WEBVTT 00:00.750 --> 00:02.020 All right. 00:02.020 --> 00:03.450 Good morning. 00:03.450 --> 00:05.700 The subject of today's lecture is options. 00:08.610 --> 00:13.990 And I think, maybe I'd better first define what an option 00:13.990 --> 00:20.140 is, before I move to say anything about them. 00:20.140 --> 00:22.580 Because some of you may not have encountered them, because 00:22.579 --> 00:26.839 they're not part of everyday life for most people, although 00:26.840 --> 00:28.010 they are, in a sense. 00:28.010 --> 00:29.100 I'll get back to that. 00:29.100 --> 00:31.540 Let me just define the term here. 00:37.770 --> 00:47.920 [SIDE CONVERSATION] 00:47.920 --> 00:52.090 PROFESSOR ROBERT SHILLER: So there's two kinds of options. 00:52.090 --> 00:58.040 There's a call and a put, OK? 00:58.040 --> 01:05.440 A call option is an option to buy something at a specified 01:05.440 --> 01:15.430 price, and the price is called the ''exercise price'' or 01:15.430 --> 01:20.660 ''strike price.'' Those are synonyms. 01:20.660 --> 01:26.160 And a put option is the right to sell something at the 01:26.160 --> 01:30.290 specified exercise price. 01:30.290 --> 01:40.170 And it has another term it has to be specified, and that's 01:40.170 --> 01:41.890 the exercise date. 01:51.150 --> 01:52.370 OK. 01:52.370 --> 01:57.030 Options go back thousands of years. 01:57.030 --> 02:02.230 It must have happened before we have any recorded records. 02:02.230 --> 02:07.510 If you're thinking of buying something from someone, but 02:07.510 --> 02:11.100 you don't want to put up the money today, you go to some 02:11.100 --> 02:15.010 lawyer, and say, write up a contract. 02:15.010 --> 02:18.060 I want to buy an option to buy this thing. 02:18.060 --> 02:21.530 So, for example, if you are thinking of building a 02:21.530 --> 02:28.670 building on land that is owned now by a farmer, but you're 02:28.670 --> 02:30.650 not ready to do it. 02:30.650 --> 02:34.030 You may be thinking about it. 02:34.030 --> 02:37.550 You can go to the farmer and say, I'd like to buy that 02:37.550 --> 02:41.100 corner of that acre there. 02:41.100 --> 02:42.250 I'd like to have the right to buy it. 02:42.250 --> 02:44.260 I'll pay you now for the right. 02:44.260 --> 02:46.690 And you get a lawyer and you write up a contract. 02:46.690 --> 02:49.190 And that's an option. 02:49.190 --> 02:55.530 You have an option to buy at the exercise price until the 02:55.530 --> 02:58.900 exercise date. 02:58.900 --> 03:06.930 Now, in modern terminology, we have two kinds, 03:06.930 --> 03:09.660 American and European. 03:14.970 --> 03:19.570 It doesn't refer to geography, those two terms. The terms 03:19.570 --> 03:25.810 refer, instead, to when you can exercise. 03:25.810 --> 03:28.540 So, the American option is better than the European 03:28.540 --> 03:32.420 option for the buyer, because the American option can be 03:32.420 --> 03:37.970 exercised at any time until the exercise date. 03:37.970 --> 03:42.520 Whereas the European option can be exercised only on the 03:42.520 --> 03:44.230 exercise date. 03:44.230 --> 03:48.770 But you see the American option has to be better, or 03:48.770 --> 03:50.070 not worse than -- 03:50.070 --> 03:51.570 I don't know if it's strictly better -- but not worse than 03:51.570 --> 03:53.840 the European option, because you have more options. 04:03.060 --> 04:05.160 I think, we've defined what they are. 04:05.160 --> 04:09.150 Do you understand well enough what they are? 04:09.149 --> 04:11.679 They occur naturally in life. 04:11.680 --> 04:17.380 I remember, Avinash Dixit was writing about options and he 04:17.380 --> 04:20.570 said, well, when you're dating someone and you know the 04:20.570 --> 04:24.030 person will marry you, you have an option that you can 04:24.030 --> 04:30.100 exercise at any time by agreeing to marry. 04:30.100 --> 04:33.750 Now, one of the theorems in option theory is, you usually 04:33.750 --> 04:38.010 don't want to exercise a call option early. 04:38.010 --> 04:44.950 And so, Dixit would say, well, maybe that's why a lot of 04:44.950 --> 04:47.220 people have trouble getting married. 04:47.220 --> 04:50.770 They don't want to exercise their option early. 04:50.770 --> 04:53.680 What we'll see is that options have option value. 04:53.680 --> 04:56.690 They give you a choice, and so there's something there. 04:56.690 --> 04:59.080 When you exercise an option, that is, when you actually buy 04:59.080 --> 05:03.140 the thing, or in the case of a put, sell the thing, then 05:03.140 --> 05:04.740 you're losing the choice. 05:04.740 --> 05:06.280 So, you've given up something. 05:08.980 --> 05:12.980 Of course, you have to also exercise eventually, if things 05:12.980 --> 05:14.770 are going to make sense. 05:18.020 --> 05:20.440 Usually, when we talk about options, we're talking now 05:20.440 --> 05:23.720 about options to buy a share of stock, or 100 shares of 05:23.720 --> 05:28.010 stock, and that's the usual example. 05:28.010 --> 05:31.800 But they occur all over the place. 05:31.800 --> 05:37.550 Let me mention some other examples of options. 05:37.550 --> 05:39.930 The usual story is the stock option. 05:39.930 --> 05:44.500 You go to your broker and you say, I'd like to buy an option 05:44.500 --> 05:47.790 to buy 100 shares of Microsoft. 05:47.790 --> 05:51.140 I don't want to buy Microsoft, I want to buy an option to buy 05:51.140 --> 05:55.800 Microsoft, which happens to be cheaper, by the way, usually. 05:55.800 --> 06:00.560 Usually, it costs more money to actually buy the thing than 06:00.560 --> 06:03.250 to buy the right to buy the thing at another price. 06:03.250 --> 06:05.810 We'll get back to that. 06:05.810 --> 06:10.800 But in a sense, let's think about this, stocks themselves 06:10.800 --> 06:17.210 are options in a sense, with a zero exercise price. 06:17.210 --> 06:19.730 Maybe, I'll have to get back and explain, but 06:19.730 --> 06:22.220 what I mean is -- 06:22.220 --> 06:29.130 let me get back and explain that in a minute. 06:29.130 --> 06:32.530 But let me go ahead to other examples, mortgages. 06:32.530 --> 06:36.890 An ordinary home mortgage has an option characteristic to 06:36.890 --> 06:42.690 it, in the sense that, if the price of your home drops a 06:42.690 --> 06:48.880 lot, you can just walk away from the mortgage, and say, 06:48.880 --> 06:49.470 I'm out of here. 06:49.470 --> 06:52.430 It's like not exercising an option. 06:52.430 --> 06:55.120 It's analogous. 06:55.120 --> 06:58.480 Or I can choose to prepay a mortgage early, and that's 06:58.480 --> 07:00.150 like exercising an option. 07:00.145 --> 07:04.425 So, option pricing gets into all sorts of things. 07:07.970 --> 07:09.220 OK. 07:13.640 --> 07:16.700 I thought I should say something about the purposes 07:16.700 --> 07:25.550 of options, before I move on to try to discuss what their 07:25.550 --> 07:28.640 properties and pricing are, which is the main subject of 07:28.640 --> 07:30.200 this lecture. 07:35.510 --> 07:42.200 I can give two different justifications for options. 07:42.200 --> 07:45.250 Why do we have options? 07:45.250 --> 07:47.180 Some people cynically think that options are 07:47.180 --> 07:49.350 just gambling vehicles. 07:49.352 --> 07:50.652 It's another way to gamble. 07:50.650 --> 07:53.650 You can go to the casino, you can play poker, 07:53.650 --> 07:55.940 or you can buy options. 07:55.940 --> 07:59.440 Well, I think for some people that's just what it is, the 07:59.440 --> 08:02.090 volatile risky investments that can make 08:02.090 --> 08:03.710 you a lot of money. 08:03.710 --> 08:10.890 But I think, they have a basic purpose, or purposes. 08:10.890 --> 08:15.060 First of all, theoretical. 08:15.064 --> 08:20.364 If we were trying to design the ideal financial system, 08:20.360 --> 08:21.610 what would we do? 08:30.030 --> 08:34.180 Some people thought of ideal economic systems without 08:34.179 --> 08:36.969 reference to finance, like Karl Marx -- 08:36.970 --> 08:39.750 I come back to him -- the great communist, who thought 08:39.750 --> 08:43.410 that we would have an ideal communist state and there'd be 08:43.410 --> 08:44.760 no financial markets. 08:47.470 --> 08:50.500 When they actually tried it and they tried to do it, I 08:50.500 --> 08:55.150 think they gradually realized that not having any financial 08:55.150 --> 08:59.960 markets makes our entrepreneurship, our 08:59.960 --> 09:03.380 management of enterprises, kind of blind. 09:03.380 --> 09:05.050 We can't see, where we're going 09:05.050 --> 09:06.500 because there's no prices. 09:06.500 --> 09:09.590 We don't know what anything is worth. 09:09.590 --> 09:13.730 There was an old joke that the communist countries survived 09:13.730 --> 09:16.830 only because they had prices from capitalist 09:16.830 --> 09:18.530 countries to rely on. 09:18.530 --> 09:22.590 Otherwise, they don't know anything about values or 09:22.590 --> 09:24.820 profits, right? 09:24.820 --> 09:26.070 So, we need prices. 09:29.520 --> 09:34.090 Many people have written about this, but I mentioned, in 09:34.090 --> 09:42.810 1964, Kenneth Arrow, who is an economic theorist, wrote a 09:42.810 --> 09:48.290 classic paper, in which he argued that, unless we have 09:48.290 --> 09:52.940 prices for all states of nature, there's a sense in 09:52.940 --> 09:56.270 which the economic system is inefficient. 