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
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—