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Q&A with Quant Expert Paul Wilmott: The Fundamental Flaw of Nearly All Risk Models

Quant expert Paul Wilmott tells Advanced Trading that Wall Street's risk models share a fundamental flaw, and that traders are all too happy to ignore their true risk exposure in search of profits.

What are the challenges for today's quant traders? Advanced Trading spoke with Dr. Paul Wilmott, a quant expert, lecturer and author based in London, who reveals all the dirty secrets. Wilmott, head of 7city Learning's quants faculty and course director for the training firm's Certificate in Quantitative Finance (CQF) program, says nearly all risk models have a basic flaw, regulators get no respect, and quant traders often bully them or fudge numbers to hide their true risk exposure.

What are the biggest concerns and challenges today in the quant trading world?

Wilmott: People really do not understand much about risk management and derivatives at all. People are very confused about the basic concepts. They think they understand something, and they don't. You see people using these complex instruments and quite frankly, they don't have a clue about the basic risk management of these things.

What is the cause of this confusion?

Wilmott: People don't really understand these products. And they never really have. There is a lot of obfuscation going on. People make the products very complex, and the mathematical models are far too complex. But there also are some fundamental issues with the risk management of derivatives.

People do get a bit confused about whether finance is an art or a science. Anyone with half a brain soon realizes that these things do not have laws in a sense like physics.

For example, there is a thing called Hooke's Law, named after Richard Hooke, a famous 17th century English mathematician who did experiments with springs. The law says that if you take a spring and pull it a little bit, the force of your pull is proportional to how far you pull it; if you pull a spring twice the distance, it is using twice the force.

Hooke's idea can be expressed mathematically: Force (F) equals some number (K) multiplied by the extension (X) of the spring; "K" is the constant. But what is K? Hooke calibrated his spring. Here's a one-pound weight, for example -- put it on the spring and see how far it stretches. Once Hooke knew how a spring responded to a one-pound weight, he could calculate K and then use the formula to weigh anything at all.

This is called "calibration," and this concept is used all the time in derivatives and risk management. We have this mathematical model for derivatives, and it includes a symbol for volatility called sigma. What is the sigma? It's the volatility of some stock in the future, but since we don't have a crystal ball, how do we know what the volatility is? I know what we'll do -- we'll calibrate it.

These people are selling this option for $70. That is the one-pound weight. Using the formula, you can figure out the volatility, or K, and you can use that to price other instruments.

Where does the problem arise?

Wilmott: But how on Earth do we know that the price to which we are calibrating in the market is correct in any sense? A couple of traders, for example, can trade a few thousand dollars worth of options based on a volatility (K) of 20 percent. But then you put that 20 percent into a million dollars worth of options? It's crazy to use a tiny trade to give you an idea of a very big trade. How do you know the volatility is correct?

When you first do this calibration, you figure out that the volatility is 20 percent. But you come back a week later and recalibrate the trade and options prices, and you find out that the market volatility is 25 percent. You have to look at the models risk managers are using -- they are assuming that volatility is constant. We can assume the models are wrong. There is a big, big, big, big difference between something that varies and a true constant.

So how do risk managers explain this to regulators?

Wilmott: A few months ago, I visited a regulator in Washington -- the idea was to speak about certain risk management techniques and tell them in a nice way that nobody really respects regulators. Certain people say regulators are not really that smart because they are not paid as much as Goldman Sachs traders and you don't get the best people. I said, "You need people to respect you, and for banks to respect you, you need a few killer questions. You can go into a bank and almost innocently ask a question that will blow their socks off." One of these questions commonly asked is "Is K [volatility] equal to 2 every week, or in their model does K change? How stable is your calibration?" And immediately the most sophisticated people will realize, "They're onto us, guys."

How do the regulators respond?

Wilmott: The problem that I found with the regulators was that while they were sophisticated mathematically, they weren't sophisticated about the modeling and the assumptions that were being used. They said, "What is wrong with the paradigm [the constant for volatility] changing? Isn't that the sign of an unstable world?"

But the minute you go around and recalibrate the model, you lose all possibility of tracking the error within the model. Why? Because when you calibrate, then your model matches the data. And then you come back a week later and you recalibrate again, and the model still matches the data. The problem is, you are recalibrating and changing the parameters and therefore the model was never correct.

So these regulators were going into banks and asking, "Do you recalibrate?" and if the bank said, "No, because it's unstable and doesn't work," the regulators said, "You must recalibrate." By saying that, the regulators were telling the banks, "You must hide risk." That's all this recalibration does. It hides risk. It doesn't help you see what risk there is. So the regulators, by understanding the math and not the concepts, were effectively encouraging banks to hide risk.

Does running risk checks and calibrating and checking risk models slow down trading? Can trading opportunities evaporate as the risk team does its job?

Wilmott: Yes. It always has been a constant struggle between risk managers and traders. One risk manager at a bank told me about a classic example a few weeks ago: He was asked by a trader to come up with some risk numbers and he went off and came back and said the risk in your portfolio is this. But the trader said in a knowing way, "That is not the risk in my position." He told the risk manager to go back and re-do the numbers. What he meant was, go back and fudge the model so it looks like there is less risk than there is -- which this person did because he wanted to keep his job. Phil Albinus is the former editor-in-chief of Advanced Trading. He has nearly two decades of journalism experience and has been covering financial technology and regulation for nine years. Before joining Advanced Trading, he served as editor of Waters, a monthly trade journal ... View Full Bio

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