09:56.270 --> 10:00.490 You really need the price of everything, including the 10:00.490 --> 10:03.440 price of some possibility. 10:03.440 --> 10:10.240 In a sense, that's what options are giving you, the 10:10.240 --> 10:14.710 existence of options is giving you. 10:14.710 --> 10:22.680 So, Steven Ross, who used to teach here at Yale, a friend 10:22.680 --> 10:31.090 of mine, lives here in New Haven, in 1976, in The 10:31.090 --> 10:34.490 Quarterly Journal of Economics, wrote a classic 10:34.490 --> 10:39.500 paper about options, showing that, in a sense, they 10:39.500 --> 10:41.930 complete the state space. 10:41.930 --> 10:48.850 They create prices for everything that affects 10:48.850 --> 10:50.460 decision-making. 10:50.460 --> 10:52.720 I'm not going to get into the technicalities of the paper, 10:52.720 --> 10:55.670 but I wanted to start with a theoretical justification for 10:55.670 --> 10:58.090 options, so you'll see why we're doing this. 10:58.090 --> 11:01.240 I don't want this to come across as a lecture, on how 11:01.240 --> 11:03.690 you can gamble in the options market. 11:03.690 --> 11:07.660 This is about making things work right for the economic 11:07.660 --> 11:10.840 system, improving human welfare. 11:10.840 --> 11:14.510 But a lot of people don't get that. 11:14.510 --> 11:16.920 That's why Karl Marx was so successful. 11:16.920 --> 11:18.400 It seems too abstract. 11:18.400 --> 11:20.530 What does this options market do for us? 11:23.530 --> 11:26.160 Let me just go back to the example I started out with. 11:26.160 --> 11:28.410 You're a construction firm, and you're thinking of 11:28.410 --> 11:31.280 building something, a new supermarket, where people can 11:31.280 --> 11:32.550 buy their food. 11:32.550 --> 11:37.880 And you note that there's a pair of expressways crossing 11:37.880 --> 11:40.320 somewhere, and you think, that's the perfect place to 11:40.320 --> 11:42.970 build a mega supermarket, because everyone can 11:42.970 --> 11:45.100 get there by car. 11:45.100 --> 11:47.320 And there's a lot of land, I can build a big 11:47.320 --> 11:50.060 parking lot, perfect. 11:50.060 --> 11:53.390 But before you think further, you go to buy an option on the 11:53.390 --> 11:54.700 land, right? 11:54.700 --> 11:57.080 So, you knock on the door at the farmhouse, and there's a 11:57.080 --> 12:00.700 farmer with all these acres, and you say, I'm thinking of 12:00.700 --> 12:03.340 building a mega supermarket here. 12:03.340 --> 12:06.520 I'd like to buy an option on your farm. 12:06.520 --> 12:08.650 You learn something at that moment. 12:08.650 --> 12:11.950 You might learn that the farmer says, I've already sold 12:11.950 --> 12:15.220 an option, so I can't do it. 12:15.220 --> 12:17.670 You could try to talk to the person I sold it to, and see 12:17.670 --> 12:20.390 if you can buy it from him. 12:20.390 --> 12:23.190 Or the farmer might say, I've had three other offers, and 12:23.190 --> 12:26.320 I'm raising my price to some millions 12:26.320 --> 12:28.750 and millions of dollars. 12:28.750 --> 12:30.850 Then, you have second thoughts about doing it. 12:30.850 --> 12:32.250 You see what I'm saying, that the price 12:32.250 --> 12:33.490 discovery is in there? 12:33.490 --> 12:35.930 It's making things happen differently. 12:35.930 --> 12:37.570 You're learning something. 12:37.570 --> 12:39.510 The farmer is learning something. 12:39.510 --> 12:42.440 You are learning something from the options market, and 12:42.440 --> 12:47.390 ultimately it decides where that supermarket will go. 12:47.390 --> 12:50.880 So, that's the theoretical purpose of options. 12:53.930 --> 12:55.560 I wanted to talk, also, about a 12:55.560 --> 13:02.590 behavioral purpose of options. 13:05.360 --> 13:09.850 It's a little fuzzier about the actual benefits of options 13:09.850 --> 13:15.010 from this standpoint. 13:15.010 --> 13:24.350 The behavioral theory of options says that -- 13:24.350 --> 13:27.720 Very many different aspects of human behavior tie into 13:27.720 --> 13:36.970 options, but I would say it has something to do with 13:36.970 --> 13:41.520 attention anomalies and salience. 13:44.900 --> 13:48.330 Psychologists talk about this, that people make mistakes very 13:48.330 --> 13:52.180 commonly in what they pay attention to, what strikes the 13:52.180 --> 13:54.450 fancy of their imagination. 13:54.450 --> 13:57.390 Salience is something psychologists also talk about. 14:04.310 --> 14:07.290 Salient events are events that tend to attract attention, 14:07.290 --> 14:08.540 tend to be remembered. 14:12.280 --> 14:15.960 Now, when you think of options, a lot of options are 14:15.960 --> 14:19.670 what are called incentive options, OK? 14:23.310 --> 14:26.450 And when you get your first job, you may discover this. 14:26.450 --> 14:28.310 They'll give you options to buy shares in the 14:28.310 --> 14:30.210 company you work for. 14:30.210 --> 14:32.470 Why do they do that? 14:32.470 --> 14:35.370 I think it's because of certain human behavioral 14:35.370 --> 14:38.430 traits that I mention here, your 14:38.430 --> 14:41.260 attention and your salience. 14:41.260 --> 14:44.040 It's not necessarily very expensive for a company to 14:44.040 --> 14:49.300 give you options to buy shares in the company, but it puts 14:49.300 --> 14:52.420 you in a situation, where you start to pay attention to the 14:52.420 --> 14:53.870 value of the company. 14:53.870 --> 14:57.150 It becomes salient for you, and you start hoping that the 14:57.150 --> 14:59.630 price of the company will go up, because you have options 14:59.630 --> 15:02.190 to buy it, at a strike price. 15:02.190 --> 15:05.560 You hope that the company's price per share goes above 15:05.560 --> 15:07.170 your strike price, because then your 15:07.170 --> 15:08.340 options are worth something. 15:08.340 --> 15:11.190 They're in the money. 15:11.190 --> 15:14.140 So, it may change your motivation and your morale at 15:14.140 --> 15:16.680 work, or sense of identity with the company. 15:16.680 --> 15:20.420 All these sorts of things figure in. 15:20.420 --> 15:23.140 That's why we have incentive options. 15:27.440 --> 15:30.020 They can also give you peace of mind. 15:38.890 --> 15:43.170 Insurance is actually related to options in the sense that, 15:43.170 --> 15:46.570 when you buy insurance on your house, it's like buying a put 15:46.570 --> 15:49.540 option on your house, although it may be not directly 15:49.540 --> 15:52.660 connected to the home's value, right? 15:52.660 --> 15:55.600 When you buy an insurance policy in your house, and the 15:55.600 --> 15:59.880 house burns down, you collect on the insurance policy. 15:59.880 --> 16:02.310 Well, the price of your house fell to zero. 16:02.310 --> 16:04.510 If you had bought a put option on the house, it would do the 16:04.510 --> 16:05.940 same thing, right? 16:05.940 --> 16:10.040 You would have an option to sell it at a high price on 16:10.040 --> 16:12.160 something that's now worthless. 16:12.160 --> 16:17.020 So, insurance is like options, and insurance gives 16:17.020 --> 16:19.910 you peace of mind. 16:19.910 --> 16:24.040 So, people think in certain repetitive patterns, and one 16:24.040 --> 16:28.080 of them is, that I would like to not worry about something. 16:28.080 --> 16:32.800 So, I can get peace of mind, if I have a put option on 16:32.800 --> 16:36.520 something that I might otherwise worry about. 16:36.520 --> 16:39.860 All right, maybe that's enough of an introduction, but I'm 16:39.860 --> 16:42.230 giving you both theoretical reasons for options and 16:42.230 --> 16:44.530 behavioral reasons. 16:44.530 --> 16:46.810 I think of them as basically inevitable. 16:49.430 --> 16:52.490 You may have people advising you not to bother 16:52.490 --> 16:54.220 with options markets. 16:54.220 --> 16:59.290 That might be right for you, in a sense, but I think that 16:59.290 --> 17:01.750 they're always going to be with us, and so it's something 17:01.750 --> 17:03.000 that we have to understand. 17:11.920 --> 17:18.440 I have a newspaper clipping that I cut out. 17:18.440 --> 17:22.170 I've been teaching this course for over 20 years, so 17:22.170 --> 17:25.280 sometimes I don't update my newspaper clippings. 17:25.280 --> 17:28.210 I have a newspaper clipping from the options page that I 17:28.210 --> 17:31.850 made in 2002, OK? 17:31.850 --> 17:33.600 So, that's nine years ago. 17:33.600 --> 17:36.880 But I can't update it anymore, because newspapers don't print 17:36.880 --> 17:38.110 option prices anymore. 17:38.110 --> 17:41.260 So, I could go on some electronic trade account and 17:41.260 --> 17:43.380 get an updated option page. 17:43.380 --> 17:48.250 But why don't we just stick with The Wall Street Journal? 17:48.250 --> 17:54.080 This is a clipping from The Wall Street Journal, April 17:54.080 --> 18:00.770 2002, when they used to have an options page, OK? 18:00.770 --> 18:02.840 I just picked America Online. 18:06.460 --> 18:06.940 I don't know why. 18:06.940 --> 18:07.830 It's an interesting company. 18:07.830 --> 18:10.310 You remember America Online, a web presence? 