John C. Cox, a professor of finance at the Sloan School of Management at MIT, is one of the vanguards of options modeling. His work in the mid-1970s with Steve Ross explored the foundations of option valuation and established the principle of risk-neutral valuation. His later research in asset pricing led to a widely used model of the term structure of interest rates. He has also done work on the use of option technology to analyze corporate securities and on intertemporal portfolio policies. With Mark Rubinstein, he coauthored Options Markets, the first popular college textbook on derivatives. Cox has been a consultant for a number of securities firms and has served as an adviser to government agencies in several countries. He spoke with senior editor Nina Mehta in January.

Derivatives Strategy: How did you get started as an options modeler?

JC: I've been lucky. I finished my Ph.D. at the University of Pennsylvania in 1975. That was when the original work that Black, Scholes and Merton did was just coming out, but nothing was well understood. The gate to the orchard was unlocked but nobody had gone in yet. There were all these low-lying plums just waiting to be picked.

DS: But financial engineering didn't quite exist at that time. How did you wind up in this area?

JC: I wish I could say it was all foresight and grand design, but it wasn't. My original interest in the area was purely intellectual. At the time, I didn't have the slightest inclination of how important all these option pricing problems would turn out to be for the financial industry. No one did. On the other hand, in retrospect, it was not a complete surprise because the kinds of things that options do were the kinds of things that finance theory had already identified as being valuable services—that is, that options could be used to control risk and tailor risk more effectively than what was then available.

DS: Has your main contribution to the field been the development of risk-neutral pricing?

JC: That's one thing I'm particularly proud of. It came about from work Steve Ross and I did after he joined the faculty at Penn. Our motivation was to try to understand what things were fundamental to option pricing models and what were not.

"The Cox-Ross-Rubinstein model simplified the arguments that went into the Black-Scholes derivation, which were initially mysterious enough to everybody, and for masters students totally inaccessible.”

We had already developed what you could call a two-state model. It was our analog to the Black-Scholes equation. It was formulated in continuous time, like the Black-Scholes model. In each instant, a given stock could either take a discrete jump or not. We realized that one could hedge this kind of situation the same way one could in the Black-Scholes world, even though it was a totally different state of affairs. But we couldn't solve the equation. Eventually, we realized what was needed was not more mathematics but some economics. That led us to the realization that there was a basic pricing methodology that would have to apply to all problems like this. In other words, the proper valuation of any derivative that you could hedge or duplicate in some way would have to be consistent with what we termed risk-neutral pricing.

DS: What exactly does risk-neutral pricing enable people to do?

JC: It provides a very powerful way to establish a benchmark for the proper relative values among various instruments.

Actually, risk neutrality might be a bit of a misnomer. It isn't that anyone involved is risk-neutral, but rather that the relative pricing of derivative instruments has to be consistent with the basic features of the pricing that would prevail if people were risk-neutral—namely, that all securities would have to have an expected rate of return equal to the risk-free interest rate and that the prices of all securities would have to be their discounted expected values with no further adjustment for risk. Those are the basic features by which one would price derivatives by the risk-neutral method.

DS: Did you and Ross have doubts about your theory of risk neutrality?

JC: No. We just thought, ‘This is great.' It was exactly the insight we needed to solve what we were doing, and we realized it was just what people needed to solve a whole lot of other stuff as well. We didn't think anybody would have any doubts about it, because its utility was obvious once you thought about it.

DS: It didn't take time to catch fire?

JC: Not really. The people working in that area very quickly caught on to the idea.

DS: Around that time, you also developed the binomial model. How did this relate to the Black-Scholes model, and what made the Cox-Ross-Rubinstein model so popular?

JC: It was easy to use and easy to understand. Its purpose was to simplify the arguments that went into the Black-Scholes derivation, which were initially mysterious enough to everybody, and for masters students totally inaccessible because they were couched in terms of complicated mathematical techniques. It was important to have a way to explain to MBA students what was happening, rather than just presenting the final result in a black box. Sometimes that has to be done, but that's not really the way education should happen.

