The King of Quants: A Conversation with Emanuel Derman
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By Emanuel Derman | TradingMarkets.com | May 09, 2008 06:44 PM

In his book, My Life as a Quant: Reflections on Physics and Finance,¬ Emanuel Derman describes his journey from South African physicist to Wall Street financial engineer. An expert in two fields - theoretical physics and quantitative financial analysis - Derman's book was filled with stories, anecdotes and insights into two worlds that are largely incomprehensible to the average person.

Derman is responsible for some of the pioneering work on modeling financial behavior, being co-creator of the Black-Derman-Toy model, among the first interest rate models, as well as Derman-Kani local volatility, one of the first effective models of the volatility smile.

Earning his doctorate in theoretical particle physics at Columbia University, Derman began his career on Wall Street in 1985 at Goldman Sachs, where he worked in the fixed income department. From 1990 to 2000, Derman headed the Quantitative Strategies division of the Equities division at Goldman. In 2002, Emanuel Derman retired from Wall Street and took a position at Columbia where he is currently director of financial engineering.

TradingMarkets CEO and co-founder Larry Connors spoke with Emmanuel Derman this spring about his work at Goldman Sachs, his early days modeling interest rates and volatility, the battle between the objectivity of mathematical models and "the world as it really works" and his thoughts on where the financial engineers of tomorrow are coming from (hint: most will need visas to work on Wall Street).

What follows is Part One of Three, all to be published as part of our Big Saturday Interview series.

Enjoy!

Connors: Your primary responsibilities early on at Goldman. What were you hired to do?

Derman: I was hired into what was then called, "financial strategies," which was like a fixed income research group.

And when I got there, I started working on building a model. The exotic product in those days was simpler than it is now. It was options on bonds, which were a bit like options on stocks that Black-Scholes had developed.

Connors: Alike, but different?

Derman: Yes. They were more complicated because bonds take coupons and they have yields. The stock price can do anything it likes for the next 50 years. But a bond is going to mature in 30 years and be worth $100 no matter what.

And so it was a harder problem. In a sense it should have been easier because you knew much more about the future behavior of bonds than you did about stocks. But in a way, it was harder mathematically because you had to incorporate all that knowledge into a consistent model.

Anyway, it was a trading desk. We were trading options on bonds and making markets in it and there was a lot of demand for those options because interest rates were coming down.

A lot of fixed income investors were getting less and less interest. What they wanted to do was to sell options on their bonds to collect premium. So they would sell us calls to get premium; and we would hedge those calls by buying listed options on the Chicago Exchange.

Connors: Yes.

Derman: But they didn't match perfectly so you had to hedge the difference. So they needed a good model for doing that and that's what I worked on.

Connors: That was basically the beginning of your financial engineering.

Derman: Yeah, it was. I did that alone at first and then it got more important and Fischer Black was upstairs in equity and not in fixed income, but he working on it, and eventually we built a much more sophisticated model â€" him and me and a guy called, Bill Toy; and everybody calls it "BDT," which stands for "Black-Derman-Toy." It was one of the early models to value bond options consistent with a current yield curve. It was sort of, it was an extension of Black-Scholes.

Connors: How did you know early on that you were correct? When was that "ah-ha!" moment where it's like you really saw that you had something that no one else had?

Derman: That's a good question. What everybody was doing before that was using Black-Scholes in a slightly hooky way to value â€¦ how much do you know about options?

Connors: I've got some pretty good knowledge of options.

Derman: Okay. 
Well, so every time you value a call on a different stock, you just put in the stock price and the volatility. And so people did the same thing for bonds. They put in the bond price and the volatility. But you can't really do that.

The trouble is that you want to model them out to maturity, but two years from today the five-year bond is going to be a three-year bond.

So there are all sorts of inconsistencies that developed from the fact â€" you know, if you write an option â€" if you value an option on IBM ( IBM | Quote | Chart | News | PowerRating) it's not gonna be Sun Microsystems ( JAVA | Quote | Chart | News | PowerRating) tomorrow, you know? But if you value an option on a five-year bond it's gonna be a three-year bond tomorrow.

Connors: Of course.

Derman: So the model in order not to get nonsense and arbitrage violations has to know what five-year rates are, what four-year rates are, what three-year rates are and all their volatilities so that it doesn't produce nonsense between â€" or conflicts between two different values. The model we built was able to value all bonds in a consistent way.

Connors: And you were the first to come up with that.

Derman: Yeah, there were other people â€" there were two people â€" Hoo and Lee â€" that did something similar around the same time. I think ours was a little more realistic in the sense that there approach allowed interest rates to go negative and ours didn't.