18:10.305 --> 18:12.165 It used to be bigger than it is now. 18:14.700 --> 18:21.650 And actually, in 2000, America Online merged with Time 18:21.650 --> 18:24.400 Warner, OK? 18:24.400 --> 18:28.030 So, we actually have two different rows 18:28.030 --> 18:29.680 corresponding -- 18:29.680 --> 18:36.020 Forget Ace Limited, the second row says AOL.TW. 18:36.020 --> 18:40.350 That's America Online Time Warner, the merged company, 18:40.350 --> 18:44.460 and then below that, they have America Online itself. 18:47.760 --> 18:53.310 These were options that were issued before the merger, and 18:53.310 --> 18:59.510 they apparently are being exercised in terms of the same 18:59.510 --> 19:01.720 AOL Time Warner stock. 19:01.720 --> 19:05.700 AOL, by the way, was spun off by Time Warner last year, so 19:05.700 --> 19:06.440 they had a divorce. 19:06.440 --> 19:08.170 They were married in 2000. 19:08.170 --> 19:10.930 They were divorced in 2010. 19:10.930 --> 19:19.240 So, you can get back to it, AOL options, now. 19:19.240 --> 19:24.160 So, anyway, it shows the price of the 19:24.160 --> 19:28.000 share at $21.85 a share. 19:28.000 --> 19:35.610 So, you take any of these rows, and it shows you, for 19:35.610 --> 19:43.580 various strike prices, what the options prices are. 19:43.580 --> 19:47.190 So, let's go to the top row. 19:47.185 --> 19:57.615 A strike price of $20.00, expiring in May of 2002, which 19:57.620 --> 19:59.270 is one month into the future. 19:59.270 --> 20:03.310 Remember, it's April 2002 right now. 20:03.310 --> 20:06.300 The volume is the number of options that were traded 20:06.300 --> 20:12.880 yesterday, and the $2.55 up there is the price of a call 20:12.880 --> 20:18.570 option, the last price of the option to be traded yesterday. 20:18.570 --> 20:19.830 This is the morning paper. 20:19.825 --> 20:21.925 It's reporting on yesterday morning's prices [correction: 20:21.928 --> 20:24.318 yesterday's prices at closing]. 20:24.320 --> 20:26.720 And then, there's put options traded. 20:26.720 --> 20:28.880 A lot more puts were traded on that day. 20:28.880 --> 20:35.100 There were 2000 put options traded on that day in April 20:35.100 --> 20:42.920 2002, and the last price of the put option was $0.85. 20:42.920 --> 20:51.320 For $0.85, you could buy the right to sell a share of AOL 20:51.320 --> 20:56.590 Time Warner at $20.00, OK? 20:56.590 --> 20:59.170 And similarly, you could buy the right to buy it 20:59.170 --> 21:02.390 at $20.00 for $2.55. 21:02.392 --> 21:04.992 So, these are different strike prices and 21:04.990 --> 21:06.290 different exercise dates. 21:11.020 --> 21:11.490 This one -- 21:11.490 --> 21:13.020 I can reach it -- 21:13.020 --> 21:17.390 is to buy it at, if it's a call, $25.00 strike price, 21:17.390 --> 21:21.240 costs you $0.45 to buy that. 21:21.240 --> 21:26.080 But if you want to buy a put, it costs you $3.60. 21:26.080 --> 21:28.820 And we want to try to understand these prices, OK? 21:28.820 --> 21:33.020 That's the purpose here. 21:33.020 --> 21:44.900 So, let me say one thing more before I get into that. 21:44.900 --> 21:47.840 This is presented for the potential buyers, OK? 21:47.840 --> 21:50.550 These are options prices. 21:50.550 --> 21:53.190 There's also the seller of the option. 21:53.190 --> 21:56.330 They're called the writer of the option. 21:56.330 --> 21:59.450 I gave you an example before, when I talked about the farmer 21:59.450 --> 22:01.990 and you thinking of building a supermarket. 22:01.990 --> 22:05.410 So, you are the buyer of the option and the farmer is the 22:05.410 --> 22:06.700 writer of the option. 22:11.040 --> 22:15.780 The farmer is writing the option to you. 22:15.780 --> 22:18.930 You could also consider buying an option from someone else, 22:18.930 --> 22:20.840 who's not even the farmer, right? 22:20.835 --> 22:23.135 It could be some speculator. 22:23.140 --> 22:24.470 You don't have to go to the farmer. 22:24.470 --> 22:27.780 You can go to somebody else and say, I'd like to buy an 22:27.780 --> 22:30.230 option on that farm over there. 22:30.230 --> 22:32.810 And someone would say, sure, I'll sell you an option on it. 22:32.810 --> 22:33.640 And then I'm good for it. 22:33.640 --> 22:36.070 That means I have to go and buy it at whatever price from 22:36.070 --> 22:36.870 the farmer. 22:36.870 --> 22:38.450 Maybe that's not such a good idea. 22:38.450 --> 22:41.750 He might sense my urgency to buy it. 22:41.750 --> 22:44.710 But if it's a stock, someone can write an option, who 22:44.710 --> 22:46.170 doesn't even own the stock. 22:46.170 --> 22:50.060 And so, that's called a naked seller of an option, OK? 22:52.670 --> 22:54.620 Neither the buyer nor the seller ever have to 22:54.620 --> 22:55.450 trade in the stock. 22:55.450 --> 22:58.390 This is a market by itself. 22:58.390 --> 23:01.870 You could buy an option, and then you could sell it as an 23:01.870 --> 23:04.280 option without ever exercising it. 23:07.550 --> 23:11.660 The writer could write an option, and then buy an option 23:11.660 --> 23:14.360 to cancel it out later, and then, essentially, get out of 23:14.360 --> 23:15.470 that contract. 23:15.470 --> 23:19.690 So, the option becomes a market of its own, where 23:19.690 --> 23:23.390 prices of options start to look like an independent 23:23.390 --> 23:26.480 market, and this is called a derivatives market. 23:32.610 --> 23:36.560 There's an underlying stock price, but this is a 23:36.560 --> 23:38.250 derivative of the stock price. 23:43.420 --> 23:49.080 The first options exchange was the Chicago Board Options 23:49.080 --> 23:55.000 Exchange, which came in in 1973. 23:55.000 --> 23:58.570 Before that, options were traded, but they were traded 23:58.570 --> 24:02.150 through brokers and they didn't have the same presence. 24:02.150 --> 24:05.640 You didn't see all these options prices in newspapers. 24:05.640 --> 24:09.840 It's when they opened the market for options, that the 24:09.840 --> 24:12.150 options trading became a big thing. 24:12.150 --> 24:16.040 So, options markets are relatively new, if you 24:16.040 --> 24:17.990 consider '73 new. 24:17.990 --> 24:20.090 You weren't born then. 24:20.090 --> 24:23.570 It's not really that long ago. 24:23.570 --> 24:28.300 Since then, there are many more options exchanges, but 24:28.300 --> 24:30.100 CBOE is the first one. 24:30.100 --> 24:33.010 They're now all over the world. 24:33.010 --> 24:37.860 And we also have options on futures. 24:37.860 --> 24:41.750 And so, futures exchanges now routinely trade options on 24:41.750 --> 24:44.560 their futures contracts. 24:44.560 --> 24:49.800 So, that's a derivative on a derivative, but it's done. 24:54.980 --> 24:59.710 So, let me draw a simple picture of option pricing. 24:59.710 --> 25:11.410 So, this is the stock price and this is the 25:11.410 --> 25:19.900 option price, OK? 25:19.900 --> 25:23.610 And I'm going to mark here, the exercise price. 25:32.310 --> 25:37.620 Let's look at the exercise date, the last day. 25:37.620 --> 25:43.110 The option is about to expire, and this is your last chance 25:43.110 --> 25:44.090 to buy the stock. 25:44.090 --> 25:46.070 Then, it doesn't matter, on that day, whether it's an 25:46.070 --> 25:47.610 American or European option. 25:47.610 --> 25:50.300 They're both the same on the last day. 25:50.300 --> 25:53.230 What is the price of the option as a function of the 25:53.230 --> 25:55.060 stock price? 25:55.060 --> 25:59.460 Well, if the stock price is less than the exercise price, 25:59.460 --> 26:02.870 the option is worthless, right? 26:02.870 --> 26:04.970 It will not be exercised. 26:04.970 --> 26:09.010 You won't exercise an option to buy it for more than you 26:09.010 --> 26:10.290 could just buy it on the market, right? 26:10.290 --> 26:12.780 STUDENT: You have to say ''call''. 26:12.780 --> 26:14.080 PROFESSOR ROBERT SHILLER: Did I not say call? 26:14.080 --> 26:15.670 Yes, I'll put it up here. 26:15.670 --> 26:17.630 We're talking about call options. 26:20.240 --> 26:22.560 Thank you. 26:22.560 --> 26:30.370 But if it's above the exercise price, this is a 45 degree 26:30.370 --> 26:34.570 angle, that's a line with the slope of one, the option 26:34.570 --> 26:37.870 prices rises with the stock. 26:37.870 --> 26:41.270 In fact, it just equals the stock price minus the exercise 26:41.270 --> 26:42.990 price, right? 26:42.990 --> 26:47.170 So, this region, we say, is ''out of the money.'' The 26:47.170 --> 26:52.570 option is out of the money, when its prices 26:52.569 --> 26:54.299 [clarification: the stock price], for a call, is less 26:54.300 --> 26:55.860 than the exercise price. 26:55.860 --> 26:58.490 Here, it's ''in the money.'' I'll put it up 26:58.490 --> 26:59.740 here, in the money. 27:02.330 --> 27:05.050 And then, on the exercise date, it will always equal the 27:05.050 --> 27:08.410 stock price minus the exercise price. 27:08.410 --> 27:10.230 So, it's very simple. 27:10.230 --> 27:13.970 Now, one confusion that's often made: I gave the example 27:13.970 --> 27:18.200 of building a shopping center or a supermarket on a farm. 27:18.200 --> 27:21.330 Now, someone might think that you buy an option on it, so 27:21.330 --> 27:24.650 that you can think about it and make up your mind later. 