In the final episode of Season 1, Alex and Tyler explore one of the most consequential quests in the history of economics and finance: the decades-long search for a formula to price options. From Louis Bachelier's groundbreaking work in 1900 to the eventual triumph of Black, Scholes, and Merton in the 1970s, they trace how brilliant minds across mathematics, physics, and economics gradually unlocked the how to properly price financial instruments like calls and puts. Along the way, they examine how this theoretical breakthrough revolutionized modern markets, sparked the creation of the Chicago Board Options Exchange, and transformed our understanding of uncertainty and risk management. The conversation ranges from the hidden histories of early options traders to how options theory now shapes everything from portfolio insurance to oil well investments to mega-sized chip plants. They close by reflecting on how options theory has become fundamental to modern decision-making far beyond trading floors, revolutionizing how we think about and manage uncertainty across the entire economy. 

Watch the video

Read the full transcript

TABARROK: 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. It’s a quest that involves some of the greatest minds in economics: Samuelson, Merton, Fischer Black, even Einstein will make an appearance. Now, maybe we should give our audience some background on what an option is.

COWEN: Sure. Why don’t you just start by telling us what’s a call and what’s a put?

TABARROK: 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. For example, I might have the right to buy a stock for a price of $10 any time in the next three months. In this example, $10 is the exercise or the strike price, and three months is the time period. 

Now, the other important option is called a put. 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. For example, I might have the right to sell a stock for a price of $150 at any time in the next three months.

COWEN: Just for further background, options of that sort have been traded in public markets in the United States, basically starting in the 1970s. 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. Much longer term, going back at least to the 17th century, options have been traded in places such as Italy and the Dutch Republic.

TABARROK: The quest is to figure out what an option is worth. How much should I be willing to pay to buy a put or a call? What makes this interesting is that we have some ideas of what it might be worth. 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.

Then the option, it’s got to be worth like $90. You have a right to buy something which is trading for a price of $100. You could buy it for $10, and the price is not going to change very much in the next few hours so it’s got to be worth $90. We have some ideas at the extremes. Similarly, 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.

COWEN: Of course, volatility is your friend in these circumstances, right?

TABARROK: Exactly. That then is the key case. 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 three months. 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 three months.

If the stock is volatile, the price could go up and the option could be worth a lot. If it’s volatile downward, it could be worth nothing. 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.

COWEN: 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.

Louis Bachelier's contribution

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

COWEN: His chair was Henri Poincaré, which is amazing. Poincaré didn’t think much of him. He didn’t promote him. He said, “Whatever, you go ahead and do this.”

TABARROK: Exactly right. Poincaré, I think, was a little bit confused by this guy. 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. I always tell my students, if you’ve got to work while doing it, it’s not a good idea, first of all. If you have to work while doing your dissertation, try and do your dissertation about your job, something that you’re doing.

Bachelier took this advice, and he was working for the Paris Bourse, the stock exchange in Paris. He knew something about stocks and options. He said, “Okay, I’m going to apply mathematics.” Really for the first time, he’s going to apply mathematics to figure out the pricing of these options. I think Poincaré thought, the guy’s pretty smart, but why is he doing this weird stuff?

COWEN: It’s striking to me how 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. 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. The French, my goodness, it’s mathematical, and just there it is. It arrives.

TABARROK: Exactly right. The Cournot Equilibrium—Cournot is Nash equilibrium, right?

COWEN: That’s right. In 1838, no one knew and not many people cared. I think Dupuit cared.

TABARROK: Dupuit has got a natural monopoly.

COWEN: Marginal cost pricing.

TABARROK: He’s got a third-degree price discrimination. He’s got it all done. The amazing thing is, is that the economists pay no attention to these guys because I think that mathematics is actually too advanced for them at the time. Only much later do they get the recognition that they deserve. That was true for Cournot. It’s also true for Bachelier. 

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

TABARROK: Should we be paying attention to the econophysicist a little bit more?

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

TABARROK: Maybe. He writes this, Bachelier, he writes this amazing dissertation, which is a combination of economic reasoning and really high-level mathematics. He knows from his time at the Bourse, that stock prices look random. 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. The only thing that should move prices would be news. News, by definition, is random. He’s got Fama’s right there, right?

