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The World According to Emanuel Derman

Emanuel Derman, head of the quantitative strategies group at Goldman Sachs, occupies a critical position at the firm. His team of 30 quants constructs equity derivatives models and systems used by the firm's formidable equity derivatives trading desk.

Derman himself has impeccable quant credentials. A former particle physicist who cut his teeth on neutrinos, quarks and leptons, he went on to become a research scientist at Bell Labs before joining Goldman in 1985. There he began working with Goldman colleagues Fischer Black and William Toy on a model for valuing bond options. The Black-Derman-Toy model, published in 1990, has since become one of the leading tools for pricing interest rate options. Derman spoke with editor Joe Kolman in January.

DS: You're a creator of models, but you also work with real live traders. How far do models go? Where does their value stop? When can you put too much trust in them?

ED: I've been forced to be fairly pragmatic about them. There was a trading desk head who said that giving somebody a Black-Scholes calculator doesn't make him a trader. The models give you some way of thinking about the problem you're tackling, but they don't necessarily give you the answer.

I like to think of models as a Gedankenexperiments-the imaginary experiments physicists used to try to think about something they couldn't do, like sitting on the edge of a light beam and travelling at the speed of light.

I think that's what models are good for in finance. In most cases the world doesn't really behave in exactly the way as the model you've constructed. You're trying to make a poor approximation of reality, though it has big advantages. You can ask, "What happens if volatility goes up or interest rates go down?" It allows you to stress-test your view of the world in some way and then come up with a price based on what you can understand.

Before Black-Scholes nobody knew a methodology for pricing an option. Some of the things you want to price in the world are horribly nonlinear. You couldn't possibly extrapolate them in your mind.

DS: Like what?

ED: Like option prices as a function of strike. An at-the-money may be worth $10, but if you go to out-of-the money you suddenly drop to almost nothing. If you didn't have a model, it would be very hard to do that, to ride that curve, because it's not a straight line.

DS: What does a good trader do with a good model? What does he or she add?

ED: First they need an understanding of how the model works. They need to understand its limitations, its applicability to the case they're dealing with and what it doesn't catch-such as transaction costs, liquidity, infrequency of hedging. And then they can make a good estimate of how to overlay those things in some way onto the actual bare-bones price of the model and decide whether that's a price they can live with.

DS: Quickly.

ED: Yes, quickly. Traders sometimes need to have skills that quants don't.

DS: You seem to be at the nexus of traders and quants in your particular function. They are radically different cultures. Is it a mutual cross-fertilization or do you find the different ways of thinking troublesome?

ED: Both. I tend to find that the quantitative people think about things one way, traders think about things another way, and we bounce off each other. But its difficult because the quants who develop models, at least in my group, mostly all like to do one thing deeply, and do one thing for a long time, whereas the traders are forced to do many things simultaneously. Not that they are shallow-they've got to deal with a lot of information.

The biggest shock quants get when they join our group from university life is that they want to spend six months developing one program or model uninterruptedly. Instead, they're forced to juggle calls from the desk or develop software or talk to people about this or that. That's the biggest culture shock. They have to learn to do many things badly, but not too badly.

The second thing is that traders tend to think much more dynamically than quants do. Quants tend to think about how you value something, whereas traders tend to think about what will happen to the value between today and tomorrow. Quants tend to think from the perspective of today's present value, whereas traders tend to think of the change in value and the hedging point of view. Those two things are connected, but it sometimes makes it hard to talk.

DS: A lot of it seems to be political. You might work very hard at developing a model, but you actually have to convince traders that it's valuable in order for it to be used.

ED: That's definitely true. It's less true if you're pricing something they have no idea the price of. So when you come up with a valuation method for a really new product, like a barrier option, or a quanto, to some extent they have no choice. They have to trust you because they have to come up with a price and their intuition doesn't work. They can't extrapolate from an ordinary option to a barrier option. It's not linear, so they need a model to do the extrapolation for them. There you have less resistance.