27:24.650 --> 27:27.030 Well, in a sense, you could do that. 27:27.030 --> 27:31.070 But the thing is, you will exercise the option whether or 27:31.070 --> 27:34.870 not you build the shopping mall or this supermarket, if 27:34.870 --> 27:36.810 it's in the money, right? 27:36.810 --> 27:39.960 Suppose, you changed your mind, and I don't want to 27:39.960 --> 27:41.360 build the supermarket. 27:41.360 --> 27:45.330 But I'm sitting on an option that I bought, to buy his land 27:45.330 --> 27:48.900 for a price, which is less than the market price for it. 27:48.900 --> 27:50.410 Of course, I'll buy it. 27:50.410 --> 27:52.660 So, you're going to buy it, whether you build the shopping 27:52.660 --> 27:55.030 center or not. 27:55.030 --> 27:57.660 You always exercise the option, if it's in the money 27:57.660 --> 27:58.400 on the last day. 27:58.400 --> 27:59.610 That's the assumption. 27:59.610 --> 28:01.590 I mean you could not, I suppose, if you like the 28:01.590 --> 28:03.610 farmer and you want to be a nice guy. 28:03.610 --> 28:04.630 I don't know. 28:04.630 --> 28:11.730 But usually, what it is, it's a non-linear relation between 28:11.730 --> 28:13.940 the stock price and the derivative. 28:13.940 --> 28:20.020 So, the derivative is a broken straight line function of the 28:20.020 --> 28:20.890 stock price. 28:20.890 --> 28:24.290 Whereas all the portfolios we construct, are linear. 28:24.290 --> 28:25.160 They're straight lines. 28:25.160 --> 28:26.790 They don't have a break in them. 28:26.790 --> 28:30.830 So, the option creates a break in the function of 28:30.834 --> 28:33.134 the stock price -- 28:33.130 --> 28:35.670 and this is why Ross emphasized that options price 28:35.670 --> 28:37.880 something very different, that's not priced 28:37.880 --> 28:39.060 in the regular -- 28:39.060 --> 28:45.380 no portfolio shows you this broken straight line relation. 28:45.380 --> 28:47.530 Now, I wanted to then talk about a put. 28:47.530 --> 28:49.050 What is a put? 28:49.050 --> 28:51.640 Let me erase, where it says in and out of the money. 28:51.640 --> 28:54.550 I'll show it. 28:54.550 --> 28:59.290 I'll do this with a dashed line, so that you'll see which 28:59.290 --> 28:59.650 one is which -- 28:59.650 --> 29:01.470 I'm leaving the call line up. 29:01.470 --> 29:04.220 With a put, a put is out of the money up here -- 29:07.680 --> 29:10.620 I can't really show it too well -- 29:10.620 --> 29:16.340 if the stock price is above the exercise price, because 29:16.340 --> 29:17.660 you're selling now. 29:17.660 --> 29:23.150 And it's in the money, if the stock price is less than the 29:23.150 --> 29:24.280 exercise price -- 29:24.280 --> 29:25.670 I didn't draw that very well. 29:25.670 --> 29:28.820 That's supposed to be a 45 degree line. 29:28.820 --> 29:32.830 That's a 45 degree angle, has a slope of minus one, right? 29:32.825 --> 29:34.075 That's on the exercise date. 29:41.980 --> 29:44.730 Now, it's interesting that there's a pretty simple 29:44.730 --> 29:48.900 pattern here between puts and calls. 29:48.900 --> 29:56.160 What if I buy one call and I short one put, all right? 29:56.160 --> 30:00.070 Or write a put, writing a put and shorting a put are the 30:00.070 --> 30:03.140 same thing, all right? 30:03.140 --> 30:06.730 What does that portfolio look like? 30:06.730 --> 30:15.700 Well, if I put that portfolio together, I want to have plus 30:15.700 --> 30:20.860 one call minus one put, all right? 30:20.860 --> 30:28.500 My portfolio relation to the stock price is going to look 30:28.500 --> 30:29.290 like that, right? 30:29.290 --> 30:30.540 It's just going to be a straight line. 30:34.710 --> 30:39.710 So, the value of my portfolio is equal to the stock price 30:39.710 --> 30:41.350 minus the exercise price. 30:41.350 --> 30:43.220 Simple as that. 30:43.220 --> 30:48.290 And my portfolio can be negative now, because I've 30:48.290 --> 30:49.110 shorted something. 30:49.110 --> 30:51.410 I can have a negative portfolio value. 30:55.310 --> 30:58.520 That's very simple, can you see that? 30:58.520 --> 31:04.420 This leads us to the put-call parity equation. 31:08.280 --> 31:11.260 If a put minus a call [correction: a call minus a 31:11.260 --> 31:13.840 put] is the same thing as the stock minus the exercise 31:13.840 --> 31:18.480 price, then the prices should add up too, right? 31:18.480 --> 31:21.600 So, put-call parity -- 31:26.560 --> 31:29.120 there's different ways of writing this. 31:29.120 --> 31:46.490 But it says that the stock price equals the call price 31:46.490 --> 31:58.080 minus put price plus exercise price on the last day, on the 31:58.080 --> 31:59.270 exercise day, right? 31:59.270 --> 32:00.520 It's simple. 32:03.240 --> 32:06.160 This is put-call parity on the exercise date. 32:12.490 --> 32:16.420 Now, let's think about some day before the exercise date. 32:16.420 --> 32:17.700 Well, you know this is going to happen on 32:17.700 --> 32:19.210 the exercise date. 32:19.210 --> 32:23.320 So, at any date before the exercise date, the same thing 32:23.320 --> 32:26.810 should hold, except that we've got to make 32:26.810 --> 32:30.200 this the present value. 32:30.200 --> 32:34.890 Present discounted value of the exercise price. 32:34.890 --> 32:38.580 And also we have to add in, in case there is any dividends 32:38.580 --> 32:42.060 paid between now and the exercise date, plus the 32:42.060 --> 32:49.150 present discounted value of dividends paid between now and 32:49.150 --> 32:50.570 the exercise date. 32:50.570 --> 32:52.150 Because the stock gets that, and the option 32:52.145 --> 32:54.475 holders don't, OK? 32:54.480 --> 32:58.790 So, that's called the put-call parity relation. 32:58.790 --> 33:01.780 And now I can cross out ''exercise date.'' This should 33:01.780 --> 33:05.600 hold on all dates. 33:05.600 --> 33:08.640 Because if it didn't hold, there would be an arbitrage, 33:08.640 --> 33:11.430 or profit opportunity. 33:11.430 --> 33:17.990 So, it should hold on this page, except for minor 33:17.990 --> 33:21.620 failures to hold. 33:21.620 --> 33:23.710 It should hold approximately on this page. 33:23.710 --> 33:25.750 And let me give you one example. 33:25.750 --> 33:28.260 See, if it holds. 33:28.260 --> 33:32.390 Let's consider the one that I can reach. 33:32.390 --> 33:35.790 OK, oh, this is the stock price. 33:35.790 --> 33:36.970 So, what do I have? 33:36.970 --> 33:43.890 The biggest thing here is the strike price, exercise price. 33:43.890 --> 33:45.140 So, we want to do -- 33:47.440 --> 33:56.530 we'll do this line, $25.00 plus $0.45 minus $3.50, and 33:56.530 --> 33:58.040 I'm assuming there's no dividend paid 33:58.040 --> 34:01.150 between now and May. 34:01.152 --> 34:04.032 It comes out very close to $21.85. 34:04.030 --> 34:06.450 I can't do the arithmetic in my head. 34:06.449 --> 34:10.539 It may not hold exactly, because these prices may not 34:10.540 --> 34:13.050 all have been quoted at exactly the same time, and 34:13.050 --> 34:18.330 there's some transactional costs that limit this. 34:18.330 --> 34:19.210 Do you see that? 34:19.210 --> 34:22.760 So, because of the put-call parity relation, The Wall 34:22.755 --> 34:26.565 Street Journal didn't even bother to put the put prices 34:26.570 --> 34:29.990 in, because you can get one from the other. 34:32.650 --> 34:35.480 But they do put them in, just because people like to see 34:35.480 --> 34:42.140 them, and some people might be trying to profit from the 34:42.139 --> 34:45.109 put-call parity arbitrage. 34:45.110 --> 34:48.970 But for our purposes, we only have to do call pricing. 34:48.970 --> 34:51.870 Once we've got call pricing, we've got put prices. 34:51.870 --> 34:54.950 So, I just use the put-call parity relation and I get put 34:54.950 --> 34:56.440 price prices. 34:56.440 --> 34:58.930 So, now let's think about how you would price puts 34:58.930 --> 35:02.220 [correction: calls]. 35:02.220 --> 35:08.220 The price of a put [correction: call], 35:08.220 --> 35:11.050 we know what it is on the exercise date, right? 35:11.050 --> 35:13.700 I'm going to forget the dashed lines. 35:13.700 --> 35:15.760 There's no dashed lines here anymore. 35:15.760 --> 35:18.130 We're just talking about call prices. 35:18.132 --> 35:28.062 All right, so this shows the price of a put on 35:28.060 --> 35:29.850 the last day -- 35:29.850 --> 35:32.430 of a call on the last day. 35:32.430 --> 35:35.390 Now, what about an earlier day? 35:35.390 --> 35:35.530 [clarification: The following argument about price bounds 35:35.530 --> 35:35.630 solely applies to call options. 35:35.630 --> 35:35.790 It also abstracts from dividend payments of the 35:35.790 --> 35:37.040 underlying stock.] 35:39.350 --> 35:43.870 Well, the price of a call can never be negative, right? 35:43.870 --> 35:46.680 So, the call price has to be above this line. 35:49.690 --> 35:55.090 It can never be worth less than the stock price minus the 35:55.090 --> 36:02.480 exercise price, even before the exercise date. 36:02.480 --> 36:04.180 And also, it can't be worth more than 36:04.180 --> 36:05.430 the stock price itself. 36:05.430 --> 36:07.440 I'll draw a 45 degree line from the origin. 