But yeah, it was partly a point of view in the sense they had been very clever bond option models before â€" or yield curve models before by a guy called Vasicek, who's pretty famous â€" he's part of KMV, which was bought by Moody's.

He had done some very clever stuff before, but people looked at it through the wrong lens. Those guys thought they were modeling the yield curve and the future stochastic or a random behavior of the yield curve. They weren't interested in bond options. They were interested in trying to explain the future yield curve.

Connors: And that was not your project.

Derman: We were sort of working backwards. We were not interested in predicting the yield curve. We were interested in just being consistent with the yield curve and then valuing options. Am I sorta making sense?

Connors: It makes a lot of sense.

Derman: See, if you value a call on a stock, you want to make sure that the stock price is right. You don't want to quibble about whether you've got the wrong or right stock price; that's just a given. And in the same way, if you value a call on a bond, you want your model to start off by having the prices of all bonds right.

And that's what we kind of did.

The previous models were equally clever, but they were trying to predict what bond prices should be rather than accept them for what they were and then try to value options on them.

So we were sort of - it's an inverse problem. Those guys were going forward, which is start from some assumptions and calculate the yield curve. And we were going backwards with the idea of: given the yield curve, what assumptions do you need to match it.

Connors: Interesting. What would you say goes into creating a great model like what you did back in the '80s? What do you look for to create a "great model?"

Derman: I've changed my mind a lot over the years. In physics if you want to explain something that's sort of superficial that you see in the world, it makes sense to drop down several levels and build something very fancy, like quantum mechanics or discover something very fancy like quantum mechanics or Newton's laws or general relativity - not discover, sort of have an active inspiration, you know, about what the laws are and then come back and apply them to it. You understand what I mean?

Connors: Yes.

Derman: I think in finance that doesn't work as well. People do that but the financial world is sort of much more changeable and nonpermanent and â€" what's the word I want â€" ephemeral. So I think dropping down to a very low level to write something really fundamental and then come up again, doesn't work very well because you don't know how things work at that low fundamental level.

And active inspiration about what the fundamental laws of finance are, well, you don't get them right most of the time because the world is changing the whole time. Maybe there aren't any fundamental laws.

So I think one thing I look for is models that don't get you too far away from the things you can already see, that use as inputs things you can see.

Connors: Most of our readers are going to be equity readers, so what would you â€" what would those things be in the equities markets?

Derman: Okay. Implied volatilities of equity options?

Connors: Yes.

Derman: Equity index prices, interest rates, obviously, but yeah, sort of those things. People build stochastic volatility models where volatility itself is a unknown quantity, which is correct. But when you drop down too low, you can write very pretty models, but you don't really know that much about how volatility varies, so that's only dropping down level.

It makes sense to do it, but you can't really get it right. I mean, you want two things: 1) You want consistency, which means no arbitrage violations. You don't want to write models where two things that have the same cash flow sell for different prices.

Connors: Explain it. Explain further for the readers â€"

Derman: What I like to say is that in physics there are a whole bunch of laws, not many, but they explain almost everything. In finance, there's only one law and it's kind of a trivial one.

People say it very fancily by calling it the "law of one price." But it really says is, if you want to know the fair price of something illiquid â€" whose value the market doesn't tell you â€" your best guess is to find a portfolio of other securities that behave as closely as possible like the thing you're interested in.

They should be listed and have liquid prices.

And so what all the successful models do is say: here is a bunch of stocks and bonds and maybe a couple of other things that when put together, have exactly the same behavior as this weird exotic option that you're trying to price. And if it has the same behavior under all future circumstances then it'd better have the same price today. All that modeling consists of is: 1) specifying what you mean by all future circumstances, and then, 2) showing that the portfolio you've created out of liquid things whose prices you know, behaves pretty much in the future like the illiquid thing whose specification you know.

Am I making sense?

Connors: Yes. It sounds like volatility encompasses a great deal of that assumptive behavior.

Derman: Yes, that's exactly right because what you have to do is specify all the scenarios which could happen in the future, which is related to the volatility.

Connors: Why implied volatility instead of historical volatility?

Derman: That's a good question too. None of these models are perfect; they're all missing things. When you build Black-Scholes, you assume stocks are infinitely liquid, that you can short stocks, that there are no transaction costs, that stock prices never jump. None of those things are strictly true. All of these prices are subject to supply and demand that sort of go beyond--a little beyond the model.

So in the end, people take the model as a sort of platonic thing and then force it to fit the data and the number that comes out is implied volatility. So it's sort of implied in the sense it's saying, "If the market price is right, then this is what the future volatility would have to be."

