The Quest to Price Options

Good morning, Tyler.

Good morning, Alex.

So today we're going to look at one of the most exciting quests in the history of economics and finance, the quest for a formula, the formula to price options. And it's a quest that involves some of the greatest minds in economics: Samuelson, Merton, Fisher-Black, even Einstein will make an appearance. Now, Maybe we should give our audience some background on what an option is.

Sure, why don't you just start by telling us what's a call and what's a put?

Okay, a call option gives the owner the right to buy a stock or an asset for a certain price, which is called the exercise or the strike price, up until a specified time. So for example, I might have the, the right to to buy a stock for a price of $10 anytime in the next 3 months. So in this example, $10 is the exercise or the strike price, and 3 months is, is the time period. Now the other important kind of option is called a put, and a put option gives the owner the right to sell a stock for a certain price, again called the exercise or the strike price, for a specified time. So for example, I might have the right to sell a stock for a price of $150 anytime in the next 3 months.

And just for further background, options of that sort have been traded in public markets in the United States basically starting in the 1970s, but option-like instruments go back much further. Warrants, which are options on stocks but not fully traded options, have been around for much longer. A lot of the early developments of option pricing theory were actually on warrants. And much longer term, going back at least to the 17th century, options have been traded in places such as Italy and the Dutch Republic.

Right. So the quest is to figure out what an option is worth. How much should I be willing to pay, you know, to buy a put or a call? And what makes this interesting is that we have kind of some— we got some ideas of what it might be worth. So for example, suppose the option gives the right to buy a stock for a strike price of $10, and suppose the stock is currently trading at $100, and the option is going to expire in the next few hours. Well, then the option, it's got to be worth like $90, right? You have a right to buy something which is trading for a price of $100, You could buy it for 10, and it's only going to— the price is not going to change very much in the next few hours. So it's got to be worth 90, right? So we kind of have some ideas at the extremes. Similarly, I mean, if you have the right to buy a stock for a price of 500 and the stock is selling for 20 and the option is about to expire, the option is worthless.

But of course, volatility is your friend in these circumstances, right?

Exactly. So that then is the key case, right? Suppose we have a right to buy a stock for $100 and the current price of the stock is $100, but the option is not going to expire for 3 months. Well, like literally, if you were to exercise the option, you have the right to buy something for $100, which is worth $100. You get nothing, but you've got 3 months. So if the stock is volatile, the price could go up and the option it could be worth a lot. If it's volatile downwards, it could be worth nothing. So in the middle is where we're not sure, what is this thing worth? And that's what this quest for a formula is all about.

And just for further background, there's both what are called American options and European options. The European you can exercise only at expiration. The American you can exercise at any time throughout.

Exactly, exactly. So this problem took a long time to be solved, almost 70 years, but it was almost solved in 1900 by this guy, Louis Bachelier. Don't know if I'm saying his name right. He was a French mathematician and he wrote this incredible dissertation.

And his chair was Henri Poincaré, which is amazing. And Poincaré didn't think much of him.

Yeah.

He didn't promote him. He's like, whatever, you go ahead and do this.

Exactly, exactly right. So Poincaré, Poincaré, I think was a little bit confused by this guy because evidently a smart guy, but he'd had some misfortunes in his life. His parents had died young. He'd had to take care of his siblings and he had to work while he was doing his dissertation. And, you know, I always tell my students, You know, if you've got to work while doing it, it's not a good idea, first of all. But if you have to work while doing your dissertation, try and do your dissertation about your job, you know, something that you're doing, you know. And Bachelier took this advice and he was working for the Paris Bourse, the stock exchange in Paris. So he knew something about stocks and options and he said, okay, I'm going to apply mathematics really kind of for the first time, he's going to apply mathematics to figure out the pricing these options. And I think Poncaire thought, the guy's pretty smart, but like, why is he doing this weird stuff, right?

It's striking to me how this, this whole French tradition of either mathematicians or engineers coming out of nowhere with no other background— Cournot in 1838, Jules Dupuit in 1844— and just inventing full cloth out of their head. Significant parts of economics, and then they often go on and do something else, and they're often ignored by the rest of the world for quite some period. It's a French thing, not a British thing. The British tradition is you have people working on political economy for decades, they correspond with each other, they publish pamphlets, the pamphlets become books. But the French, my goodness, it's mathematical and just— there it is, it arrives.