What's much harder, for instance, is persuading traders to use a new model for something they already value. We would argue that they should look at delta hedges in a slightly different way, for instance.

DS: But they already have a way of delta-hedging that they're comfortable with and that works when they're under pressure. Why should they learn a new one?

ED: So when you say, "I think you're delta-hedging wrong," or "I have another model to price this"...that is much tougher. That's what we ran into with the Black-Derman-Toy for a long time.

It's just that people have an intuition that comes with doing things for a long time, which is not necessarily right. And you really have to struggle to convince them that they have to change their intuition and do things a different way, and, in a sense, a more disciplined way. Because when they price complicated products they tend to use a simple model and then add some sort of intuition about them...

DS: Some fudge factor?

ED: Yes. And they're often in the right direction, but you're telling them that you've got a more disciplined way of doing this, and they have to give up some control at the same time and just take the answers from the model. They're right to be a little resistant.

DS: You spend a lot of your time working on the systems that support the models and designing the interface with the traders. That seems to be a critical role.

ED: I think in some sense the name of the game for all of us is portfolio risk management. It's not pricing. It's interesting to price individual things, but ultimately, the guys on the desk own a whole portfolio of options in equity derivatives around the world with different currencies, different indices, and they have to manage the whole thing.

Of the 30 people in our group, only five or six are really working on models. The vast majority are working on product databases for all the different derivatives, and schemes to calculate the exposure of different indices and the different currencies of the whole desk. There are easily two or three people working around the model, integrating the model into the trading environment, for every one person actually building the model. And those things are actually much more work.

DS: Why?

ED: Models are a pure thing. But some guy at the desk wants to enter a trade, have it go to the back office, have it go into the database, see what his exposure is, and then, at the end of the day, see what his exposure to the S&P is for everything he owns. That takes a lot of networking, intercommunication and building of reasonably user-friendly screens.

DS: It seems odd that every major dealer has the same problems, yet they all have to build their systems separately and individually...

ED: Yeah, that's true.

DS: You'd think that by now or at some point in the future there would be some way to avoid constantly reinventing the wheel at every shop.

ED: I think fixed-income software is getting better, although I don't really work in fixed income much anymore. There is Renaissance and C*ATS and Infinity, and all of them seem to be able to at least get you started in having a risk-management system and a back-office system. I think equity derivatives is much harder, as there is much less out there.

DS: What makes equity derivatives such a different problem?

ED: For one, there are 5000 stocks instead of the bonds of seven countries. So just the data problems are much harder, right away. The models are actually less sophisticated than fixed-income models. In fact, all the implied tree models we worked on in our group descended in some sense from fixed-income models. They were inspired by trying to take fixed-income models and apply them to the equity world. And I think the models are simpler because the products are harder. A stock looks very simple, but it's much harder to model than a bond, because in a bond you've got fixed cash flows for 30 years and it's not very hard to figure out what its worth. With a stock, who knows what it's going to be worth 30 years from now?

DS: A lot of people are talking about this ideal of real-time global risk management. Is that something you aspire to or are actually able to produce?

ED: We try. Most of our time goes toward trying to calculate the exposure to different things and calculate the risk of our global positions. The simple ones are all in there-the listed options, some of the exotic options.

Probably the reason why there isn't a system for everybody is that there are new products coming up every day or every few months. The latest ones you model, but if you only model it once and do one or two deals, it's not so easy to get into your system, no matter what anybody says.

We try to do it, but obviously some things fall outside our scope, because if somebody comes up with some strange kind of average option tomorrow, it's not going to be in our standard risk-management system.

DS: Do you think that all of Wall Street is moving toward some sort of approach that JP Morgan has, with a risk report at 4:15 p.m.?

ED: I think all the big places are trying to do something like that, calculate their mark-to-market and Value- at-Risk. At the end of the day Bob Litterman over at firm-wide risk management gets our equity derivatives numbers, and other people feed him mortgage numbers or currency and commodity numbers. He tries to aggregate them all and give somebody on the management committee an idea of the firm's risk each night.

