Monday, September 19, 2011
Obituary: David Heath will be remembered for taking mathematics to Wall Street
David C. Heath, professor emeritus and former Orion Hoch Professor of Mathematical Sciences at Carnegie Mellon University, died August 11 of complications related to Alzheimer's disease. Prior to joining CMU's faculty, David was the Merrill Lynch Professor of Financial Engineering at Cornell University. He is survived by his wife Judi and three children, Kelley Allen, Michael Heath and Susan Heath, four grandchildren, and his sister Janet Heath.
David was a world leader in theoretical and applied research in financial risk management and the co-creator of one of the financial industry's most widely used models for interest rate risk management, the Heath-Jarrow-Morton (HJM) model.
"Even though it is 25 years since I first met him, I have yet to come across someone with his wisdom and intellect and smoothness of dealing with almost every circumstance. I was very lucky to have a man like him play such an important role in my life," said Andrew Morton, who as a graduate student worked with David on the HJM model.
David earned a Bachelor of Arts degree from Kalamazoo College in 1964, and a Master of Arts degree in 1965 and Ph.D. in Mathematics in 1969 from the University of Illinois. In addition to Cornell and CMU, David served on the faculties of the University of Minnesota, the University of California at Berkeley, and the University of Strasbourg. He retired from CMU in 2006.
At various times in his career, David was a consultant for the U.S. Army Corp of Engineers, Quaker Oats, the Department of Energy, IBM, Alcoa, Morgan Stanley, Dupont, Credit Suisse, options trading firms, and government agencies, and he served on the boards of directors of multiple financial firms.
David was also a noted educator. He supervised 16 Ph.D. students, and while at Carnegie Mellon he served on the Department of Mathematical Sciences' Steering Committee and was an instructor in the Master of Science program in Computational Finance. He relished teaching undergraduates how to use mathematics as a tool for solving practical problems, a craft at which he was a master.
"He has been gone from the university for five years, but I still find myself quoting David's gems of wisdom. He was a wonderful colleague," said William Hrusa, Acting Head of Mathematical Sciences. "When he started having cognitive problems, rather than going into denial, he consulted a doctor, reported the diagnosis to the university, and arranged a graceful exit from the university that minimized the impact on his students and colleagues."
Aside from the numerous students he taught and inspired, David's most lasting contribution is the Heath-Jarrow-Morton (HJM) model, which models the term structure of interest rates. Following the publication in 1973 of the Nobel-prize-winning Black-Scholes formula for stock option pricing and hedging, mathematicians and financiers searched to develop an analogous methodology for fixed-income markets. Unlike stock from a single firm, which has no maturity, bonds of a single issuer are differentiated by their maturity date. Researchers found it difficult to create a model for bonds and related derivative securities that ensured the prices produced by the model were realistic and consistent across different maturities.
David and his colleagues Robert Jarrow and Andrew Morton were able to solve this problem, and HJM models have since been adopted by most major banks for asset valuation and risk management. Because these models can accurately reflect the volatility of changes in the term structure of interest rates, essential to correctly pricing securities, they changed banking in fundamental ways, allowing banks to offer financial instruments tailored to the needs of their clients. HJM models have been extended to model foreign exchange risk, risky bonds, and commodities futures.
David's later work, as part of a 1995 consulting assignment from Société Générale, changed the way that financial institutions measure risk. The standard risk measure used by banks and mandated by regulators at that time was Value-at-Risk (VaR), which estimated the probability of a major loss. Banks using VaR would then try to minimize this probability. Unfortunately, this approach did not take into account how catastrophic the major loss might be.
After a conference in Boston, when all the CMU faculty and graduate students in mathematical finance were preparing to board the same return flight to Pittsburgh, David noted that this was the VaR approach. The probability of a major loss would be greater if several different flights were used -- a crash of any one of them would be costly to CMU. Minimizing the probability of loss by putting everyone on the same flight and ignoring how catastrophic the loss would be if it occurs is exactly how VaR regulations direct banks to behave.
In contrast to VaR, David and his co-authors Philippe Artzner, Freddy Delbaen and Jean-Marc Eber conceptualized risk measure as a function whose input is a portfolio and whose output is the cash reserve a bank should have in order to safely hold the portfolio. They listed a set of properties that this function should have and then characterized the set of risk measures satisfying these axioms. They called these coherent risk measures. The set of coherent risk measures turns out to contain many potentially useful risk measures, but it does not include VaR. Since this work, VaR has lost its status as the unquestioned standard, and firms have begun to experiment with coherent methods of risk measurement.
At David's retirement dinner, Steven Shreve, who succeeded David as Orion Hoch Professor, summarized his career with the following words:
"Mathematicians do not build monuments such as buildings and bridges. They leave behind a legacy of ideas and students. The work of mathematicians can be divided into two classes. First, there are the theorems that are appreciated primarily by other mathematicians. They are deep and beautiful, and substantial study is required to understand what they are about. But there is a second type of mathematical research, the kind resulting in theorems designed to address applied problems. For this work, the depth is in understanding the application, and the challenge is to find the appropriate mathematics. These theorems have the power to change our lives. Dave's legacy is of the second kind. In our universities, we train students to be the first kind of mathematician. Once in a while, through some accident of nature, the second kind of mathematician comes along and teaches all of us, faculty as well as students, by example."
Donations in David's memory can be made to the Alzheimer's Association.