COWEN: That’s right.

TABARROK: Efficient markets.

COWEN: 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. That was just brilliant. Jevons was playing around with ideas of Brownian motion, but he got it wrong. Finally, Bachelier had a not completely correct version of the idea, but correct enough to lead to further progress.

TABARROK: Absolutely. Brownian motion, this is where Einstein comes in, because a few years later, Einstein also has a prediction, has an explanation for Brownian motion. Robert Brown, a botanist, had first noticed that if you had these little seeds embedded in water or something like that, they would actually jump around. They would actually fluctuate, move back and forth. Other people had noticed this in the air as well.

Einstein gives this explanation, which is that they’re being bombarded by atoms. This is one of the first proofs that atomic theory might actually represent something in the real world. Einstein actually derives the mathematics and makes some predictions about Brownian motion and about atoms, which later turned out to be correct. It’s one of Einstein’s biggest papers.

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 runs the track all around Einstein. It’s got much better mathematics than Einstein did.

Enter Paul Samuelson

COWEN: What I find quite interesting is the story of how this got passed down. Supposedly, I think it was Stanislaw Ulam who worked on the Manhattan Project. He was a Monte Carlo theorist. He first mentioned Bachelier to Samuelson early on, nothing happened. 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.” He sent one of those postcards to Samuelson. It was a postcard that changed history. Obviously, there’s no email at this point in time but prepare your postcards. 

TABARROK: It’s like a tweet. 

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

TABARROK: This is after Bachelier is dead. He has a decent career but he’s never lauded in it.

COWEN: Mostly known for other things if you look at his pattern of—

TABARROK: Probability theory, but yes, 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. Samuelson, just to give some background, he’s not the GOAT, right? 

COWEN: No, he is not.

TABARROK: He’s not the GOAT but he’s definitely a contender, right?

COWEN: 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.

TABARROK: I would argue he’s the most influential economist of the 20th century.

COWEN: Maybe. Probably.

TABARROK: In terms of—

COWEN: It’s Keynes, right?

TABARROK: I mean influential not on the world but on economics.

COWEN: Yes.

TABARROK: He’s totally changed how economics was done.

COWEN: That’s right.

TABARROK: He comes in and in his dissertation, which is the Foundations of Economic Analysis—it reads like a graduate text in economics today. He totally changes how economics is done. In any case, he gets this postcard from Jimmie Savage and he immediately goes to the library. He finds Bachelier’s dissertation. He reads it in French.

COWEN: Itself an achievement.

TABARROK: Exactly. He immediately sees that Bachelier is totally on the right track. 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 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” is option pricing, so warrant is very similar to an option. In it, he credits Bachelier and he says he’s been working on this for 10 years. It’s a great paper but he doesn’t quite solve it and there’s an interesting part of this. There’s an appendix of the paper which is written by a mathematician. Samuelson is not asking other people to write his appendices very often, so this is tough stuff.

COWEN: It’s interesting at the same time there are at least two people, actually more than that, running across the same ideas. Sheen Kassouf 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. They’re trying to make money off this. One of my favorite stories in the option pricing lore, Sheen Kassouf was one of the people who hired me for my first academic job.

TABARROK: Oh, wow.

COWEN: This was early 1988. I’m interviewing at UC Irvine and of course, there’s no internet back then. You’re interviewing but you don’t always know that much about the people who are interviewing you. I meet with Sheen Kassouf who was teaching at Irvine, and I more or less ask him like, “What have you done?” He says, “I invented options pricing theory.”

The way he said it, in a way that was both credible but not too boastful. Then I recall it was very hard for me to react properly because he was going to vote on my candidacy. I was like, “Did you really?” was what I wanted to say but I 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.

I was colleagues with Sheen Kassouf for two years. He was a very nice man, always supportive of me. 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?” 

TABARROK: There is a hidden history here, as often there is. In fact, let’s come back to Thorp a little bit later. 

COWEN: Who is still alive by the way, at age 91, promoting longevity analysis.

TABARROK: He’s a very interesting guy. 

Black, Scholes, and Merton
TABARROK: So we’ll come back to the hidden history, but let’s go ahead with a little bit more on the standard history. Then we’ll come back and talk about the hidden history. 