Yeah, exactly right. So Cournot, you know, the Cournot equilibrium Cornot's Nash equilibrium.

That's right, in 1838. No one knew and not many people cared. I think Dupuit cared, but—

Yeah, and Dupuit has got a natural monopoly and marginal cost pricing. Yeah, and he's got third-degree price discrimination. Yeah, he's got it all done. And yeah, the amazing thing is, is that the economists pay no attention to these guys. Because I think the mathematics is actually too advanced.

That's right.

For them, you know, at the time. And only much later do they get the recognition that they deserve. And that was true for Cournot. It's also true for Bachelier. So he writes—

It's interesting, you know, Keynes in his probability treatise cites Bachelier, but not for options pricing. You know, it's for general work on probability. So Keynes knew of the guy, had no notion that what he was doing was important, though Keynes himself was an investor and trader. So just this theme of blindness in the history of economic thought, I find it very interesting. And you've got to wonder, like, what is it we're blind to now?

Yeah, should we be paying attention to the econophysicists a little bit more?

Maybe we are already. That could be our next episode.

Maybe. So he writes this bachelor's, he writes this amazing dissertation, which is a combination of economic reasoning and really high-level mathematics. So he knows from his time at the Bourse that stock prices kind of look random, and in his dissertation, he reasoned that a speculator couldn't predict what tomorrow's price would be, because if they could, they would buy today until the price today was equal to the expected price tomorrow. So the only thing that should move prices would be news. And news, by definition, is random. So he's got Fama's right there, right?

That's right.

Efficient markets.

And some notion of Brownian motion, which now we take for granted, but at the time, people were still working out. He understood something like that, which has now morphed into ideas more like random walk and martingale. But something like that was the correct starting point. And that was just brilliance. Jevons was playing around with ideas of Brownian motion, but he got it wrong.

Yeah.

And finally, Bachelier had a not completely correct version of the idea, but correct enough to lead to further progress.

Absolutely. So Brownian motion, this is where Einstein comes in, because a few years later, Einstein also has a prediction, has an explanation for Brownian motion. Brownian motion was this— Robert Brown, a botanist, had first noticed that if you had these little seeds, you know, embedded in kind of water or something like that, they would actually jump around. They would actually fluctuate, move back and forth. And other people had noticed this in the air as well. And Einstein gives this explanation, which is that they're being bombarded by atoms. So this is some— one of the first proof that atomic theory might actually represent something in the real world. And Einstein actually derives the mathematics and makes some predictions about Brownian motion and about atoms, which later turned out to be correct. So it's one of Einstein's biggest papers. But interestingly, Samuelson, who we'll come to a little bit later— Samuelson later looks back in the 1970s and he's reading Bachelier and Einstein And he says Bachelier like runs, you know, runs the track all around Einstein. He's got much better mathematics than Einstein did.

What I find quite interesting is the story of how this got passed down. So supposedly, I think it was Stanislav Ulam who worked on the Manhattan Project. He was a Monte Carlo theorist. He first mentioned Bachelier to Samuelson early on. Nothing happened. And then much later, Leonard Savage, of Friedman and Savage fame, he wrote a bunch of postcards to famous people and just told them, oh, you ought to check out Bachelier. And he sent one of those postcards to Samuelson. So a postcard that changed history. Obviously, there's no email at this point in time. But prepare your postcards.

It's like a tweet.

I get so many emails. Sending someone a postcard, perhaps once again, is the right way to reach them with an important idea. And if Savage, or someone like Savage, sent me a postcard, I would take it very seriously.

Yeah, yeah, yeah. So, uh, and this is after Bachelet is dead. So he has a decent career, right? But he's never lauded in his—

Mostly known for other things. If you look at his patterns—

Probability theory, but yeah, that's right, that's right. He has a decent career. He's never lauded in his lifetime. The mathematicians, they pay a little bit of attention. The economists don't know about his work. Until, as you say, Paul Samuelson gets this postcard. And Samuelson, just to give some background, I mean, he is— he's not the GOAT, right?

