.369 --> 1:00:39.579 futures exchanges to create futures markets for home prices 1:00:39.577 --> 1:00:41.967 and, ultimately, for commercial real 1:00:41.974 --> 1:00:44.454 estate prices and other economic variables. 1:00:44.449 --> 1:00:49.519 We went to--we started campaigning almost twenty years 1:00:49.515 --> 1:00:54.675 ago, but recently we have been talking with the Chicago 1:00:54.676 --> 1:00:59.926 Mercantile Exchange and they created futures markets for 1:00:59.933 --> 1:01:04.813 single-family homes in May of 2006 using the S&P 1:01:04.808 --> 1:01:07.578 Case-Shiller Indexes. 1:01:07.579 --> 1:01:12.389 That was our objective, but when we went there the CME 1:01:12.389 --> 1:01:17.469 said, well why don't we start options as well--options on 1:01:17.471 --> 1:01:20.531 futures. So, we have a futures contract 1:01:20.530 --> 1:01:23.290 and they launched options on home prices. 1:01:23.289 --> 1:01:26.769 You can see all these things on the Chicago Mercantile Exchange 1:01:26.768 --> 1:01:27.328 website. 1:01:27.330 --> 1:01:32.100 1:01:32.099 --> 1:01:37.679 What we have now are both puts and calls for ten U.S. 1:01:37.675 --> 1:01:39.375 cities. Unfortunately, 1:01:39.380 --> 1:01:43.150 they're not doing well; they're not selling well, 1:01:43.150 --> 1:01:48.650 but they're still going and we're hoping that we can get 1:01:48.650 --> 1:01:52.400 them to connect. Often markets are slow at 1:01:52.396 --> 1:01:56.826 first, so I hope that that's the story--that it's just a slow 1:01:56.829 --> 1:01:59.219 beginning. Let me say what we have; 1:01:59.219 --> 1:02:03.869 maybe it's a good down to earth way to illustrate the value of 1:02:03.868 --> 1:02:06.458 options. I was telling you how to price 1:02:06.463 --> 1:02:09.523 options, but I didn't tell why would you buy one. 1:02:09.519 --> 1:02:12.099 Well, I did tell a story at the beginning. 1:02:12.099 --> 1:02:16.239 I talked about an investor wanting to invest money in 1:02:16.242 --> 1:02:20.542 options and a writer hoping that the option will expire 1:02:20.543 --> 1:02:23.813 unexercised and hoping to make money. 1:02:23.809 --> 1:02:29.199 I didn't really go behind that and emphasize why you would do 1:02:29.201 --> 1:02:32.811 that. I think the example of a home 1:02:32.812 --> 1:02:36.312 price option is very easy to see. 1:02:36.309 --> 1:02:40.339 Let's consider a situation that someone--I don't think any of 1:02:40.335 --> 1:02:43.015 you are homeowners here at this point; 1:02:43.019 --> 1:02:45.929 maybe some of you are--probably not. 1:02:45.929 --> 1:02:50.429 But imagine--try to imagine that you bought a house a couple 1:02:50.428 --> 1:02:54.468 years ago and now the housing market is collapsing. 1:02:54.469 --> 1:02:57.809 You bought that house probably on a mortgage, 1:02:57.811 --> 1:03:02.291 so you borrowed 80 to 90% or maybe even more of the money to 1:03:02.292 --> 1:03:05.932 buy the house. Now, the home is falling and 1:03:05.934 --> 1:03:08.864 you're thinking, hey wait a minute. 1:03:08.860 --> 1:03:12.990 This house is worth less than my debt and you start to get 1:03:12.990 --> 1:03:14.570 upset. You're thinking, 1:03:14.574 --> 1:03:17.464 well you know I'd like to move to another city, 1:03:17.461 --> 1:03:19.911 but then you realize, I can't do it. 1:03:19.909 --> 1:03:23.859 If I sell my house, I won't be able to pay off the 1:03:23.862 --> 1:03:27.612 mortgage; I'll be bankrupt before I--I 1:03:27.606 --> 1:03:30.236 can't move. This is very real. 1:03:30.239 --> 1:03:33.169 In fact, economy.com, a consulting firm, 1:03:33.172 --> 1:03:37.462 estimates that in the United States today 10% of all homes 1:03:37.458 --> 1:03:39.938 are underwater in that sense. 1:03:39.940 --> 1:03:43.590 The mortgage debt is greater than the value of the home and 1:03:43.593 --> 1:03:47.183 that number is increasing everyday as home prices continue 1:03:47.184 --> 1:03:50.394 to fall. Some people are very upset. 1:03:50.390 --> 1:03:52.820 So, what can they do? 1:03:52.820 --> 1:03:57.100 Well, one thing they can do or they could have done a couple of 1:03:57.099 --> 1:03:59.929 years ago if they had thought to do it, 1:03:59.929 --> 1:04:04.869 they could buy a put on the home--on homes in the city where 1:04:04.874 --> 1:04:06.554 they have a house. 