At that time, in the fall of 1975, I was scheduled to teach a course on option pricing at Stanford. Mark Rubinstein was doing the same at Berkeley, so we were thinking about what material would go into the courses and how to present things as simply as possible. It was a conversation I had with my colleague Bill Sharpe at Stanford that was critical to our seeing what was the simplest way by far to present these ideas. That was what really led to the binomial model.

"The very thing that gives an arbitrage model its strength—that it depends on only a small number of factors—is also a weakness, since it gives you no way to relate other variables in the economy to what's in front of you.”

There are basically two attributes that make the binomial model easy to understand. One is the possibility that you can have only two outcomes from the current position. The other is that changes take place over discrete periods of time. The two-outcome part of the description came from the original work Steve and I did that led to risk-neutral pricing, but what we did not see was the additional value of formulating it in discrete-time steps rather than in continuous time, which was the way the original Black-Scholes model was formulated. I have to stress again that the insight of Bill Sharpe was absolutely essential to that happening, because Steve, Mark and I had plenty of opportunity to think of it on our own. The discrete-time side of it just didn't occur to us. It wouldn't have happened without Bill's suggestion.

In some ways, I think the role we played in binomial option pricing was similar to the role that Harrison and Kreps played in risk-neutral pricing. They took the basic idea and developed it to its completion in every mathematical detail. That's essentially what we did with the binomial model when we published our article in 1978.

DS: You then published the first college textbook on pricing options.

JC: Yes. Once Mark and I began preparing more materials for the courses, we decided to turn our work into a book. So the book evolved over a long period of time. The first chapters were appearing right after we started the course, but it wasn't until the mid-1980s that the book was published.

DS: Now people have gone on to create better pricing models.

JC: That's true, in terms of how they're actually used. But I still don't think there's anything better than the binomial model to introduce people to the essence of option pricing, and I don't think there ever will be.

DS: Tell me how your term structure model for interest rates came about.

JC: That was a lot of fun. Steve was part of that, plus Jon Ingersoll. Our goal there—we circulated the first version of the Cox-Ingersoll-Ross paper in 1977—was different from the focus of most term-structure models now. Almost the exclusive focus now is on using term-structure models to find the proper relative pricing relationships among various instruments that are tied to interest rates in one way or another.

These newer models are basically arbitrage models. The very thing that gives an arbitrage model its strength—that it depends on only a small number of factors—is also a weakness, in the sense that it gives you no way to relate other variables in the economy to what's in front of you. So from the point of view of academic economists, there's virtually no interest in anything happening in the term-structure literature anymore. Our model was a general-equilibrium model. It offered a way, at least in principle, to say how fundamental changes in other variables in the real economy would affect the term structure of interest rates. In a sense, our treatment of the term structure was a little like the way Black and Scholes originally developed the option pricing model—Fischer, in fact, always thought about it in general-equilibrium terms.

"Sometimes a little thinking can prevent a lot of misguided math, and sometimes a little math can prevent a lot of misguided thinking.”

Another feature of our work was that the yield curve implied by our model could be made to be consistent with the currently observed yield curve. So our paper was really the first to employ that argument. In retrospect, we should have pursued that much harder, because we didn't really elaborate on how that could be done. Ho and Lee and others did that later.

DS: Is it a mistake the way interest rate models have evolved since then?

JC: No, not at all. There is an extremely important need for exactly what they do, and the models have evolved to meet that need in quite impressive ways. It's just that in serving best one purpose, they necessarily have to be less good at serving other purposes.

DS: Do you have regrets about not spinning off into a particular area of financial engineering that you now find intriguing?

JC: I couldn't really say that in terms of a whole area. In retrospect, I probably would have devoted more time and attention to writing articles that discussed the practical applications of some of these ideas. I never really did that. I always wrote for purely academic journals, leaving it to other people to do more of the popularizing or marketing of the ideas. So I wish I had written more articles that were aimed at industry journals.

DS: In the mid-1970s, you had an unplowed, wide-open field before you. I've recently heard our times described as a fallow period for modelers. Do you think that's true?

