Emanuel Derman

The Illusions of Dynamic Replication

While modern financial theory holds that options values are derived by dynamic replication, they can be correctly valued far more simply by long familiar static and actuarial arguments that combine stochastic price evolution with the no-arbitrage relation between cash and forward contracts.

Metaphors, Models & Theories

Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.

A stochastic-difference-equation model for hedge-fund returns

We propose a stochastic difference equation of the form X n = A n X n−1 + B n to model the annual returns X n of a hedge fund relative to other funds in the same strategy group in year n. We fit this model to data from the TASS database over the period 2000 to 2005. We let {A n } and {B n } be independent sequences of independent and identically distributed random variables, allowing general distributions, with A n and B n independent of X n−1, where E[B n ] = 0. This model is appealing because it can involve relatively few parameters, can be analysed, and can be fitted to the limited and somewhat unreliable data reasonably well. The key model parameters are the year-to-year persistence factor γ ≡ E[A n ] and the noise variance . The model was chosen primarily to capture the observed persistence, which ranges from 0.11 to 0.49 across eleven different hedge-fund strategies, according to regression analysis. The constant-persistence normal-noise special case with A n = γ and B n (and thus X n ) normal provides a good fit for some strategies, but not for others, largely because in those other cases the observed relative-return distribution has a heavy tail. We show that the heavy-tail case can also be successfully modelled within the same general framework. The model is evaluated by comparing model predictions with observed values of (i) the relative-return distribution, (ii) the lag-1 auto-correlation and (iii) the hitting probabilities of high and low thresholds within the five-year period.

Financial engineering at Columbia University

Columbia University is home to a vibrant community of financial engineering research and education. Faculty and students from business, engineering, mathematics and statistics share classes and collaborate on research in all areas of quantitative finance, including derivative securities, risk management, portfolio optimization, trading strategies, asset pricing, computational methods and econometrics. Faculty expertise, recognized through numerous awards and publications, covers the whole range from theory to practice. Columbia also takes full advantage of its New York location, drawing on expert practitioners for teaching, seminars, conference participation, research collaborations and internships for students. This overview of financial engineering at Columbia describes degree programs and research activities and highlights some connections with industry. 2. Degrees and programs

Apologia Pro Vita Sua

Honest assessment of the ethical behavior of our financial institutions and markets over the recent past has made many former defenders rather uncomfortable. In this article, whose Latin title translates as “a defense of one’s life,” Derman reflects on the moral dimensions of the derivatives business—in particular, the practice of financial engineering, which creates the models that drive the markets. He offers a “Modeler’s Hippocratic Oath,” similar to the oath that guides the medical profession, whose precepts are meant to clarify and limit the proper role of abstract modeling in guiding financial decision making.