1:04:06.550 --> 1:04:11.220 I put in, say, around--let's say I put in 1:04:11.221 --> 1:04:17.881 $500,000 into a house and I'm worried that its price might 1:04:17.878 --> 1:04:21.438 fall. Well, if you buy a house and 1:04:21.441 --> 1:04:26.201 you buy a put on that house together, the two together 1:04:26.196 --> 1:04:28.256 eliminate your risk. 1:04:28.260 --> 1:04:31.750 Let's think of it as just buying a put on a house rather 1:04:31.753 --> 1:04:32.963 than on an index. 1:04:32.960 --> 1:04:39.710 I buy the house for $500,000; I put up $400,000 and so--I put 1:04:39.710 --> 1:04:43.090 up $100,000; the mortgage puts up $400,000. 1:04:43.090 --> 1:04:46.930 I'm underwater if the house drops $100,000. 1:04:46.929 --> 1:04:51.239 I've lost--my mortgage debt exceeds my--I don't want that to 1:04:51.239 --> 1:04:55.109 happen, so why don't I just buy a put on the house, 1:04:55.110 --> 1:05:01.700 which is a right to sell the house at $400,000 until some 1:05:01.697 --> 1:05:06.387 exercise date; then, I can't possibly be 1:05:06.390 --> 1:05:09.730 underwater. If I ever decide to move or if 1:05:09.728 --> 1:05:13.308 it's an American option, I can just--if the price of my 1:05:13.306 --> 1:05:17.146 house is less than $400,000, I'll just exercise my put. 1:05:17.150 --> 1:05:19.680 There's no way for me to get wiped out. 1:05:19.679 --> 1:05:24.099 In fact, I could buy a put at $450,000 and that way I would 1:05:24.103 --> 1:05:27.463 always be sure that I'd have $50,000 left. 1:05:27.460 --> 1:05:32.800 So, that's the idea of using options as a hedging mechanism. 1:05:32.800 --> 1:05:36.610 1:05:36.610 --> 1:05:39.560 While I gave an example in terms of real estate and it's 1:05:39.561 --> 1:05:43.891 not widely used that way, this same idea is used a lot by 1:05:43.893 --> 1:05:49.193 investors in other domains, so I think options have a very 1:05:49.193 --> 1:05:52.173 real risk management purpose. 1:05:52.170 --> 1:05:57.360 In a sense, an insurance contract is like a put option. 1:05:57.360 --> 1:06:02.120 If I buy fire insurance on my house, then it's like buying a 1:06:02.121 --> 1:06:06.241 put option on my house, but it's only exercisable if 1:06:06.236 --> 1:06:08.996 there's a fire. What it says is, 1:06:08.998 --> 1:06:12.758 if my house burns down, the put option--I can sell 1:06:12.760 --> 1:06:16.910 whatever remains at a price, which is determined by the 1:06:16.907 --> 1:06:20.567 insurance contract; it's the same as a put option. 1:06:20.570 --> 1:06:26.320 Insurance is not fundamentally different from finance. 1:06:26.320 --> 1:06:29.780 We've had a little trouble deciding whether we want home 1:06:29.778 --> 1:06:33.298 equity insurance or just puts--home equity puts--so we've 1:06:33.299 --> 1:06:34.619 created the puts. 1:06:34.619 --> 1:06:37.829 At some point, we want to also create 1:06:37.832 --> 1:06:40.512 insurance on homes, someday; 1:06:40.510 --> 1:06:41.790 I hope that happens. 1:06:41.789 --> 1:06:43.859 There is no home equity insurance. 1:06:43.860 --> 1:06:46.900 1:06:46.900 --> 1:06:49.420 These are just different incarnations of the same risk 1:06:49.417 --> 1:06:50.317 management ideas. 1:06:50.320 --> 1:06:54.580 The fundamental idea here in finance is that you can 1:06:54.584 --> 1:06:58.434 create--options are examples of derivatives; 1:06:58.429 --> 1:07:05.519 I should add that a derivative is a financial contract that 1:07:05.523 --> 1:07:09.563 derives from another financial. 1:07:09.559 --> 1:07:13.899 So, an option is a derivative because the price of the option 1:07:13.903 --> 1:07:18.393 in the options market depends on the price of something else in 1:07:18.391 --> 1:07:21.071 another market--the stock market. 1:07:21.070 --> 1:07:24.710 So, our real estate options are another example of derivative. 1:07:24.710 --> 1:07:28.460 The price of the put option depends on--in the option 1:07:28.460 --> 1:07:33.220 market--depends on the price of the house in the housing market. 1:07:33.219 --> 1:07:36.229 One of the themes in my forthcoming book, 1:07:36.230 --> 1:07:40.450 which I'm writing right now, is that derivatives are like 1:07:40.446 --> 1:07:43.066 insurance. They're fundamentally important 1:07:43.066 --> 1:07:46.146 to risk management vehicles and they could have helped prevent 1:07:46.148 --> 1:07:49.178 the subprime crisis that we're now in if they had just gotten 1:07:49.180 --> 1:07:51.000 established and more developed.