Connors: Right, right.

Derman: Then they use the model for hedging or for valuing other things.

It's a sort of a weakness of all financial models in that they don't predict the world, they are forced to fit the world by adjusting some of the parameters.

Connors: So what happens? Now we're at the point of creating the model and so we have a model versus what is the real world, meaning that we can't accurately or fully predict ...

Derman: Yeah. So what do you do?

Connors: So what do you do â€" yes.

Derman: Well, I think what you do if you're sensible is you pick out the salient features that are important to the thing you're trying to calculate. So for example, if it's an equity option the most important thing is volatility.

Connors: Yes.

Derman: And you assume interest rates aren't going to change and dividend yields aren't going to change or bunch of things like that, and you kept to the biggest â€" the thing that's most important and try to model that; and then if you've got energy and an ability you and it becomes important in that the market spreads become tighter.

Then you start trying to add small corrections for other facts of life that you've ignored. So for example, if you live in Brazil and interest rates are very volatile, you might start to take account of that.

Connors: Yes. Yes.

Derman: Or if dividend yields are changing all the time, you might take account of that. Or if you're in a period where stock prices are--have some possibility of really, you know, crashing, you might make corrections for that.

But it's hard to build a perfect model, so I think what you always do is try to model the dominant feature and then add corrections for less important things.

Connors: So you're on a go-forward basis. The model is being adjusted to reflect new knowledge that you gain between the time you created the model and the time you're making those adjustments?

Derman: Yes, for sure, and also let me give you an example like that Black-Derman-Toy model that we built. It's not bad for pricing options, but it has a constant volatility for the volatility of interest rates. So it's not bad for pricing options on bonds, but sometimes people are interested in options on the slope of the yield curve.

It's a bad model for that because - it's not a bad model, but it's a limited model for that because there isn't a second random variable that represents the slope of the yield curve, and so if you're writing options or making a market in options on the ten-year yield minus the two-year yield, that wouldn't be a good model to use because it's missing that. That's not so important for bond options, but it's important if the underlying thing you're looking at is actually the ten-year minus the two-year.

So you've got to be a little bit pragmatic. You've got to take your model really seriously and build a consistent model that captures the biggest effect or maybe some of the smallest effects that affect the value of the thing you're pricing.

You want to be very mathematically consistent, but then at the end you want to step back and say, "Is this the way the world really works?"

And it's not, you know? So you've got to allow for the fact that you're not discovering general relativity. You're just trying to engineer some solution that's approximate, that's reasonably okay in some sort of range.

Be sure to catch Part II of "The King of Quants: A Conversation with Emanuel Derman" next weekend, available Friday evening on May 16.

The King of Quants: A Conversation with Emanuel Derman, Part 2
May 16, 2008 By Emanuel Derman

In Part One of “The King of Quants: A Conversation with Emanuel Derman,”  Derman discussed his early days at Goldman Sachs and the development of the  Black-Derman-Toy model for interest rates. Derman also discussed the difficulty  of matching models to the reality of the financial markets – “the world as it  really works.”

Here in Part Two, Emanuel Derman looks at additional problems in building models – such as risk management and dealing with dirty data. Derman and Connors also talk about the relationship between the researcher and the trader, and begin a conversation on the contemporary problems in the credit markets that will extend into next week’s third and final part of the interview.

Emanuel Derman is currently the director of the financial engineering program at Columbia University, where he is a professor. Derman is the author of My Life as a Quant: Reflections on Physics and Finance,¬ which was recognized by BusinessWeek as one of the best business books of 2004.

Emanuel Derman spoke with TradingMarkets co-founder and CEO Larry Connors in March 2008. What follows is Part Two of their conversation. For Part One, click href=”http://www.tradingmarkets.com/.site/stocks/commentary/satinterview/-76805.cfm”>here

Connors: So is that where we almost, in a sense, get into risk management?

Derman: Yes –

Connors: Which is real broad term, but it sounds like what you’re saying is that one is going to take the model and then the risk management comes in saying, “OK, what is the degree of this model needing to be adjusted in the future?”

Derman: Yes, that’s very perceptive and I think that’s dead right. I mean, it’s like what I was saying earlier â€” I’m stepping back a bit, but I was saying, the art of modeling is: 1) figuring out all the possibilities in the future, and 2) doing this replication, which is valuing the complicated thing by making it out of simpler things. Am I making sense?

Connors: Yes.

Derman: And where human imagination fails is we can’t picture all the things that will happen in the future.

Connors: Right, right.

