Pricing Interest-Rate Derivatives: A Fourier-Transform Based Approach (Repost)

In a hypothetical conversation between a trader in interest-rate derivatives and a quantitative analyst, Brigo and Mercurio (2001) let the trader answer about the pros and cons of short rate models: ”… we should be careful in thinking market models are the final and complete solution to all problems in interest rate models … and who knows, maybe short rate models will come back one day…”
In his dissertation Dr. Markus Bouziane contributes to this comeback of short rate models. Using Fourier Transform methods he develops a modu- lar framework for the pricing of interest-rate derivatives within the class of exponential-affine jump-diffusions. Based on a technique introduced by Lewis (2001) for equity options, the payoffs and the stochastic dynamics of interest- rate derivatives are transformed separately. This not only simplifies the ap- plication of the residue calculus but improves the efficiency of numerical eval- uation schemes considerably. Dr. Bouziane introduces a refined Fractional Inverse Fast Fourier Transformation algorithm which is able to calculate thou- sands of prices within seconds for a given strike range. The potential of this method is demonstrated for several one- and two-dimensional models.
As a result the application of jump-enhanced short rate models for interest- rate derivatives is on the agenda again. I hope, Dr. Bouziane’s monograph will stimulate further research in this direction.
Tübingen, November 2007 Rainer Sch¨ obel