JC: I think that's true in almost every field. There are always diminishing returns. As more gets accomplished and more and more people enter a field, it becomes more difficult to make an important contribution. It's certainly not a matter of people working in the field today being less smart than those who worked on problems in the past. It's just that so much more is known now and so many things have been pretty well solved that the scale of the problems remaining—in what you could call purely derivatives technology—isn't of the same order that it once was.

DS: What are some of the thornier pricing problems that are still unaddressed?

JC: I suppose you can think of progress in two ways. One would be working in the basic spirit of accepted technology but extending it a bit further in one direction or another—and that's hard to do. The other possibility is a revolution of some kind—bringing in some completely new angle or way of thinking that's not at all represented in current derivatives technology. That would be a major breakthrough and would open the door for all kinds of new work. But innovations like that are not perfectly predictable and you never know when they could happen or what they might be.

DS: But how many innovations like that have you seen? There was Black-Scholes, and then what?

JC: In derivatives technology, there's nothing that compares with the original insight of Black, Scholes and Merton. There have been other things in finance that are comparable, like the Modigliani-Miller theorems. The work that Franco Modigliani and Merton Miller did in corporate finance completely revolutionized the way people thought about things. The Capital Asset Pricing Model of Bill Sharpe is another example. The work in portfolio theory that was done by Markowitz and Tobin was another breakthrough for all sorts of issues that are absolutely fundamental to modern finance. In derivatives technology, there are a lot of landmarks, but there is nothing that was as totally revolutionary as that original insight.

One development that has the potential to be something of a revolution is what people sometimes call behavioral finance. It's basically an attempt to combine economics and psychology in a useful way and to bring more insights from psychology into economic models. Traditionally the two were separate fields with virtually no overlap.

DS: Andrew Lo at MIT has moved into that area, much to his own surprise, I think.

JC: Well, informally. I think Andy's position is probably like my own—we're both intrigued by the potential, but cautious about how to make the most of it and feeling some reservations about some of the things that have recently been put forward. But at least in principle, that's a way of thinking that could cause big changes in many areas of finance and possibly in derivatives technology as well. But at the moment that's still in the future.

DS: If you were just starting out now, what area in the field would beckon to you?

JC: Well, if I were giving advice as an academician to someone who was thinking about an academic career, I would hesitate to encourage the person to try to make a career of studying derivatives—simply because the field is relatively mature right now. I think a young person has a better chance of establishing himself or herself and being productive in a fresher, newer field.

DS: What are you working on now?

JC: One thing is lifetime financial planning for individuals. You could think of it as wealth management, like the services that a private bank provides to clients. Wealth management is partly about getting an edge on the markets and generating a positive alpha. But it's also about structuring the ideal portfolio to meet specific needs and adjusting that portfolio in the best way over time. It's this second part that I'm focusing on.

DS: Does option theory play a role in this?

JC: Maybe. In principle, option technology can be applied to planning problems. Think of the kind of world described by Black and Scholes. The key thing that makes that work is the ability to use stocks and bonds to control a portfolio so that over time you end up with exactly the payoff to the option. Once you realize that, you realize that there's nothing special about the payoff of an option, and that you could do exactly the same thing for any kind of payoff. In particular, you could use this to properly price and synthetically produce a security that would pay off a dollar if and only if a particular state of nature occurred. In the Black-Scholes case, a state would be a particular final stock price or particular path of the stock price.

If separate markets existed for all of these securities, one for each possible way things could turn out over time, a person would not need to make a dynamic decision. He could decide everything today by simply looking at a huge menu of prices and the payoffs of all these securities, and could in principle today plan out his entire financial life by the amount he chooses to purchase of all of the securities. That would be the solution to a static problem. But those markets don't exist, so this would be a whimsical exercise if there were not some way to turn it into an action you could really take. And that's where the option pricing technology would come in. It tells you how you should trade and manage your portfolio over time in such a way that you end up with an ultimate payoff that is exactly what you would have ideally liked to have.

Of course, all of this sounds hopelessly abstract. The challenge is to make something useful out of it.

DS: Do you usually sit in a chair and think about this, or do you put math down on paper?

JC: A combination of both. They reinforce each other. Sometimes a little thinking can prevent a lot of misguided math, and sometimes a little math can prevent a lot of misguided thinking.