Introduction to Fast Fourier Transform in Finance

Many MBA students are daunted by the requirement that calculus is a prerequisite for the program. But those who are already familiar with finance know that most of the “hard stuff” of calculus is rarely used in practice. The real key is to develop an intuitive understanding of what calculus is about and to know a few basic kinds of things, like taking a derivative. A similar kind of angst hit the finance profession 30 years ago, when continuous-time mathematics was introduced. But today, pretty much everyone has developed the intuition, and knows how to use It9s formula, so continuous-time models have become familiar. The methods of option pricing introduced in the 1970s led to the Black-Scholes formula and a number of extensions, but they are not able to handle things like stochastic volatility, jumps, or non-Gaussian innovations in any convenient way. In the 1990s, researchers began to model these features using powerful mathematical techniques based on Fourier transforms and similar methods, that allow closed-form valuation equations for much more general returns processes. But once again, the new technology seems pretty daunting. In this article, Cerný offers some valuable intuition on what the fast Fourier transform does (think about bicycle wheels!). He also provides some very useful details about key differences in how to do it in several common software packages.