Samuelson is working on this problem and he has a great student. He gets a great student who is Robert Merton, who is the son of Robert Merton, the sociologist. The father is Robert K. Merton and the son is Robert C. Merton, I think.

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

TABARROK: He’s got greatness in the family, and he is Samuelson’s teaching assistant and research assistant. Samuelson says, “Look, go learn all of this fancy mathematics on random processes.” 

At the same time as Samuelson and Merton are working on this problem, there’s another team which is Fischer Black and Myron Scholes. 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 with Marvin Minsky on artificial intelligence, but then he has a weird career. He goes into management consulting. Through consulting, he starts to learn finance, especially from this guy Jack Treynor. Finance at the time is being revolutionized.

COWEN: By CAPM, right?

TABARROK: Exactly.

COWEN: Arbitrage, efficient markets hypothesis.

TABARROK: It was a real backwater of heuristics and rules of thumb and stuff like that. Then a bunch of guys come along including Treynor, who’s developed CAPM, which is the capital asset pricing model. This 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. If you want a higher return, you’ve got to take more risk. Now, so far, it 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 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 of a stock with a portfolio. Now we get, really for the very first time, a scientific understanding of what risk is in the financial markets. 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 better.

COWEN: Methodologically, you have a whole class of researchers who approach every problem by asking, “What’s the no-arbitrage condition? How do we apply that to solving this problem?” That’s going to turn out to be critical for options pricing. 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. 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.

TABARROK: Fischer Black, he becomes a devotee of this CAPM model. He does exactly what you say, he starts thinking about, “This CAPM model is good for pricing stocks, how do we use it to price other assets?” He thinks, “Well, we could use it to price options.” He’s able to derive from this a differential equation. He writes down the equation but he can’t quite solve it.

COWEN: 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 Itô's lemma, which is another story. It was an arbitrage insight that Black brought to the party, so to speak.

TABARROK: Did Black bring it to the party, or did Merton bring it to the party?

COWEN: And Scholes, yes, but Black and company.

TABARROK: 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. The arbitrage argument actually comes from Merton.

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 that he can say, “Well, this doesn’t matter, this does matter,” and together, they solve the options. They solve the differential equation.

COWEN: Here’s one of the great ironies of option pricing history that Merton Sr., you referred to him before, 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.

TABARROK: Exactly.

COWEN: That 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. The son lived out this notion that his father had about credit being unfairly distributed.

TABARROK: About the right name not being given. Indeed, we tend to call it the Black-Scholes option pricing formula.

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

TABARROK: Exactly.

COWEN: Merton did win a Nobel Prize so we don’t need to feel too sorry for him. He won it for other things.

TABARROK: Black and Scholes, they start shopping the paper around and actually, it doesn’t receive very good reception.

COWEN: It’s rejected at some journals.

TABARROK: It’s rejected.

COWEN: Finance doesn’t matter. Finance was low status then. That was low pay. What are you people doing? Why this?

TABARROK: In fact, they show the paper to Merton, and Merton, he doesn’t like the CAPM derivation. He says, “Yes, maybe you should use some kind of arbitrage argument.” That pushes them in the direction of arbitrage. Then kind of a remarkable thing happens, is that the Journal Political Economy finally agrees to, after rejecting it once, they agree to publish the Black-Scholes paper after Merton Miller—there’s a different Merton, also a famous guy in finance—after Merton Miller and Fama intervene.

They say, “Look, you got to publish this. Really good paper.” They go to the editors and they say, “We’re going to push this.” Interesting, they have some ulterior or extrinsic motives for doing this. They like the paper, of course, but at the same time, James Lorie, who was then the head of the Center for Research in Security Prices, he and Merton, Merton Miller, and Fama, they are working to create at the Chicago Board of Trade, an exchange to actually buy and sell options, which has not been done before.

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. Chicago really gets a huge amount of credit for advancing the theory.

COWEN: The city, just the actual city of Chicago, the Board of Trade, a number of different people there, the overall environment. And the Black-Scholes paper’s published in ’73, just to be clear on that.

TABARROK: The SEC approves the Board of Exchange for options in 1971. It opens for business in 1973. Everything is coming together and within years of the paper being published and the exchange established, billions of dollars’ worth of options are being traded.

