The King of Quants: A Conversation with Emanuel Derman, Part 2

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 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 – 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 – 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 – I'm getting a little off the subject – 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 – 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 mistakes— numerical mistakes or implementation mistakes that you're not aware of.

So you always to have one level of thinking which is strictly mathematical and another level which says, in a qualitative way, "This is what I'd expect to happen." And check whether there's consistency and, if there isn't, to understand which side is wrong.

Connors: Do you see today a higher correlation among markets than what you saw 10-15-20 years ago?

Derman: I can't really prove this, but my opinion is that all the electronic linking and all the increased liquidity, when it's there, tends to dampen volatility for most of the time.

But then when bad things happen the liquidity exaggerates it because everybody's trying to get out of everything at the same time and it snowballs. You saw it from the subprime problems.

Then other things start to get hurt and then, eventually, there's the revulsion from credit altogether.

Connors: Yes. I remember there was a day back in August where soy beans, I believe, were down limit and the only reason why they were down limit is because there were hedge funds that were long beans that had forced liquidation. They needed cash. So if one is putting together models, he has to maybe anticipate that markets will be more and more correlated as time passes.

Let me ask three last questions here. One is tied into data – the integrity of data, especially in the equity markets and especially in the international equity markets. If someone is trying to put together models on pricing in – let's say international markets where the integrity of that data may not be as clean – well, how do you overcome that? Is it an issue?

Derman: I think it is an issue. People without too much experience think of data as a minor problem but then realize that it's intrinsic to everything you do in this field. For example, (and this is not a very sophisticated example) if you're trying to look at implied volatilities and you're interested in the tails of the distribution and out-of-the-money options …

Connors: Yes.

Derman: Then the quotes are much fewer and far between. So with a 20% out-of-the-money option, you're going see a trade that doesn't match the true close of the underlying market.

It's the same with collecting tick data if you're trying to do statistical arbitrage. People say, "Oh, you know, if we could just get the data right." But the data's the critical part, you know. It's not something you can look at afterwards and say, "Oh, everything's OK but for that."

Intrinsically the data has equal weight with everything else you do.

Connors: Yes. So you're basically – if someone knows that the data – if there is no such thing as clean data, one has to account for that in the models, and one way, there has to be some degree of error put into theirs – into that. Is that a fair assumption?

Derman: Yeah it is and especially option data. You have to adjust your model for the fact that your data isn't clean. The data collection and cleaning cannot be left to market-unknowledgeable people; it must be cleaned by somebody who understands what an anomaly is.

Be sure to catch the third and final part of "The King of Quants: A Conversation with Emanuel Derman" next Friday, May 23rd!