36:14.760 --> 36:17.310 That's supposed to be parallels of that. 36:17.310 --> 36:22.060 It's obvious that the call price has to be above this 36:22.060 --> 36:25.910 broken straight line, but not too far above it. 36:25.910 --> 36:28.990 Above this broken straight line, representing the price 36:28.990 --> 36:31.670 as a function of the stock price on the last day. 36:31.670 --> 36:35.420 And the closer you get to the last day, the closer the 36:35.420 --> 36:37.770 options price will get to that curve. 36:37.770 --> 36:44.830 So, on some day before the exercise date, the call option 36:44.830 --> 36:49.910 price will probably look something like that, right? 36:49.910 --> 36:55.850 It's above the broken straight line because of option value. 36:55.850 --> 36:59.390 So, think it this way, suppose an option is out of 36:59.390 --> 37:01.780 the money today -- 37:01.780 --> 37:03.410 well, you can see out of the money options. 37:06.840 --> 37:09.840 For a call, this is out of the money, right? 37:09.840 --> 37:14.700 Because its stock price is $21.85, but I've got an option 37:14.700 --> 37:16.960 to buy it for $25.00. 37:16.960 --> 37:19.540 All right, that's going to be worthless, unless the option 37:19.540 --> 37:19.830 price [correction: stock price] 37:19.830 --> 37:23.840 goes up before it expires. 37:23.840 --> 37:26.410 So, it's only worth something, because there's a chance that 37:26.410 --> 37:30.830 it will be worth something on the exercise date. 37:30.830 --> 37:33.070 And what are people paying for that chance? 37:33.070 --> 37:35.980 $0.45, not much. 37:35.980 --> 37:37.390 Why are they paying so little? 37:37.390 --> 37:42.070 Well, you can say intuitively, it's because it's pretty far. 37:42.070 --> 37:47.510 $21.85 is pretty far from $25.00, and this option only 37:47.510 --> 37:48.550 has a month to go. 37:48.550 --> 37:51.460 What's the chance that the price will go up that much? 37:51.460 --> 37:53.680 Well, there is a chance, but it's not that big. 37:53.680 --> 37:56.530 So, I'm only willing to pay $0.45 to buy 37:56.530 --> 37:58.800 an option like that. 37:58.800 --> 38:02.150 So, we're somewhere like here on that row 38:02.150 --> 38:03.400 that I've shown you. 38:07.200 --> 38:10.860 The reason you don't want to exercise an option early is, 38:10.860 --> 38:16.460 because, if you exercise it early, your value drops down 38:16.460 --> 38:19.640 to the broken straight line, right? 38:19.640 --> 38:23.630 It's always worth more than the broken straight line 38:23.630 --> 38:26.620 indicates before the exercise date. 38:26.620 --> 38:30.190 So, if you want to get your money out, sell the option. 38:30.190 --> 38:32.100 Don't exercise it early. 38:32.100 --> 38:35.300 So, that's why the distinction between European and American 38:35.300 --> 38:40.450 options is not as big or as important as you might think, 38:40.450 --> 38:40.660 at first. [clarification: American call options should 38:40.660 --> 38:40.710 indeed not be exercised early. 38:40.710 --> 38:40.780 However, there are circumstances under which it 38:40.780 --> 38:42.030 is optimal to exercise an American put option early.] 38:42.030 --> 38:53.180 So, we can just price European options, and then we can infer 38:53.180 --> 38:56.400 what other options would be, what put 38:56.400 --> 38:57.650 options would be worth. 39:01.310 --> 39:10.390 Let's now talk about pricing of options. 39:10.390 --> 39:14.490 And the main pricing equation that we're going to use is the 39:14.490 --> 39:17.640 Black-Scholes Option Pricing equation. 39:17.640 --> 39:20.930 But, before that, I wanted to just give you a simple story 39:20.930 --> 39:23.550 of options pricing, just to give you some 39:23.550 --> 39:26.930 idea, how it works. 39:26.930 --> 39:29.150 And then I'm going to not actually derive the 39:29.150 --> 39:34.580 Black-Scholes formula, but I'm going to show it to you. 39:38.220 --> 39:41.880 I'm going to tell you a simple story, just to give some 39:41.880 --> 39:48.490 intuitive feel about the pricing of options. 39:52.480 --> 39:55.050 And to simplify the story, I'm going to tell a story about a 39:55.050 --> 39:58.920 world, in which there's only two possible prices for the 39:58.920 --> 40:00.800 underlying stock. 40:00.800 --> 40:01.930 That makes it binomial. 40:01.930 --> 40:06.820 There's only two things that can happen, and you can either 40:06.820 --> 40:10.310 be high or low, all right? 40:10.310 --> 40:12.020 So, let me get my notation. 40:12.020 --> 40:19.110 I'm going to use S as the stock price, all right? 40:22.710 --> 40:26.910 I'm going to assume that the stock price, that's today -- 40:30.140 --> 40:32.950 this is also a simple world in that there's only one day. 40:32.950 --> 40:34.380 The option expires tomorrow. 40:34.380 --> 40:36.940 There's only one more price we're going to see. 40:36.940 --> 40:40.440 So, the stock is either going to go up or down. 40:40.440 --> 40:47.260 So, u is equal to one plus the fraction that it goes up. 40:47.260 --> 40:50.390 u stands for up. 40:50.390 --> 40:55.060 And d is down, is one plus the fraction down. 40:59.820 --> 41:05.230 So, that means that stock price either becomes Su, which 41:05.230 --> 41:10.950 means it goes up by a fraction, multiple u, or it is 41:10.950 --> 41:15.620 Sd, which means it goes down by a multiple d. 41:15.620 --> 41:17.250 And that's all we know, OK? 41:17.250 --> 41:22.890 But now we have a call option: Call C the price of the call. 41:25.920 --> 41:28.590 We're going to try to derive what that is. 41:28.590 --> 41:33.670 But we know, from our broken straight line analysis, we 41:33.670 --> 41:39.910 know what C sub u is, the price if the stock goes up. 41:39.910 --> 41:46.880 And we know what C sub d is, it's the price if down, OK? 41:46.880 --> 42:02.240 So, suppose the option has exercise price E, all right. 42:02.240 --> 42:04.160 Do you understand this world? 42:04.160 --> 42:05.820 Simple story. 42:05.820 --> 42:10.870 Now, what I want to do is consider a portfolio of both 42:10.870 --> 42:13.950 the stock and the option, that is riskless. 42:16.500 --> 42:24.980 I'm going to buy a number of options equal to H. H is the 42:24.980 --> 42:39.350 hedge ratio, which is the number of shares purchased per 42:39.350 --> 42:40.120 option sold. 42:40.120 --> 42:44.740 So, I'm going to sell a call option to hedge the stock 42:44.740 --> 42:49.340 price, to reduce the risk of the stock price, OK? 42:49.340 --> 42:57.720 And so, hedge ratio is shares purchased over options. 42:57.720 --> 43:01.950 Each option is to buy one share, OK? 43:01.950 --> 43:04.950 So, what I'm going to do is, write one 43:04.950 --> 43:08.180 call and buy H shares. 43:08.180 --> 43:11.940 So, let me erase this and start over again. 43:17.500 --> 43:22.080 I'm on my way to deriving the options price for you -- 43:22.075 --> 43:23.465 a little bit of math. 43:27.810 --> 43:46.780 So, I'm going to write one call and buy H shares, OK. 43:46.780 --> 43:53.200 If the stock goes up, if we discover we're in an up world 43:53.200 --> 44:00.600 next period, my portfolio is worth uHS 44:00.600 --> 44:04.810 minus C sub u, right? 44:04.810 --> 44:08.370 Because the share price goes from S to uS, and I've got H 44:08.370 --> 44:15.010 shares, and I've written a call, so I have 44:15.010 --> 44:18.890 to pay C sub u. 44:18.890 --> 44:28.250 If it's down, then my portfolio is dHS 44:28.250 --> 44:34.310 minus C sub d, OK? 44:34.310 --> 44:37.050 This is simple enough? 44:37.050 --> 44:40.450 Now, what I want to do is eliminate all risk. 44:40.450 --> 44:44.980 So, that means I want to choose H, so that these two 44:44.980 --> 44:46.560 numbers are the same. 44:46.560 --> 44:48.550 And if I do that, I've got a riskless 44:48.550 --> 44:51.170 investment, all right? 44:51.170 --> 44:55.860 So, set these equal to each other. 44:55.860 --> 44:59.230 And that implies something about H. We can drive what H 44:59.230 --> 45:04.010 is, if I just put these two equal to each other and solve 45:04.010 --> 45:15.110 for H. And I get H equals C sub u minus C sub d, all over 45:15.110 --> 45:21.990 u minus d times S, OK? 45:21.990 --> 45:25.640 So, I've been able to put together a portfolio of the 45:25.640 --> 45:30.260 stock and the option that has zero risk. 45:30.260 --> 45:34.410 If I do this, if I hold this amount of shares in my 45:34.410 --> 45:38.770 portfolio, I've got a riskless portfolio. 45:38.770 --> 45:43.840 So, that means that the riskless portfolio has to earn 45:43.840 --> 45:46.440 the riskless rate, right? 45:46.440 --> 45:48.750 It's the same thing as a riskless rate [correction: 45:48.752 --> 45:49.972 same thing as a riskless investment], so it has to earn 45:49.970 --> 45:51.130 that [clarification: earn the riskless rate]. 45:51.130 --> 45:53.940 If I can erase this now, I'm almost there, 45:53.940 --> 45:57.000 through option pricing. 