DS: I think that's being done at the big firms. But other firms, a lot of the second or third tier, haven't gotten there yet.

ED: I honestly don't know. It's easier to do if you start from scratch because you don't have all these legacy systems that you are still trying to support. Every time we do something, the back-office machines are probably years old and everybody is trying to integrate a lot of different things. So in a way if you really start from scratch, it might almost be easier, but we can't do that.

DS: What's your goal for your own risk-management group in the next few years?

ED: From a risk-management point of view, we'd like to have real-time risk management for every single product in one system, which is something we're always moving toward, but we're never totally there. Even with the best models we have, I think our models are, to some extent, one step ahead of our risk-management system. It's much harder to put a complex model into a system and apply it to hundreds of securities than to apply it to just one. If you want to do an exotic deal, you can use a complicated model to value it, but it is hard to integrate that complicated model into a system that prices thousands of things. It gets too slow, for starters.

From a modeling point of view, the hardest thing is to make your models price things in the real world rather than in the abstract world that most models work in. We want to try to get models that take account of liquidity and transaction costs and all of the more practical dislocations that the models don't usually account for.

DS: Where you think modeling will be moving in the next decade?

ED: We'd like to do two things. First, it's very hard to price something absolutely, and so what we always try to do is try to determine relative value. What an option model is doing is not telling you what the option is worth. It's telling you, "You tell me what the stock is worth and what the bond is worth, and I'll tell you what the option is worth." It's like "You tell me two things, and I'll tell you a third."

What we try to do more and more is say, "You tell me the price of six vanilla options and I'll tell you the price of an exotic option." We're always trying, in some sense, to ask you for market prices of a bunch of things that are liquid and then calculate the price of something that is more complicated and isn't liquid. That's the easiest way to proceed, and I think that's where we are headed.

DS: What do you think about Value-at-Risk?

ED: I think VAR is the right thing to do for a firm, but it's not the right thing to do for a trading desk. It's right that Goldman Sachs has some sense of how much the firm is risking in a statistical sort of way every day, but it's too crude for running a derivatives desk where you don't just want to know what you're likely to lose in a day, you actually want to know what you will lose if the market moves down three points or four points or if volatility goes up. VAR is just an average of all those things. It's how much you would lose in one day if the market moved four standard deviations. But you need more than that to actually run a book.

DS: How helpful has the derivatives software industry been to your firm? How much do you use it?

ED: When we started building some equity derivatives software in UNIX in early 1990, there really wasn't much on the market that suited us, so we developed our own risk-management tools. That's why we can regard our group as a software company focused on finance in some way. More people are doing software than financial modeling. We've bought Reuters for a feed, and we've bought a couple of software tools, but we've almost never bought a risk-management system or even a model from anybody.

I suppose if we started now, we could go out and save ourselves all that trouble, because a lot of our work goes into supporting this stuff. On other hand, the value of what we do is in the integration. You want to look at a whole portfolio and you'd have to start all over again with new risk reports...

The world is getting more complicated vis-á-vis regulators. In London, with the SFA, if you want to change the way you delta-hedge, you have tell them that you're using a different model and different risk reports. So I think we're sort of committed to extending things the way we do it now. If somebody comes to us and says "We have a new model, why don't you buy it?" it doesn't help me that much because the value is cumulative in having everything working together.

DS: The danger would be that your people would not be able to use some sort of technological advance from the outside.

ED: I don't think that's happened, but we could get left behind that way. If somebody gave us a model that we didn't support, somebody on the desk would eventually want us to model something slightly different, and we'd want to be able to go into the model and change it a little bit and run it again in our system. It would be a massive job to throw away everything we have and install a new system and make sure it does everything our current system does.

Even if we make a new release of some risk-management system, it takes ages to get people from one and onto the other. You have to run them in parallel for a while and you have to iron out the bugs. Whenever we build something new, we're forced to go to great trouble in some inefficient way to make it not too much different from what we had before, so traders don't have to make a big changeover. One of the constraints is always, "Don't change the way it looks on the outside too much because you can't get 30 people to start using something different in one day."