No, he's not.

He's not the GOAT, but he's definitely a contender, right?

And he's one of the most impressive minds. For having an impressive mind alone, maybe he would be the GOAT, but of course other things matter too.

Yeah, yeah, yeah, yeah. And he certainly— I would argue he's the most influential economist of the 20th century.

Maybe, probably.

I mean, in terms of—

well, by Keynes, right?

Well, what I mean, influential not on the world but on economics. Yes, totally changed how economics was done.

That's right.

Right, so he comes in and in his dissertation, which is the Foundations of Economic Analysis, I mean, it reads like a graduate text in economics today. I mean, he totally changes how economics is done. In any case, he gets this postcard from Jimmy Savage, and he immediately goes to the library, finds Bachelet's dissertation, he reads it in French. Yes, itself an achievement. Exactly, exactly. And he immediately sees that Bachelet is totally on the right track, okay. He understands also that he's got a big advantage.. And that is that the mathematics of random processes has advanced tremendously. And he can then draw on that. But this kind of is tough. It's tough stuff, even for Samuelson. And he takes a first crack at the problem in 1965. He writes what is really a great paper, which is the Rational Theory of Warrant Pricing, option pricing. So warrant is similar, very similar to an option. And in it he credits Bachelier, and he says he's been working on this for like 10 years. And it's a great paper, but he doesn't quite solve it. And there's an interesting part of this. There's an appendix to the paper which is written by a mathematician. So like it's telling you, you know, like Samuelson is not asking other people to write his appendices.

That's right.

Very often. So this is kind of tough stuff.

Now it's interesting, at the same time, there are at least two people, actually more than that, running across the same ideas. Soshin Kasuf writes an economics dissertation at Columbia University. I think that's 1965 also, but it's in the early to mid-'60s. And Edward Thorp, and they're looking for ways to beat the market. So they're trying to make money off this. Now one of my favorite stories in the option pricing lore. Sheen Kasoof was one of the people who hired me for my first academic job. Oh wow. So this was early 1988. I'm interviewing at UC Irvine, and of course there's no internet back then, so you're interviewing but you don't always know that much about the people who are interviewing you. And I meet with Sheen Kasoof, who was teaching at Irvine, and I more or less ask him, like, you know, what have you done? And he says, well, I invented options pricing theory. And the way he said it in a way that was both credible but not too boastful. And then I recall it was very hard for me to react properly because he was going to vote on my candidacy. And I was like, did you really? Was what I wanted to say. But I sort of smiled and nodded and tried to look as if I fully believed him. In fact, he was not exaggerating, though he didn't get the full picture either. And I was colleagues with Sheen Kasoo for 2 years. He was a very nice man, always supportive of me. And that's what I always remember is meeting Sheen and hearing that he invented options pricing theory. And I'd never heard that before. And it's like, are you just making this up?

Yeah, there is kind of a hidden history here, as often there is. In fact, let's come back to Thorpe a little bit later.

He's still alive, by the way, at age 91, promoting longevity analysis.

He's a very interesting guy. So we'll come back to the hidden history. But let's go ahead with the, a little bit more on the standard history.

Sure.

And then we'll come back and talk about the hidden history. So Samuelson is working on this problem and he is a great student. He gets a great student who is Robert Merton, who is the son of Robert Merton, the sociologist.

That's right.

I guess the father is Robert K. Merton and the son is Robert C. Merton, I think.

Since we're on tape, I'm reluctant to commit myself on this issue.

Yeah. So he's got greatness in the family, and he is Samuelson's teaching assistant and research assistant. And Samuelson says, look, go learn all of this fancy mathematics, okay, on random processes. Now at the same time as Samuelson and Merton are working on this problem, there's another team, which is Fisher-Black and Myron Scholes. Now, Fischer-Black has never taken a course in finance or in economics. He's jumped around in physics and mathematics. He's been kicked out of his PhD program at least once. He does eventually get a PhD in applied mathematics, working actually on, with Marvin Minsky, on artificial intelligence.