45:57.000 --> 46:03.940 The option pricing then says that, since I'm derived what H 46:03.935 --> 46:10.035 is, the portfolio has to be worth one plus the interest 46:10.040 --> 46:20.140 rate times what I put in, which is HS minus C. And that 46:20.140 --> 46:26.520 has to equal the value of the portfolio at the end, which is 46:26.520 --> 46:35.840 either uHS minus C sub u, or dHS minus C sub d, 46:35.840 --> 46:38.930 the same thing, OK? 46:41.440 --> 46:45.560 So, I've already derived what H is, and I substituted into 46:45.560 --> 46:54.900 that, and I solved for C. So, substitute H in and solve for 46:54.900 --> 46:59.880 C, and we get the call price, OK? 46:59.880 --> 47:06.230 It's a little bit complicated, but the call option price has 47:06.230 --> 47:17.310 to equal one plus r minus d, all over u minus d, times C 47:17.310 --> 47:26.540 sub u over one plus r, plus u minus one minus r, all over u 47:26.540 --> 47:33.410 minus d, times C sub d all over one plus r. 47:33.410 --> 47:36.870 And I'll put a box around that because that's our option 47:36.870 --> 47:41.590 price formula, OK? 47:41.590 --> 47:45.030 Did you follow all that? 47:45.030 --> 47:47.070 This is derived -- 47:47.070 --> 47:50.920 This option price formula was derived from a 47:50.920 --> 47:52.810 no arbitrage condition. 47:57.910 --> 48:04.120 Arbitrage, in finance, means riskless profit opportunity. 48:04.120 --> 48:08.550 And the no arbitrage condition says, it's never possible to 48:08.550 --> 48:13.270 make more than the riskless rate risklessly, all right? 48:13.270 --> 48:16.330 If I could, suppose I had some way -- suppose the riskless 48:16.330 --> 48:22.870 rate is 5%, and I can make 6% risklessly, then I will borrow 48:22.870 --> 48:27.050 at the riskless rate and put it into the 6% opportunity. 48:27.050 --> 48:29.400 And I'll do that until kingdom come. 48:29.400 --> 48:31.150 There's no limit to how much I'll do that. 48:31.150 --> 48:32.400 I'll do it forever. 48:34.800 --> 48:40.090 It's too much of a profit opportunity to ever happen. 48:40.090 --> 48:43.390 One of the most powerful insights of theoretical 48:43.390 --> 48:47.190 finance is, that the no arbitrage 48:47.190 --> 48:49.100 condition should hold. 48:49.100 --> 48:52.260 It's like saying, there are no $10 bills on the pavement. 48:52.260 --> 48:55.190 When you walk down the street and you see a $10 bill lying 48:55.190 --> 49:00.030 there on the street, your first thought ought to be, are 49:00.030 --> 49:02.530 my eyes deceiving me? 49:02.530 --> 49:04.500 Because somebody else would have picked it 49:04.500 --> 49:05.430 up if it were there. 49:05.430 --> 49:06.780 How can it be there? 49:06.780 --> 49:08.490 I once actually had that experience. 49:08.490 --> 49:11.180 I was walking down the street in New York. 49:11.180 --> 49:13.000 It was actually a $5 bill. 49:13.000 --> 49:14.850 It was just lying there in the street. 49:14.850 --> 49:18.530 And so, I reached down to pick it up, and then, suddenly, it 49:18.530 --> 49:19.610 disappeared. 49:19.610 --> 49:22.400 And it was people on one of the stoops of one of these New 49:22.400 --> 49:25.820 York townhouses playing a game. 49:25.820 --> 49:28.250 They'd tied a string to a $5 bill. 49:28.250 --> 49:31.240 And they would leave it on the street, and watch people reach 49:31.240 --> 49:33.320 for it, and they'd snatch it away. 49:33.320 --> 49:36.690 That's the only time in my life I ever saw a $5 bill on 49:36.690 --> 49:37.980 the pavement. 49:37.980 --> 49:40.860 And so, it's a pretty good assumption that, if you see 49:40.860 --> 49:43.040 one, it isn't real. 49:43.040 --> 49:46.390 And that's all this is saying, that if the option price 49:46.390 --> 49:50.150 didn't follow this formula, something would be wrong. 49:50.150 --> 49:52.190 And so, it had better followed this formula. 49:55.340 --> 49:58.160 Now, that is the basic core option theory. 49:58.160 --> 50:02.460 Now, the interesting thing about this theory is, I didn't 50:02.460 --> 50:07.190 use the probability of up and the probability of down. 50:07.190 --> 50:10.330 So somebody says, wait a minute, my whole intuition 50:10.330 --> 50:13.820 about options is: I'd buy an option, because it 50:13.820 --> 50:16.330 might be in the money. 50:16.330 --> 50:20.150 When I was just describing this here, this is $0.45, I 50:20.150 --> 50:22.110 said, that's not much, because it probably 50:22.110 --> 50:26.240 won't exceed $25.00. 50:26.240 --> 50:29.880 It's so far below it. 50:29.880 --> 50:34.100 So, it seems like the options should really be fundamentally 50:34.100 --> 50:39.370 tied to the probability of success. 50:39.370 --> 50:40.790 But it's not here at all. 50:40.790 --> 50:42.070 There's no probability in it. 50:42.070 --> 50:43.600 You saw me derive it. 50:43.600 --> 50:45.840 Was I tricking you? 50:45.840 --> 50:48.310 Well, I wasn't. 50:48.310 --> 50:49.280 I don't play tricks. 50:49.280 --> 50:50.740 This is absolutely right. 50:50.740 --> 50:54.130 You don't need to know the probability that it's in the 50:54.130 --> 50:58.210 money to price an option, because you can price it out 50:58.210 --> 51:02.930 of pure no-arbitrage conditions. 51:02.930 --> 51:08.050 So, that leads me then to the famous formula for options 51:08.050 --> 51:12.840 pricing, the Black-Scholes Option Pricing Formula, which 51:12.840 --> 51:14.420 looks completely different from that. 51:14.420 --> 51:20.490 But it's a kindred, because it relies on the same theory. 51:20.490 --> 51:22.080 And there it is. 51:22.080 --> 51:29.000 This was derived in the late 70's, or maybe the early 70's, 51:29.000 --> 51:35.190 by Fisher Black, who was at MIT at the time, I think, but 51:35.190 --> 51:45.130 later went to Goldman Sachs, and Myron Scholes, who is now 51:45.130 --> 51:49.900 in San Francisco, doing very well. 51:49.900 --> 51:55.120 I see him at our Chicago Mercantile Exchange meetings. 51:58.280 --> 51:59.700 Fisher Black passed away. 52:03.930 --> 52:06.220 It doesn't have the probability that the option is 52:06.220 --> 52:09.460 in the money, either, but it looks totally different from 52:09.460 --> 52:12.800 the formula that I wrote over there. 52:12.795 --> 52:20.615 The call price is equal to the share price, S, times N of d 52:20.623 --> 52:27.833 sub 1, where d sub 1 is this equation, minus e to the minus 52:27.830 --> 52:32.380 r, the interest rate, times time to maturity, T, times the 52:32.380 --> 52:37.230 exercise price times N of d sub 2, where this is d sub 2. 52:37.230 --> 52:39.780 And the N function is the cumulative normal 52:39.780 --> 52:41.680 distribution function. 52:41.676 --> 52:46.726 I'm not going to derive all that, because it involves 52:46.730 --> 52:49.650 what's called the calculus of variations. 52:49.650 --> 52:52.190 I don't think most of you have learned that. 52:54.690 --> 52:58.360 In ordinary calculus, we have what's called differentials, 52:58.360 --> 53:01.380 dy, dx, et cetera. 53:01.380 --> 53:04.750 Those are fixed numbers in ordinary calculus. 53:04.750 --> 53:09.620 In the mid 20th century, mathematicians, notably the 53:09.620 --> 53:14.900 Japanese mathematician Ito, developed a random version of 53:14.900 --> 53:19.430 calculus, where dx and dy are random variables. 53:19.430 --> 53:22.130 That's called the stochastic calculus. 53:22.130 --> 53:25.320 But I'm not going to use that. 53:25.320 --> 53:26.730 I'm not going to derive this. 53:26.730 --> 53:34.580 But you can see how to price an option using Black-Scholes. 53:34.580 --> 53:39.460 But Black-Scholes is derived, again, by the no-arbitrage 53:39.460 --> 53:42.210 condition and it doesn't have the probability. 53:42.210 --> 53:45.180 Oh, the other variable that's significant here is sigma, 53:45.180 --> 53:49.290 which is the standard deviation of the change in the 53:49.290 --> 53:51.050 stock price. 53:51.050 --> 53:53.930 So, once we put that in, someone could say, well, 53:53.930 --> 53:58.410 probabilities are getting in through the back door, because 53:58.410 --> 54:02.450 this is really a probability weighted sum of the changes in 54:02.450 --> 54:04.510 stock prices. 54:04.510 --> 54:08.340 Well, probability is not really in here at all, but 54:08.340 --> 54:11.340 maybe there's something like standard deviation, even in 54:11.340 --> 54:12.850 this equation. 54:12.850 --> 54:15.410 Because we had C sub u and C sub d, and that would give you 54:15.410 --> 54:16.280 some sense of the variability. 54:16.276 --> 54:16.326 [clarification: In the binomial asset pricing model, 54:16.332 --> 54:16.432 u and d give you some sense of the variability of the 54:16.428 --> 54:16.488 underlying stock price, analogous to sigma in the 54:16.492 --> 54:17.742 Black-Scholes formula.] 54:20.770 --> 54:22.530 I'm going to leave this equation just 54:22.530 --> 54:25.270 for you to look at. 54:25.270 --> 54:31.080 But what it does do is, it shows the option price as a 54:31.080 --> 54:33.350 nice curvilinear relationship, just like the 54:33.350 --> 54:36.020 one I drew by hand. 54:36.020 --> 54:44.250 Which then, as time to exercise goes down, as we get 54:44.250 --> 54:48.800 close to the exercise date, that curve eventually 54:48.800 --> 54:51.090 coincides with the broken straight line. 54:53.630 --> 55:01.060 Now, I wanted to tell you about implied volatility. 55:01.060 --> 55:04.950 This equation can be used either of two ways. 55:04.950 --> 55:10.920 The most normal way to do it, to use this equation, is to 55:10.920 --> 55:13.500 get the price that you think is the right price for an 55:13.500 --> 55:16.650 option, to decide whether I'm paying too much or too little 55:16.650 --> 55:18.770 for an option. 55:18.770 --> 55:22.850 So with this formula, I can plug in all the numbers. 55:22.850 --> 55:26.620 To use this formula, I have to know what the stock price is. 55:26.620 --> 55:29.990 That's S. I have to know what the exercise price is. 55:29.985 --> 55:32.175 And I have to know what the time to maturity -- 55:32.180 --> 55:35.900 these are all specified by the stock price and the contract. 