Derman: So you have to allow for that sort of error in your model. That means there are three sorts of potential errors in your model: 1) “Do you know all the inputs you should put in to calibrate it?”

2) “Can you really do the replication?” Meaning, can you make the portfolio of liquid securities have the same payoff under all those scenarios as the thing you’re trying to value? You’re always trying to value something that’s a little bit more exotic than what you can easily trade.

Connors: Yes.

Derman: Lastly, 3) “Did you really think of all the future things that can happen in the world?” And the answer to that is, , always, “No.”

And so you’ve got to keep that in mind or try to use a range of different models to figure it out. People call it model risk, but it’s not even model risk; it’s sort of model uncertainty.

Connors: Yes. It’s interesting that we’re talking now â€” this is March of ’08. If we were talking in March of ’07, there were things like what’s going on in the credit markets. Those things certainly were not factored into a number of models out there.

The models couldn’t possibly have reflected what has just happened. So that’s where that risk management comes in. How do you measure that unknown? That becomes the whole key to this.

Derman: Yeah, I think that’s right, and you have to have good market sense, as well as good model sense.

Connors: Yes. I know a lot of people sometimes think that the model’s there, press a button and that’s it. But for you it’s more than this. You talk about the team that has to go on the execution of the model. What does that infrastructure, in your mind, look like?

Derman: Well, I was going to say two things: First, you always have to overlay the model with a lot of common sense because it’s imperfect.

Connors: Yes.

Derman: There are things that happen in the world that aren’t reflected in the model and you have to somehow transmit that knowledge into the model by changing some of the parameters in a way that approximates the things that don’t fit in there.

So for example â€” I’m getting a little off the subject â€” maybe you should make the volatility a little bit bigger because you know you can’t really predict it accurately and you know you can’t hedge perfectly. So charge more in some way to account for that.

Connors: Yes.

Derman: But then the second thing is that a model written down as a pure mathematical formula is inadequate. The markets are electronic. You handle big portfolios. You know, I used to estimate you need, maybe three or four computer guys who understand options but are basically there to build your trading system, three or four of them for every sort of purely quantitative guy.

Connors: Yes.

Derman: Because you can’t use a model without applying it to a whole portfolio and getting electronic price feeds and hedging â€” you know, the 4,000 equity options you own. The world’s gone too far. When I first came to Goldman they really did just use a single model on a little program.

What you really need is a portfolio system and that takes large scale software development and planning and debugging and building. I think it’s gotten more and more like that as markets have gone electronic.

Connors: Yes. So how much of a role in the model does the trader play, a trader who will observe certain behavior going on? Do you then go back in and have to adjust the model to take into account the input of what the trading team is seeing?

Derman: When I was doing this for a desk all the time, the only time it ever worked really well was when there was some trader who had a genuine interest in not just trading but in trying to build an environment for trading.

Connors: Yes.

Derman: And who will really interact with you a lot. We had people like that when times were good, who would tell you the way they looked at things, and had the patience to work at developing a uniform trading ENVIRONMENT.

Connors: Yes.

Derman: A) you want good ergonomics so that they can trade easily and get the information they need out of your system easily.

Much of the value you can have comes from simply making the mechanics of trading easier.

And then B), the second thing is that the good traders have a lot of intuition, from everyday experience, about how to handle complicated products and how to hedge them, simply from seeing the way they behave day-to-day.

You want to extract that intuition and use your own intuition and then build something that’s more robust and rigorous.

Connors: Yes.

Derman: But you’ll always want to understand models intuitively. You don’t want to just build black boxes that give you numbers because it’s very easy to go wrong without knowing it, or even easier to make mistakesâ€”

The King of Quants: A Conversation with Emanuel Derman, Part 3
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By Emanuel Derman | TradingMarkets.com | May 24, 2008 03:08 AM

In this, the third and final part of our conversation with financial engineer and author of My Life as a Quant,¬ Emanuel Derman, TradingMarkets CEO and co-founder Larry Connors discuss the practical side of financial engineering, how to get started in the field, what opportunities there are for mathematically inclined analysts and traders and whether or not financial institutions were greedy or just got it plain wrong when it came to the subprime mortgage debacle.

Larry Connors: I'll give you a hypothetical: I've got a son or daughter that's 18 years old and decides he or she decides to become a financial engineer. Give me the path for them for the next ten years.

Emanuel Derman: Get a bachelor's degree in solid subjects like math, statistics, applied math, - physics, yes or no. I'm a physicist but I don't think that's critical. But a lot of rigorous things.