Yes. Okay.

So, But then he has a weird career. He goes into management consulting. And through consulting, he starts to learn finance, especially from this guy Jack Traynor. And finance at the time is being revolutionized.

By CAPM, right?

By CAPM, exactly.

Arbitrage, efficient markets hypothesis.

Right. So it was a real backwater of heuristics and rules of thumb and stuff like that. And then a bunch of guys come along, including Treynor, who's developed CAPM, which is the Capital Asset Pricing Model. Okay? The model has two assumptions. Maybe we should talk about it a little bit. Seems pretty obvious. First of all, investors shouldn't buy a few stocks, but instead invest in a large diversified portfolio. That's point one. Point two, no reward without risk.

OK?

Now, if you want a higher return, you've got to take more risk. Now, so far, this seems pretty obvious, right? Don't put all your eggs in one basket. No risk, no reward. What is less obvious is that when investors do buy a large diversified portfolio of stocks, the meaning of risk changes. Almost by definition, If you hold a large diversified portfolio, you don't care about the variance of an individual stock in the portfolio because that's going to be, you know, the law of large numbers says that will even itself out. What you do care about is how much an individual stock adds to the variance of your portfolio, and that depends upon the covariance the covariance of a stock with a portfolio. So now we get, really for the very first time, a sort of scientific understanding of what risk is, what risk is in the financial markets. And it's a new definition. It's the covariance of a stock with a portfolio. That's the risk of the stock. And now once we know the risk of the stock, we can price it much, much better.

And methodologically, you have a whole class of researchers who approach every problem by asking, uh, what's the no arbitrage condition? How do we apply that to solving this problem? And that's going to turn out to be critical for options pricing. But basically, when it came to CAPM and building an efficient portfolio, if you didn't do it properly, there was an arbitrage opportunity that you could lower your risk, but not necessarily your return, just by diversifying more. And then people realized that was a more general way to think about capital structure— Modigliani-Miller theorems, and most other issues in finance and pricing of asset returns.

So Fisher Black, he becomes a devotee of this CAPM model, and he does exactly what you say. He starts thinking about, okay, this CAPM model, it's good for pricing stocks. How do we use it to price other assets? And he thinks, well, we could use it to price options. And he writes down, he's able to derive from this a differential equation. He writes down the equation, but he can't quite solve it.

But the key thing Black did, just to be clear, that Bachelier and others didn't, is he realized that if you had an option and then hedged your option position, that the rate of return on that hedged position had to be the same as the rate of return on the safe asset. And that was the key condition to be written down for then constructing the differential equation that then would be solved by Ito's lemma, which is another story. But it was an arbitrage insight that Black Black brought to the party, so to speak.

Well, did Black bring it to the party, or did Merton bring it to the party?

And Scholes, yeah, but Black and company.

Yeah, yeah, so I think Black was initially, because if you go back and you look at the options pricing paper of Black and Scholes, which is really going to break this whole thing open, they actually have two ways of deriving the price of the option. One of them is using CAPM. And the other one is using the arbitrage argument. And the arbitrage argument actually comes from Merton because— so Black and Scholes— Black has got the differential equation. He can't quite solve it. He goes to Scholes. Scholes has got a lot of data on options. And using the data, they can kind of say, well, this doesn't matter, this does matter. And together, they solve the options— they solve the differential equation.

Here's one of the great ironies of option pricing history, that Merton Senior— you referred to him before— yeah, one of his key contributions was to suggest that a bunch of people would work on a problem but not all of them would get full credit. The credit would end up excessively concentrated. Then on options pricing theory, his son Merton is the one who doesn't get enough credit. Not to take anything away from Black and Scholes, but it ought to be seen as more of a troika than in fact it is. Exactly. So the son lived out this notion that his father had about credit being unfairly distributed.

Yeah, about the right name not being given. So indeed, we tend to call it the Black-Scholes option pricing formula.

It should be Black— well, the order you can debate, but Black-Merton-Scholes, Black-Scholes-Merton.

Exactly.

Merton did win a Nobel Prize, so we don't need to feel too sorry for him. But he won it for other things.