Here’s another point about the father and the son Merton, 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 continuous time, a more advanced actually arbitrage argument. He has a guaranteed publication ahead of Black and Scholes. 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 remarkable in the history.

COWEN: It is. I don’t hear too much of people doing that these days.

TABARROK: No. They don’t know it then, but there’s a Nobel Prize at stake here.

COWEN: That’s right.

TABARROK: For Merton to say put these guys first when it’s very clear that the first person to publish the paper that is going to in fact did result in the naming of Black-Scholes options pricing theory. That was a remarkable thing that Merton did.

COWEN: Absolutely. It’s interesting also the history of Black-Scholes in use. 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.

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. Then you look at the markets a bit after Black-Scholes, again, there’s enormous variety and diversity of what’s going on. There’s a number of papers that show, well, on average, some of these options are overpriced.

The people intuitively, before Black-Scholes, had a sense of some of what matters. They didn’t get it entirely wrong. Post Black-Scholes, there’s just a lot more going on and the methods have become far more complex and far more mathematical. 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. 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.

Kassouf, Thorp, and cashing in on options theory
TABARROK: I think the invisible hand should get some credit here too, because as I mentioned, Scholes had brought the empirical data and was using the empirical data to figure out what mattered. That was one thing. Then afterwards, Black and Scholes actually as academics are wont to do, tried to use their model to make some money.

COWEN: Sheen Kassouf and Thorp were doing this all along. They wrote this book in 1967 called Beat the Market.

TABARROK: Black and Scholes actually lose money. They find these really what looked to be underpriced options or overpriced, I can’t remember exactly. It turned out that they buy into these options, overpriced options. They sell the options. It turns out that the market was implicitly including in the price of these options, the possibility of a takeover. The market sometimes knows even more than the model knows.

COWEN: I believe Sheen Kassouf and also Thorp 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.” It seems they 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.

TABARROK: Let’s talk about Kassouf and also Thorp. Thorp people may know him better as I believe, he’s the guy who beat the casinos.

COWEN: That’s tight. Card counting.

TABARROK: Card counting. Exactly. They had the computer and the shoe and the earpiece and all that kind of stuff. He figured out all of these techniques, he made a lot of money from that. He has always claimed that he had the or an options pricing model. It’s a little bit unclear. He used whatever model he had to make money and by all accounts, he was very successful at making money.

COWEN: That’s right.

TABARROK: The hidden history is that maybe there were people in the background who actually knew.

COWEN: Thorp claims the same general method is what has kept him alive at age 91. 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. There was a profile of him in Bloomberg Business Week, not long ago. This would be April 2024.

TABARROK: I’d say anyone at 91 is in good shape.

COWEN: Exactly.

TABARROK: 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. 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 two years earlier, but it would certainly have been a three-way prize had he not died.

COWEN: He was cited in the award.

TABARROK: Sure.

COWEN: This is a very sad story for me. I knew Fischer Black. Periodically, I’d have phone calls with him, which is what he would do with people. Obviously, no internet, no Zoom call. 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.

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 a Fischer Black phone call went. 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.

I didn’t know leading up to 1995, that Fischer Black was dying. I was writing some pieces on business cycles that he was interested in, and he kept on telling me, “Well, Tyler, please send me your work. I’d like to read it as soon as possible.” My attitude was, “Well, you can’t send anything to Fischer 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.” I was using options and then suddenly he passed away and I never knew that he was dying. 

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.” That was his famous article, “Interest Rates as Options.” He just so consistently thought in terms of options. He was a remarkable guy.

TABARROK: Yes. Very remarkable guy. 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.

Other applications of options theory

TABARROK: Let’s start with insurance. Insurance, 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. If you don’t get into an accident, then you keep the car. 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. Understanding insurance as an option gives firms a new way of thinking about how to price and value insurance.

COWEN: In 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 the way of exercising your option and converting your car into the insurance payment.

TABARROK: It’s not just auto insurance. Think about all of the implicit guarantees that the FDIC and the Fed have given the banks. They’re basically saying, 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.

COWEN: Another example I find persuasive is I think, the notion of options explains some of unemployment. 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.

TABARROK: You don’t want to exercise too early.