Financial modeling isn't that rigorous and though many people may not agree with me but I think it's a mistake to start it too early. That is, unless you want to become a trader when you're 18 and know that for sure.

But if you want to be a financial engineer I think you first need a really firm basis in skills that are not ephemeral, you know? You're always going to need to know real analysis or computer programming or statistics.

I'm not saying don't do any financial engineering, but I'm a little bit wary of jumping straight into the field.

Connors: Yes.

Derman: And then, in an ideal world, learn some finance and then work for two years in the financial business. That will help you decide whether you like the research side or the trading and sales side of the business.

Then, if you want to be a financial engineer, come back and get a master's degree or a PhD in that field. And if you don't, go back and work on Wall Street or get an MBA or do something completely different.

But there is more than one way to skin a cat. You can go straight to a master's in financial engineering. Most of our students in the program actually come directly from undergraduate school, get a masters and then go out into the world and get jobs.

Connors: What's usually their first job? Do you see a common theme as a first job when they come out?

Derman: Well, I'll tell you. One common theme is that 90% of them are foreign-born, foreign-educated.

Connors: Interesting.

Derman: Americans - I am too. But Native Americans don't want to go that way, though more of them do now that quantitative people can take positions and actually trade and do statistical arbitrage. It's better than ten years ago. Because firms see that there's money to be made by using quantitative techniques.

Most of our students are foreign-born and most of them get jobs afterwards - exactly what depends on their skills.

Some as traders. Some of them as quantitative people on a trading desk helping the traders and building models. Some go into risk management. Many move into hedge funds, increasingly. I think the big difference in the last seven or eight years is that most people used to go the sell side. And now many go to the buy side, to asset management, and to hedge funds. That's where the jobs are.

Connors: The last question that I have is this. Let's look ahead over the next two-three-four-five years. We're building models today, hypothetically.

Where are the biggest edges? I remember having a conversation with a neighbor of mine - this was back on the West Coast - who was one of the larger, better commodity traders in the world back in the '80s.

When I asked him how he did it, he basically said he was in markets that nobody else was in and was doing things that, really, nobody else was looking at.

Where would you send someone today to find edges?

Derman: Well, just before I answer that, I sort of think that's true of life in general, especially if you're a little bit lazy. Whether you're in physics or you're in finance, the way to have the biggest bang for your buck is to go into some area - whether you're in trading or in financial engineering - where nobody's done virtually anything.

I mean, BDT was a little bit like that. You know, there are many more sophisticated approaches now, but you get a lot of impact if you grasp the essence of the problem even if your mathematics isn't that sophisticated.

So it's always good to be first through the door, you know? To be the guy that does the first order thing and let other people add the corrections is a nice piece of luck.

Connors: Would you say that possibly the international markets may have these opportunities? Where would you look?

Derman: People were doing emerging markets a few years ago. Japan in the early '90s was a lucrative place to trade volatility because people didn't think in volatility terms.

Ten years ago the people who bought options in Europe during the Internet boom didn't really care about volatility. They cared about getting a cheap way to leverage a bet on pharmaceutical or Internet stocks.

On the other hand, the investment banks or the trading desks that catered to them didn't care about stock up or stock down, they cared about volatility. And I'm making this a little bit more organized and simplistic than it sounds, but desks could charge higher volatility to people who didn't care about volatility but cared about stock direction.

If you can find places where people have different aims and different metrics then you can make money between the cracks - It's sort of like lotteries in the sense that people will pay a small amount of money for less-than-fair odds because they don't really care about the odds.

You can get more of that in places where there are new products, and particularly high margin products. Desks make money by custom tailoring - either by custom tailoring for people who want something that they can't acquire off-the-shelf.

Connors: So it sounds these types of edges, these opportunities, will exist over the next "x" amount of years until those markets become mature.

Derman: I think so, although it's probably harder now because everybody's plunging in and markets go electronic very quickly, where as before, they weren't -

Connors: Yes.

Derman: And so I think those opportunities get harder.

I guess there two ways to make money: one is sort of an asset management approach, where you take positions. The other way is the service side, where you're a wholesaler and you're just trying to make the spread, you know, or you make fancy stuff for people who can't get what they want in a world of simple listed securities.

As I was saying about bond options earlier. You know, you could buy bond options 20 years ago on the Chicago Board of Options Exchange, but they were generic. You couldn't buy one written on the particular bond that you owned. Am I making sense?

Connors: Yes, yes.

Derman: In other words, if you were Fidelity, you could sell a call on some bond future, you know? And you could use that in a complicated way to hedge or speculate. But that wasn't the call you wanted.

Original publication: May 24, 2008