Yeah, yeah. So Black and Scholes, they start shopping the paper around. And actually it doesn't receive a very good reception.

It's rejected at some journals.

It's rejected.

But like finance doesn't matter. Finance was low status then. Yeah. It was low pay.

Yeah, yeah.

What are you people doing?

Why this? And in fact, they show the paper to Merton, and Merton, he doesn't like the CAPM derivation. So he kind of says, yeah, maybe you should use some kind of arbitrage argument. And that pushes them in the direction of arbitrage. Yes.. And then kind of a remarkable thing happens is that the Journal of Political Economy finally agrees to— after rejecting it once, they agree to publish the Black-Scholes paper after Merton Miller— so this is a different Merton, also a famous guy in finance— after Merton Miller and Fama intervene and they say, look, you got to publish this, really good paper, to They go to the editors and they say, we're going to push this. And interestingly, they have some ulterior or extrinsic motives for doing this. They like the paper, of course. But at the same time, James Lorie, who is in the Center for Research in Stock Prices, he is— he and Merton, Merton Miller and Fama, they actually want— are working to create at the Chicago Board of Trade an exchange to actually buy and sell options, which has not been done before. Right? So all of this is going on really at Chicago all at the same time. There's a push to create an options market at the same time as there's all these advances in theory on options pricing. So Chicago really gets a huge amount of credit for advancing the theory and the city, not just the actual city of Chicago.

Absolutely. The Board of Trade, a number of different people there, the overall environment. And the Black-Scholes paper is published in '73, just to be clear on that.

Right. The SEC approves the Board of Exchange for Options in 1971. It opens for business in 1973. So everything is coming together. Within years of the paper being published, the exchange and the exchange established, there's billions of dollars worth of options are being traded. Here's another point about the father and the son burden because Fischer Black and Scholes are having all of this trouble getting this paper. Accepted at a journal. Meanwhile, Merton has his own proof of options pricing theory. He has developed it in sort of continuous time, a more advanced actually arbitrage argument. And he has a guaranteed publication ahead of Merton and Scholes. And he says to the editors—

Ahead of Black and Scholes.

Ahead of Black and Scholes, yeah, excuse me. Head of Black and Scholes. And he says to the editor, look, I want to publish this paper, but you can't publish it until Black and Scholes have published their paper. This is kind of remarkable in the history. It is. Yeah.

Yeah. I don't hear too much of people doing that these days.

No, no. And they don't know it then, but there is a Nobel Prize, you know, at stake here.

That's right.

Right. And for Merton to kind of say, I'll put these guys first, when it's very clear that, you know, the first person to publish the paper, that is going to— in fact did result in the naming, you know, of Black-Scholes, you know, options pricing theory. So that was kind of a remarkable thing that Merton did.

Absolutely. It's interesting also the history of Black-Scholes in use. So it takes a little while to be adopted. At some point, it's like programmed into portable calculators. But over time, it's actually used less, and it's just seen as a stepping stone toward other approaches. And if you look at the history empirically of how options actually were priced, before Black-Scholes, obviously fragmentary data, but it seems options are a bit overpriced. And then you look at the markets a bit after Black-Scholes. Again, there's enormous variety and diversity of what's going on, but there's a number of papers that show, well, on average, some of these options are overpriced. So the people intuitively before Black-Scholes had a sense of some of what matters. They didn't get it entirely wrong. And post-Black-Scholes, there's just a lot more going on. And, uh, The methods have become far more complex and far more mathematical, and what's going on is typically not readily transparent to human beings. It's not what they call interpretable in the AI literature. It's a lot of machine learning or neural nets, but you have things that you do and you run it and it seems to work and you can arbitrage, but the trade you make may not be valid, say, half an hour later.

Yeah, yeah, yeah, I think the invisible hand should get some credit here too because as I mentioned, Sholes had brought sort of the empirical data and was using the empirical data to kind of figure out what mattered. So that was one thing. And then afterwards, Black and Sholes actually, as academics are wont to do, tried to use their model to make some money, right?

Yeah, and Sheen Kasoof and Thorpe were doing this all along.

Yeah, yeah, yeah.