55:35.900 --> 55:38.110 I have to know with the interest rate is. 55:38.110 --> 55:42.190 And if I also have some idea of the standard deviation of 55:42.190 --> 55:46.940 the change in the stock price, then I can 55:46.940 --> 55:49.700 get an option price. 55:49.700 --> 55:52.080 But I can also turn it around. 55:52.080 --> 55:54.880 If I already know what the option is selling for in the 55:54.880 --> 56:01.340 market, I can infer what the implied sigma is, right? 56:01.340 --> 56:02.600 Because all the other numbers in the 56:02.600 --> 56:04.770 Black-Scholes formula are clear. 56:04.770 --> 56:06.200 They're in the newspaper, or they're 56:06.200 --> 56:08.210 in the option contract. 56:08.210 --> 56:12.030 There's this one hard to pin down variable, what is the 56:12.030 --> 56:15.070 variability of the stock price? 56:15.070 --> 56:18.950 And so, what people often use the Black-Scholes formula to 56:18.950 --> 56:24.780 is, to invert it and calculate the implied volatility of 56:24.780 --> 56:26.090 stock prices. 56:26.090 --> 56:31.110 So, when call option prices are high, why are they high 56:31.110 --> 56:33.150 relative to other times? 56:33.150 --> 56:35.240 Well, it must be that people think -- 56:35.240 --> 56:37.700 I'm going back to the old interpretation, that the 56:37.700 --> 56:40.530 probability of exercise is high, right? 56:40.530 --> 56:43.510 If an out of the money call is valuable, it must be people 56:43.510 --> 56:46.200 think that sigma is high. 56:46.200 --> 56:50.140 So, let's actually solve for how high that is. 56:50.140 --> 56:53.190 I can't actually solve this equation. 56:53.190 --> 56:54.740 I have to do it numerically. 56:54.740 --> 56:59.020 But I can calculate, for any call price, given the stock 56:59.020 --> 57:02.830 price, exercise price, time to maturity, and interest rate. 57:02.830 --> 57:08.590 I can calculate what volatility would imply that 57:08.590 --> 57:10.100 stock price. 57:10.100 --> 57:16.820 And so, that's where we are with Black-Scholes. 57:16.820 --> 57:24.670 So, implied volatility is the options market's opinion as to 57:24.670 --> 57:30.170 how variable the stock market will be between now and the 57:30.170 --> 57:31.420 exercise date. 57:33.860 --> 57:38.850 So, one thing we can do is compute implied volatility. 57:38.850 --> 57:43.430 And I have that here on this chart here. 57:43.430 --> 57:49.950 What I have here, from 1986 to the present, with the blue 57:49.950 --> 58:00.570 line, is the VIX, V-I-X , which is computed now by the 58:00.570 --> 58:03.660 Chicago Board Options Exchange. 58:03.660 --> 58:06.220 When the CBOE was founded, they didn't 58:06.220 --> 58:07.800 know how to do this. 58:07.800 --> 58:11.290 Black and Scholes invented their equation in response to 58:11.290 --> 58:13.370 the founding of the CBOE. 58:13.370 --> 58:18.760 And now, the CBOE publishes the VIX. 58:18.760 --> 58:21.010 And that's where I got this, off their website cboe.com. 58:23.920 --> 58:29.140 And so, they have computed, based on the front month, the 58:29.140 --> 58:35.520 near options, what the options market thought the volatility 58:35.520 --> 58:37.100 of the stock market was. 58:37.100 --> 58:39.590 That's the blue line. 58:39.590 --> 58:43.450 And you can see, it had a lot of changes over time. 58:43.450 --> 58:47.020 That means that options prices were revealing something about 58:47.020 --> 58:49.820 the volatility of the stock market. 58:49.820 --> 58:51.890 Now, the blue line is from the Chicago 58:51.890 --> 58:53.930 Board Options Exchange. 58:53.930 --> 58:59.190 What I did, and I calculated this myself, the orange line 58:59.190 --> 59:05.360 is the standard deviation of actual stock prices over the 59:05.360 --> 59:11.460 preceding year, of monthly changes, annualized. 59:11.460 --> 59:13.640 That's actual volatility. 59:13.640 --> 59:17.490 But it's actual past volatility. 59:17.490 --> 59:19.380 Let's make it clear, what this is. 59:19.380 --> 59:26.080 What the VIX is, is the sigma in the Black-Scholes equation. 59:26.080 --> 59:32.890 But it is, in effect, the market's expected standard 59:32.890 --> 59:34.620 deviation of stock prices. 59:34.620 --> 59:38.610 And to get it more precise, it's the standard deviation of 59:38.610 --> 59:45.310 the S&P 500 Stock Price Index for one month, multiplied by 59:45.310 --> 59:49.110 the square root of 12, because they want to annualize it. 59:49.110 --> 59:50.360 It's for the next month. 59:57.250 --> 59:59.420 Why do they multiply it by the square root of 12? 59:59.420 --> 1:00:02.050 Well, that's because, remember the square root rule. 1:00:02.050 --> 1:00:04.520 These stock prices are essentially independent of 1:00:04.520 --> 1:00:07.880 each other month to month, so the standard deviation of the 1:00:07.880 --> 1:00:12.240 sum of 12 months is going to be a square root of 12 times a 1:00:12.240 --> 1:00:15.460 standard deviation of one month. 1:00:15.460 --> 1:00:17.730 And this is in percent per year. 1:00:17.730 --> 1:00:19.130 So, that means that the implied 1:00:19.130 --> 1:00:25.950 volatility in 1986 was 20%. 1:00:25.950 --> 1:00:31.840 And then, it shot way up to 60%, unimaginably quick. 1:00:31.840 --> 1:00:36.260 That might be the record high, I can't quite tell from here. 1:00:36.260 --> 1:00:38.660 Remember, I told you the story of the 1987 1:00:38.660 --> 1:00:40.290 stock market crash? 1:00:40.290 --> 1:00:43.260 The stock market fell over 22% in one day. 1:00:43.260 --> 1:00:47.020 Well, actually, on the S&P, it was only 20%, but 1:00:47.020 --> 1:00:48.210 a lot in one day. 1:00:48.210 --> 1:00:50.800 It really spooked the options markets. 1:00:50.800 --> 1:00:54.420 So, the call option prices went way up, thinking that 1:00:54.420 --> 1:00:56.190 there's some big volatility here. 1:00:56.190 --> 1:00:57.570 We don't know, which way it'll be next. 1:00:57.570 --> 1:00:59.790 Maybe it will be up, maybe it will be down. 1:00:59.790 --> 1:01:04.080 It pushed the implied volatility, temporarily, up to 1:01:04.080 --> 1:01:05.400 a huge level. 1:01:05.400 --> 1:01:08.050 It came right back down. 1:01:08.050 --> 1:01:12.610 My actual volatility, I calculated this for each day 1:01:12.610 --> 1:01:14.290 as the volatility of the market over 1:01:14.290 --> 1:01:16.070 the preceding year. 1:01:16.070 --> 1:01:21.130 Well, since I put October 1987 in my formula, I got a jump up 1:01:21.130 --> 1:01:26.110 in actual volatility, but not at all as big as the options 1:01:26.110 --> 1:01:26.880 market did. 1:01:26.880 --> 1:01:31.220 See, the option market is looking ahead and I have no 1:01:31.220 --> 1:01:35.850 way to look ahead, other than to look at the options market. 1:01:35.850 --> 1:01:39.810 So, to get my actual volatility, I was obliged to 1:01:39.810 --> 1:01:44.280 look at volatility in the past, and it went up because 1:01:44.280 --> 1:01:47.350 of the 1987 volatility, but not so much. 1:01:47.350 --> 1:01:50.490 So what this means is, that, in 1987, 1:01:50.490 --> 1:01:52.320 people really panicked. 1:01:52.320 --> 1:01:54.380 They thought something is really going on 1:01:54.380 --> 1:01:55.310 in the stock market. 1:01:55.310 --> 1:01:58.440 They didn't know what it was and they were really worried, 1:01:58.440 --> 1:02:03.400 and that's why we see this spike in implied volatility. 1:02:03.400 --> 1:02:06.290 There's a couple other spikes that I've noted, the Asian 1:02:06.290 --> 1:02:10.610 financial crisis occurred in the mid 1990's. 1:02:10.610 --> 1:02:16.900 Now, that is something that was primarily Asian, but it 1:02:16.900 --> 1:02:19.720 got people anxious over here as well. 1:02:19.720 --> 1:02:25.350 You know, Korea, Taiwan, Indonesia, Hong Kong, these 1:02:25.350 --> 1:02:27.790 countries had huge turmoil. 1:02:27.790 --> 1:02:31.810 But it came over here in the form of a sudden spike in 1:02:31.810 --> 1:02:33.360 expected volatility. 1:02:33.360 --> 1:02:36.130 People thought, things could really happen here. 1:02:36.130 --> 1:02:40.500 So, all the option prices got more valuable. 1:02:40.500 --> 1:02:41.770 And then there's this spike. 1:02:41.770 --> 1:02:43.800 This is the one that you remember. 1:02:43.800 --> 1:02:46.850 This is the financial crisis that occurred in 1:02:46.850 --> 1:02:48.610 the last few years. 1:02:48.610 --> 1:02:55.070 Notably, it peaks in the fall of 2008, which was the real 1:02:55.070 --> 1:02:58.690 crisis, when Lehman Brothers collapsed, and it created a 1:02:58.690 --> 1:03:01.090 crisis all over the world. 1:03:01.090 --> 1:03:05.510 There was a sharp and sudden terrible event. 1:03:05.510 --> 1:03:10.410 And you can see, that actual volatility shot up to the 1:03:10.410 --> 1:03:14.120 highest since 1986, as well, at that time. 1:03:14.120 --> 1:03:20.320 So, implied volatility, you can't ask easily from this 1:03:20.320 --> 1:03:22.620 chart, whether it was right or wrong. 1:03:22.620 --> 1:03:27.260 People were responding to the information, and the response 1:03:27.260 --> 1:03:29.210 felt its way into options prices. 