COWEN: Now, here’s one of my worries when options become so important. We all know Hayek’s story of the market price system working and everyone can observe prices. When options are important, and we know they are, they’re much harder to observe. 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.

Price information is degraded and you observe a bunch of things not happening and you don’t know what’s the price signal. 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.

TABARROK: Yes, exactly. Without the benefit of the markets, we are reliant on models. Which is why things like when the FDIC and the Fed, they offer these huge guarantees, one reason they can do that is because nobody knows what’s the potential cost—

COWEN: That’s right.

TABARROK: —to the government.

COWEN: Highly nontransparent.

TABARROK: Highly nontransparent. You have to kind of use these models to try and figure out, well, what is the potential cost of these things? We don’t have markets to kind of give us that single price. Instead, we have to rely on the models.

COWEN: 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. Insofar as that’s the case, again, it’s something other than the price system doing the work. 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.

TABARROK: In the Hayekian-Mises business cycle theory, the interest rate is really the key thing. Everyone’s just following the interest rate. Interest rate falls because government increases supply of money or something like that and everyone just goes into investment.

COWEN: Yes. 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. The changes in the risk premium might be driving investment. How do we think about those in a business cycle context?

TABARROK: Yes. Those seem to be much more important than the pure interest rate itself. There’s a lot of investment decisions that you can think about like an option. 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? It seems obvious that the higher the price of oil, the greater should be your incentive to drill. The price of oil goes up and down. You don’t want to drill the well and then find out that oil prices have dropped below the cost of extraction.

Once the well has been drilled, the costs are sunk—literally in this case. You can think about the decision to drill the oil well as exercising the option to drill. You want to use some model to figure out when given the volatility of oil prices, is the optimal time to drill the well.

COWEN: 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.

TABARROK: 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. If there’s a lot of uncertainty, then you actually want to wait. That uncertainty can then mean that you wait, which means that you don’t invest, which is what is driving the business cycle itself, the noninvestment. The uncertainty causes a lot of people to hold back on making decisions. That means that the business cycle, that the downturn could continue.

COWEN: It’s a major problem in economic development. The Danish government is relatively credible. Many, but not all, parts of the US government are. That enables investment and growth. 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. They might even sound better but no one knows what the law will be two, three, 10 years from now. It’s just harder for them to mobilize the proper incentives.

TABARROK: Ironically, in a way, options pricing theory actually tells us the importance of the Fed talk and developing confidence and coordination of expectations. Put aside what the Fed does with interest rates, Fischer Black thought that was completely unimportant. One thing which might be important is the Fed can coordinate expectations and could get people moving in the same direction at the same time.

You don’t want to 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. This control of uncertainty, control of expectations, can actually be one of the more important things that institutions like the Fed can do.

COWEN: The presidential bully pulpit can matter in a similar way if it’s used wisely.

TABARROK: Yes. Like George Bush throwing the pitch, which seems completely ridiculous, right?

COWEN: Right.

TABARROK: Yet everyone says it was important. For those of you who don’t remember, after 9/11, Bush throws out the first pitch. He was a baseball guy, and it was a good pitch. Went over the plate. This created confidence. Oddly, options pricing theory tells us that, hey, there might be some truth to this.

COWEN: That’s right.

TABARROK: There are all kinds of these options everywhere you look. What a lot of firms are doing nowadays is trying to price them much better than the before. There is 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. That has improved investment performance.

COWEN: Lowering exit costs becomes a new way to think about policy. 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. Ex ante, you’re going to wait more. The project has to appear to be, no pun intended, in the black by a much higher degree than otherwise would be the case, because exit is very difficult.

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. That too makes people more willing to move in advance. To think backwards from the exit cost is again a different way of evaluating a lot of different policies.

TABARROK: Yes. 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.

COWEN: That’s right.

TABARROK: Your exit costs are much, much higher and that flows back into the hiring decision and how quickly you are to hire. If you want people to be quick to hire, you have to allow them to be quick to fire as well.

COWEN: 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?

TABARROK: Yes, exactly. 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 megasized chip plants. 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.

COWEN: 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.

TABARROK: Hey hey, to the French mathematicians.

COWEN: Absolutely.

TABARROK: Very good.

COWEN: Thank you, Alex.

TABARROK: Thank you, Tyler.