They wrote this book in 1967 called Beat the Market, right?

So And Black Scholes actually lose money, right? So they find these really what looked to be underpriced options or overpriced, I can't remember exactly. But it turned out that they buy into these options, overpriced options, they sell the options. But it turns out that the market was implicitly including in the price of these options the possibility of a takeover. Okay, so, uh, the market sometimes knows even more than the model knows.

I believe Sheen, Kassouf, and also Thorpe made quite a bit of money with what they were doing. And when they wrote their Beat the Market book, it's interesting, but Samuelson reviewed that book and he was very harsh. He just said this is astrology, they're not approaching it scientifically. And they, it seems, made money from what they were doing. I think Sheen lived in a very nice house in Orange County. He was a quite relaxed fellow when I got to know him.

Yeah, so let's talk about Kassouf and also Thorpe. So Thorpe, people may know him better as I believe he's the guy who beat the casinos.

That's right, card counting.

Card counting, exactly. So they had the computer and the shoe and the earpiece and all that kind of stuff. And they figured out all of these techniques. He made a lot of money from that. And he has always claimed that he had a, the, or a options pricing model. It's a little bit unclear, right? But he used whatever model he had to make money, and you know, by all accounts, he was very successful at making money.

That's right.

So the hidden history is that maybe there were people in the background who actually knew.

And Thorpe, you know, claims the same general method is what has kept him alive at age 91. And you look at photos of him, you never know with photos these days, but he seems to be in great shape and he's still active. Well, there was a profile of him in Bloomberg Businessweek not long ago. This would be April 2024.

I'd say anyone at 91 is in good shape.

Exactly.

Yeah. All right. Let's bring the history part then to a not quite satisfying close. And that is Samuelson wins the Nobel Prize in 1970. Now, he had plenty of other work deserving of the Nobel even without solving the options problem, so he's doing okay. Robert Merton and Scholes win the Nobel Prize in 1997. Now, this is not quite satisfying because Fischer Black had died just 2 years earlier, but would certainly have been— it would certainly have been a 3-way prize had he not Had he not died.

And he was cited in the award.

Sure.

This is a very sad story for me. So I knew Fisher Black. Periodically, I'd have phone calls with him, which is what he would do with people. Obviously, no internet, no Zoom call. And it was very difficult to have phone calls with him because he would often just go silent for a full minute, and he would be thinking. And maybe that's a good way to do things, but when the other person on the other side of the call doesn't know it. But I figured out this is how Fisher Black phone call went. And he would— the way he would write sometimes, he would just utter statements and then he would think about them, and he would ask very pointed questions. He was always very curious. He would entertain any idea. But I didn't know, leading up to 1995, that Fisher Black was dying. So I was writing some pieces on business cycles that he was interested in, and he kept on telling me, well, Tyler, you know, please send me your work. I'd like to read it as soon as possible. And my attitude was, well, you can't send anything to Fisher Black until it's as good as it can be. I was thinking in terms of option value, like, oh, I can always send it later, right? I was using options. And then suddenly he passed away and never knew that he was dying. And his very last piece, it's funny, but he gave the editors of the journal an option on not publishing it. There's a little note at the bottom where Black writes to the editors and he says, well, I'm not going to get to respond to all the referee comments. You have the option to publish this piece if you want. And that was his famous article, Interest Rates as Options. So he just so consistently thought in terms of options. He was a remarkable guy.

Yeah, yeah, yeah, very remarkable guy. So we have really here a great achievement running through some 70 years of history. Still, you might be wondering, aren't options a fairly esoteric financial device? With little interest outside of finance. No. It turns out that once you start to think about it, a lot of decisions that we have to make have an options-like aspect and thus can be understood with options pricing theory. So let's start with insurance. Insurance, like take car insurance for example. You can think about that as a put option. It's a right to sell the car to the insurance company for a certain price. And if you don't get into an accident, then you keep the car. But if you total the car, the insurance option gives you the right to sell the junk to the insurance company in return for a payment. And so understanding insurance as an option gives firms a new way of thinking about how to price and value insurance.