1:03:32.880 --> 1:03:35.520 There's no way to find out, ex post, whether they were right 1:03:35.520 --> 1:03:37.070 to be worried about that. 1:03:37.070 --> 1:03:44.500 But they were worried about these events, and it led to 1:03:44.500 --> 1:03:47.110 big jumps in options prices. 1:03:47.110 --> 1:03:53.880 Now, I wanted to show the same chart going back even further, 1:03:53.880 --> 1:03:57.370 but I can't do it with options prices, because I can show 1:03:57.370 --> 1:04:01.710 volatility earlier, but I can't show implied volatility 1:04:01.710 --> 1:04:06.470 before around 1986, because the options markets weren't 1:04:06.470 --> 1:04:07.180 developed yet. 1:04:07.180 --> 1:04:14.660 But I computed an actual S&P Composite volatility. 1:04:14.660 --> 1:04:17.680 Well, in my chart title, I said S&P 500. 1:04:17.680 --> 1:04:21.160 The Standard and Poor's 500 Stock Price Index technically 1:04:21.160 --> 1:04:27.400 starts in 1957, but I've got what they call the Standard 1:04:27.400 --> 1:04:32.420 and Poor's Composite back to 1871. 1:04:32.415 --> 1:04:40.645 And so, these are the actual moving standard deviations of 1:04:40.650 --> 1:04:46.720 stock prices, all the way back to the beginnings of the stock 1:04:46.720 --> 1:04:49.840 market in the U.S. Well, not the very beginnings, but the 1:04:49.840 --> 1:04:53.780 earliest that we can get consistent data for, on a 1:04:53.780 --> 1:04:55.030 monthly basis. 1:04:57.440 --> 1:04:59.660 And you can see, this goes back further 1:04:59.660 --> 1:05:02.650 than the other chart. 1:05:02.650 --> 1:05:06.860 You can see that the actual volatility of stock prices, 1:05:06.860 --> 1:05:11.340 except for one big event, called the Great Depression of 1:05:11.340 --> 1:05:16.240 the 1930s, has been remarkably stable, right? 1:05:16.240 --> 1:05:21.180 The volatility in the late 20th century, early 21st 1:05:21.180 --> 1:05:26.360 century, is just about exactly the same as the volatility in 1:05:26.360 --> 1:05:28.040 the 19th century. 1:05:28.040 --> 1:05:32.070 It's interesting, how stable these patterns are. 1:05:32.070 --> 1:05:36.250 There was this one really anomalous event that just 1:05:36.250 --> 1:05:41.350 sticks out, and that is the Great Depression. 1:05:41.350 --> 1:05:45.260 1929 precedes it, it's somewhere in here. 1:05:45.260 --> 1:05:49.710 But somehow people got really rattled by the 1929 stock 1:05:49.710 --> 1:05:51.590 market crash. 1:05:51.590 --> 1:05:54.930 And not just in the U.S. This is U.S. data, but you'll find 1:05:54.930 --> 1:05:57.080 this all over the world. 1:05:57.080 --> 1:06:02.430 It led to a full decade of tremendous stock market 1:06:02.430 --> 1:06:09.200 volatility around the world, that has never 1:06:09.200 --> 1:06:11.850 been repeated since. 1:06:11.850 --> 1:06:17.640 The recent financial crisis has the second highest 1:06:17.640 --> 1:06:21.060 volatility after the Great Depression. 1:06:21.060 --> 1:06:22.350 This isn't long ago. 1:06:22.350 --> 1:06:25.640 This is well within your memories. 1:06:25.640 --> 1:06:33.580 Just a few years ago, we had another huge impact on 1:06:33.580 --> 1:06:36.150 volatility. 1:06:36.150 --> 1:06:38.950 And as you saw on the preceding slide, it had a big 1:06:38.950 --> 1:06:42.110 impact on implied volatility as well. 1:06:44.840 --> 1:06:48.880 So, I think that we had a near miss of another depression. 1:06:48.880 --> 1:06:52.010 It's really scary what happened in this crisis. 1:06:55.740 --> 1:06:59.770 Also shown here is the first oil crisis, which we talked 1:06:59.770 --> 1:07:04.800 about, in 1974, when oil prices had been locked into a 1:07:04.800 --> 1:07:07.540 pattern because of the stabilization done by the 1:07:07.540 --> 1:07:08.980 Texas Railroad Commission. 1:07:08.980 --> 1:07:13.820 But when that broke, and OPEC first flexed its muscles, it 1:07:13.820 --> 1:07:16.900 created a sense of new reality. 1:07:16.900 --> 1:07:21.590 And it caused fear, and it caused a big spike up in the 1:07:21.590 --> 1:07:26.130 volatility of the stock market, but not quite as big 1:07:26.130 --> 1:07:27.670 as the current financial crisis. 1:07:27.670 --> 1:07:30.340 So, this is an interesting chart to me. 1:07:34.740 --> 1:07:37.770 A lot of things I learned from this chart, and let me 1:07:37.770 --> 1:07:40.910 conclude with some thoughts about this. 1:07:40.910 --> 1:07:44.000 But what I learned from this chart is that, somehow, 1:07:44.000 --> 1:07:48.170 financial markets are very stable for a long time. 1:07:48.170 --> 1:07:50.550 So, it would seem like it wouldn't be that much of an 1:07:50.550 --> 1:07:51.340 extrapolation -- 1:07:51.340 --> 1:07:53.100 when are you people going to retire? 1:07:53.096 --> 1:07:56.386 Did you pick a retirement date yet? 1:07:56.390 --> 1:07:59.470 Well, let's say a half century from now, ok? 1:07:59.470 --> 1:08:05.720 So, that would be 2060? 1:08:05.720 --> 1:08:08.820 So, you're going to retire out here, all right? 1:08:08.819 --> 1:08:10.739 Your whole life is in here. 1:08:10.740 --> 1:08:12.870 What do you think volatility is going to do 1:08:12.870 --> 1:08:14.690 over that whole period? 1:08:14.689 --> 1:08:16.849 Well, judging from the plot, it's probably 1:08:16.850 --> 1:08:18.270 pretty similar, right? 1:08:18.270 --> 1:08:20.400 That's not much more history compared to what 1:08:20.399 --> 1:08:21.579 we've already seen. 1:08:21.579 --> 1:08:24.259 It's probably just going to keep doing this. 1:08:24.260 --> 1:08:26.650 But there's this risk of something like 1:08:26.649 --> 1:08:28.679 this happening again. 1:08:28.680 --> 1:08:38.540 And we saw a near miss here, but this plot encourages me to 1:08:38.540 --> 1:08:44.090 think that maybe outliers, or fat tails, or black swan 1:08:44.090 --> 1:08:50.050 events, are the big disruptors of economic theory. 1:08:50.050 --> 1:08:55.470 Black-Scholes is not a black swan theory. 1:08:55.470 --> 1:08:59.940 It assumes normality of distributions, and so, it's 1:08:59.939 --> 1:09:01.319 not always reliable. 1:09:05.319 --> 1:09:11.149 So, this leads me to think that option pricing theory -- 1:09:11.149 --> 1:09:13.569 I presented a theory. 1:09:13.569 --> 1:09:18.249 The Black-Scholes theory is a very elegant and very useful 1:09:18.250 --> 1:09:22.820 tool, especially useful when things behave normally. 1:09:22.819 --> 1:09:25.439 But I think, one always has to keep in the back of one's 1:09:25.439 --> 1:09:33.749 mind, the risk of sudden major changes like we've seen here. 1:09:33.750 --> 1:09:35.710 So, let me just you give us some final 1:09:35.710 --> 1:09:38.090 thoughts about options. 1:09:38.090 --> 1:09:39.850 I launched this lecture by saying, 1:09:39.850 --> 1:09:42.040 they're very important. 1:09:42.040 --> 1:09:51.640 And they affect our lives in many ways. 1:09:51.640 --> 1:09:55.520 I've been trying to campaign for the expansion of our 1:09:55.520 --> 1:09:58.770 financial markets. 1:09:58.770 --> 1:10:03.050 Working with my colleagues and the Chicago Mercantile 1:10:03.050 --> 1:10:08.260 Exchange, we launched options, in 2006, on single-family 1:10:08.260 --> 1:10:10.640 homes in the United States. 1:10:10.640 --> 1:10:13.580 We were hoping that people would buy put options to 1:10:13.580 --> 1:10:17.770 protect themselves against home price declines, but the 1:10:17.770 --> 1:10:21.570 market never took off. 1:10:21.570 --> 1:10:25.270 We have, since, seen huge human suffering because of the 1:10:25.270 --> 1:10:27.360 failure of people to protect themselves 1:10:27.360 --> 1:10:29.170 against home price declines. 1:10:31.890 --> 1:10:36.700 There were various noises that were made by people in power, 1:10:36.700 --> 1:10:39.840 that suggested that maybe something could be done. 1:10:39.840 --> 1:10:43.190 President Obama proposed something called Home Price 1:10:43.190 --> 1:10:46.750 Protection Program, and it sounded like an option, a put 1:10:46.750 --> 1:10:48.160 option program. 1:10:48.160 --> 1:10:50.800 But, actually, it was a much more subtle program than that. 1:10:50.800 --> 1:10:54.910 It was a program to incentivize mortgage 1:10:54.910 --> 1:11:00.280 originators to do workouts on mortgages, if the mortgages 1:11:00.280 --> 1:11:02.350 would default -- 1:11:02.350 --> 1:11:03.880 if home prices were to fall. 1:11:03.880 --> 1:11:05.430 And nothing really happened with it. 1:11:05.430 --> 1:11:09.510 The President can't get things started, either, not always. 1:11:09.510 --> 1:11:12.070 I've been proposing that mortgages should have put 1:11:12.070 --> 1:11:14.510 options on the house attached to them. 1:11:14.510 --> 1:11:17.410 When you buy a house, get a mortgage, you should 1:11:17.410 --> 1:11:19.010 automatically get a put option. 1:11:19.010 --> 1:11:21.270 I've got a new paper on that. 1:11:21.270 --> 1:11:23.000 But these are kind of futuristic 1:11:23.000 --> 1:11:24.250 things at the moment. 1:11:26.720 --> 1:11:30.340 I'm just saying this at the end, just to try to impress on 1:11:30.340 --> 1:11:35.450 you, what I think is the real importance of options markets. 1:11:35.450 --> 1:11:39.910 People don't manage risks well in the present world. 1:11:39.910 --> 1:11:42.960 Having options or insurance-like contracts of an 1:11:42.960 --> 1:11:46.910 expanded nature will help people manage their risks 1:11:46.910 --> 1:11:51.770 better, and it will make for a better world. 1:11:51.770 --> 1:11:53.830 OK. 1:11:53.830 --> 1:11:56.190 I'll see you on Monday.