http://www.quantnet.com/interview-with-steven-shreve
Interview with Steven Shreve
To many Financial Engineering students, Steven Shreve isn’t a stranger. His books
The Binomial Asset Pricing Model and
Continuous-Time Models are the required textbooks for many MFE programs’ Stochastic Calculus courses. Professor Steven Shreve is a professor at Carnegie Mellon University and one of the co-founders of the M.S. in Computational Finance at Carnegie Mellon. We are happy to have Dr. Shreve to talk to Quant Network on several interesting topics. Our blogger
Joy Pathak conducted the interview.
What projects are you currently working on?
First of all, I am building models for limit order books using techniques from queueing theory. Secondly, I am trying to understand better the relationship between the Heath-Jarrow-Morton and Brace-Gatarek-Musiela models for the term structure of interest rates. Also, I am seeking to work out the consequences for trader behavior of different types of compensation schemes. Finally, I am concluding a project on the effect of transaction costs on optimal consumption and investment in a multi-asset model.
What do you consider your biggest achievement?
Figuring out how to teach stochastic calculus to people who are not in mathematics Ph.D. programs. The finance context helps a lot, because it brings the theorems to life.
Your books on Stochastic Calculus are de facto text books used by numerous MFE program to train generations of financial engineers. If you have a chance to rewrite your books, what would you do differently?
It is gratifying to know that my books have been helpful to so many people. They evolved from classroom notes and benefitted from discussions with many students over the years before they became books. As a result of teaching this material so frequently, I have many more exercises, which I plan to eventually include in new editions of the books. To partially satisfy the scores of requests I have gotten for solutions to the exercises, I will also put in more worked examples. I do not provide solutions to the exercises because that would compromise the usefulness of the books as texts for courses. I plan to expand the first volume, the one on the binomial model, to include material on foreign exchange and a derivation of the Black-Scholes formula starting from the binomial model. I would also like to expand the second volume, the one on continuous-time models, to include more material on forward measures and foreign exchange.
What is your take on the financial crisis and the quants and their mathematical models that were blamed for it?
Several factors came together to cause the financial crisis. Some of them are
- a sustained period of low interest rates that left trillions of dollars looking for a place to invest,
- government policies encouraging, even mandating, home loans to lowincome borrowers,
- the securitization of mortgages so that originators no longer had a stake in the credit-worthiness of the mortgages they originated,
- changes in regulations that permitted U.S. banks to increase their leverage,
- the compensation scheme for traders and bank executives that encouraged risk taking and short-term thinking, and
- increased reliance on models rather than fundamental research and judgment.
You asked about the last point. Mathematical models are no substitute for careful analysis. A good model builder/user knows the assumptions on which the model is based and has some sense of whether an application of a model violates those assumptions in some essential way. A poor model user takes the model as a black box into which one puts data in order to get out prices. I don’t know any serious quant who believed that model-based pricing and hedging of subprime-mortgage-backed assets with thousand-page descriptions was possible. Several quants have told me of their frustrations trying to get senior management to limit their exposure to these assets. So long as there are “profits” to be made, no one wants to listen to a quant worry about model risk. In fact, because there were profits to be made the ratings agencies were willing to plug numbers into formulas and conclude that some of these assets were investment grade. I hear stories of banks who marketed these assets by saying that their “quants” had studied them and found them to be safe and reliable. There was a time when cigarette companies would hire “medical researchers” whose studies minimized the health risks of tobacco. These were not serious medical researchers. Likewise, anyone who gave a model-based blessing to CDO-squared and similar arcane instruments cannot claim to be a serious quant.
In a recent article, you talked about the Gaussian Copula being one of the mathematical models behind the financial crisis. Can you elaborate a bit more on the role of the Gaussian Copula in mortgage-backed-securities and the financial crisis for our readers?
I discussed the Gaussian copula in the article “
Did Faulty Mathematical Models Cause the Financial Fiasco?” which appeared in Analytics magazine and can be downloaded from my homepage
www.math.cmu.edu/users/shreve. There is nothing inherently wrong with the Gaussian copula. It is a powerful tool for capturing correlations. However, as applied in finance, the model is static and hence cannot provide much guidance about how to hedge risk over time. Also, a simplified version of the Gaussian copula was used in which all correlations were reduced to a single parameter, and when the crisis arrived, that parameter was seen to have been incorrectly estimated. No one put into their models the possibility that housing prices would decline together across the country. It is not the fault of the model that its users overlooked this possibility.
Do you believe that the financial crisis contradicted some base assumptions behind risk-neutral valuation?
No. Risk-neutral valuation of derivative securities is justified if and only if those securities can be replicated (i.e., hedged) by trading in underlying instruments. That is never quite the case, but in liquid markets it is often almost the case, and in those markets, risk-neutral valuation is a very effective pricing tool. When replication is not possible, and it is not possible in credit markets, risk-neutral valuation is nothing more than an elaborate interpolation scheme and should be used only in combination with stringent risk management. That was true before the crisis and remains true today.
Companies are investing more and more into their trading divisions and technology nowadays. How important is Risk Management in today’s financial firms. Should there be more focus on model risk rather than just trying to develop more speculative models and quant strategies and improving technology?
Absolutely. Model risk must be taken seriously. Never trust a model fully. Knowing how much trust to place in a model requires a good understanding of the model and the market in which the model is being applied. Acquiring this knowledge is hard work, but failing to acquire it invites disaster.
As we move forward, do you see statistical models gaining more popularity compared to pure Stochastic Differential Equations approach?
Statistical methods have been used for years in asset management. More recently, the advent of algorithmic trading has increased the importance of statistical methods in finance. However, in derivative security pricing and hedging, there is no substitute for a model of asset evolution, and the best tool we have for building such models is stochastic calculus. As mentioned above, in markets where replication is not possible pricing models must be supplemented by effective risk management, and statistical methods come into play here as well. In conclusion, I believe that statistical methods will become more pervasive, but not at the expense of stochastic calculus.