New Jersey in the 1970s when I grew up, it was common practice. You could leave your car out somewhere, the door open, the keys in the ignition, and oh my goodness, the car would be stolen. It was actually stolen, but that was a way of exercising your option and converting your car into the insurance payment.

Right. And it's not just auto insurance. Think about all of the implicit guarantees that the FDIC and the Fed have given the banks. Right? So they're basically saying, you know, if the value of your assets falls below the value of your equity, you can have a put to the FDIC, to the Fed. The Fed is going to guarantee— the Fed is going to guarantee the value of your deposits. Now, what is that worth? What is that worth to the banks? How much does it cost the government to offer these huge guarantees. You actually have to use options pricing theory to think about the volatility, to think about all of the deltas, to figure out what all of these guarantees are actually worth.

Another example I find persuasive is I think the notion of options explains some of unemployment. So say you're in a business cycle downturn. Why don't you just take a job at a lesser company for a lower wage rather than be out of work? You might not even mind the work. But combined with signaling theory, in essence you're branding yourself as a lower quality worker. You would prefer to exercise that option by staying out of the labor pool and waiting for the better job to come along.

Right, so you don't want to exercise too early.

Now here's one of my worries when options become so important. So we all know Hayek's story of the market price system working, and everyone can observe prices. But when options are important, and we know they are, They're much harder to observe. So there's not an explicit market out there, or if there is, the market's very hard for almost anyone to read and infer backwards from. So price information is degraded and you observe a bunch of things not happening and you don't know what's the price signal. And that always struck me as one of the more serious criticisms of the market that people don't discuss that much. Same is true with investment. Well, you hold off on some investment The price of the capital goods might fall for a while. Still, no one does anything. You're not sure what the price signals are telling you, because what you need to read is either the option value or an estimate of the risk or something else that's not just on a posted price sticker.

Yeah, yeah, exactly. So without the benefit of the markets, we have— we are reliant on models, which is why, you know, things like when the FDIC and the Fed they offer these huge guarantees. One reason they can do that is because nobody knows, you know, what's the potential cost.

That's right.

To the government.

Highly non-transparent.

Highly non-transparent, right. So you have to kind of use these models to try and figure out, well, what is the potential cost of these things? And we don't have markets to kind of give us that single price. Instead, we have to rely on the models.

It's striking that investment does not seem very elastic with respect to changes in real interest rates, but it's probably quite elastic with respect to changes in uncertainty. But insofar as that's the case, again, it's something other than the price system doing the work. And we— I wouldn't say we need to be non-Hayekian, but we need to modify Hayek in a way that perhaps we're slightly uncomfortable with.

Right, so in the Hayekian-Mises business cycle theory, the, the interest rate is really the key thing, and everyone's just following the interest rate. The interest rate falls because of, you know, government increases supply of money or something like that, and everyone just goes into investment.

Yeah, and it was Black himself who said, no, it's changes in the risk premium that are doing the work. That was what he was working on before he died. The papers of mine he wanted to see were actually on the same idea, that changes in the risk premium might be driving investment, and how do we think about those in a business cycle context.

Yeah, those seem to be much more important than the pure interest rate itself. And there's a lot of investment decisions that you can think about like an option. So suppose you have a 10-year mineral lease which gives you the right to drill an oil well anytime in the next 10 years. Well, when should you drill? I mean, it seems obvious that the higher the price of oil, the greater should be your incentive to drill.. But the price of oil goes up and down, right? You don't want to drill the well and then find out that oil prices have dropped below the cost of extraction. So once— and once the well has been drilled, the costs are sunk, literally in this case. So you can think about the decision to drill the oil well as exercising the option to drill, and you want to use some model to figure out when, given the volatility of oil prices, when is the optimal time to drill the well.

It's related to seeing all these underdeveloped or undeveloped storefronts in American cities. Oh, there's something that used to be a store, now it's all boarded up. Why don't they put something in there? Why doesn't the price adjust? Sometimes it's regulation, legal issues, but sometimes it's option value. You're not sure what you're going to put in. You don't want to have to remodel the thing again. Maybe it should be a restaurant, but your town is not yet ready for a Brazilian churrascaria, and in the meantime everyone's waiting.

Right. And exactly as you said before, also applies to unemployment. Maybe you don't want to take the first job which is offered to you because that's a sunk cost. You have to move to a new place. So if there's a lot of uncertainty, then you actually want to wait. And that uncertainty can then mean that you wait which means that you don't invest, which is what is driving the business cycle itself, right? The non-investment. So the uncertainty causes a lot of people to hold back on making decisions. And that means that the, you know, business cycle can— the downturn could continue.

And it's a major problem in economic development. So the Danish government is relatively credible. Many, but not all parts of the US government are. That enables investment and growth. But there's plenty of countries, if you just look at the books, a lot of their laws don't sound that much worse, say, than US laws, or they might even sound better. But no one knows what the law will be 2, 3, 10 years from now, and it's just harder for them to mobilize the proper incentives.

Right. So ironically, in a way, options pricing theory actually tells us the importance of, you know, the the Fed talk, right?

Yes.

And developing confidence and getting coordination of expectations, right? So put aside what the Fed does with interest rates. Fischer Black thought that was completely unimportant. But one thing which might be important is the Fed can coordinate expectations and can get people all moving in the same direction at the same time. Like, you don't want to, you know, be the first to move, but if you think that other people are going to start investing, then maybe you want to invest as well. So this control of uncertainty, control of expectations, can actually be one of the more important things that institutions like the Fed can do.

And the presidential bully pulpit can matter in a similar way if it's used wisely.

Yeah, yeah, yeah. Like the— like George Bush throwing the pitch. Which seems completely ridiculous, right?

Right.

You know, and yet everyone says it was important. You know, for those of you don't remember, after 9/11, you know, Bush throws out the first pitch. He was a baseball guy and it was a good pitch, you know, went over the base and, and this like everyone created confidence.

Yeah.

And oddly, options pricing theory kind of tells us that, hey, there might be some truth to this.

That's right.

So there are all kinds of these options everywhere you look. And what a lot of firms are doing nowadays is trying to price them much better than the before. So these— the option to wait, the option to invest, the option to abandon a project. Airbus, the European firm, has done a lot of work on moving away from just evaluating a product from so-called net present value and instead focusing much more on trying to price the various kinds of options which are embedded in different types of decisions. And that has improved investment performance.

And lowering exit costs becomes a new way to think about policy. So in much of the EU, as you know, it can be quite difficult to fire workers or some kinds of workers. So that means a higher exit cost. So ex ante, you're gonna wait more. The project has to appear to be in the black by a much higher— no pun intended— in the black by a much higher degree than otherwise would be the case because exit is very difficult.

Right. Yeah, I see.

Bankruptcy law matters a great deal also. That's another way of lowering exit costs. The US has done a pretty good job of that, and we have this cultural phenomenon where you can be a failure and still raise money again, often, not always.. And that too makes people more willing to move in advance. So to think backwards from the exit cost is again a different way of evaluating a lot of different policies.

Yeah. Yeah, I say that in the United States when you hire someone, it's like going on a date. In Europe, when you hire someone, it's like getting married. That's right. So your exit costs are much, much higher, and that flows back into the hiring decision and how quickly you are to hire. And if you want people to be quick to hire, you have to allow them to be quick to fire as well.

And we live in a world of tenured academia where the proportion of tenured slots has been falling dramatically for quite a while now. More adjuncts are hired, and that too is an issue related to exit costs. How can a school get out of that relationship?

Okay, uh, options pricing theory. Begun by Bachelier, advanced by Samuelson, culminated in the work of Black, Scholes, and Merton. It extends well beyond the trading floors, shaping areas like the creation of new financial tools, portfolio insurance, guiding investment decisions from oil wells to mega-sized chip plants. And most importantly, options pricing theory has revolutionized the understanding and the management of uncertainty and risk, enabling more accurate pricing and better-informed decision-making.

I would sum up by saying it's one of the most important ideas in economics. It came oddly late, and as a concept, it's still underrated.

And hey hey to the French mathematicians.

Absolutely.

Very good.

Thank you, Alex.

Thank you, Tyler Cowen.