Pricing Interest-Rate Derivatives
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 ?nal 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 mo- lar framework for the pricing of interest-rate derivatives within the class of exponential-a?ne jump-di?usions. Based on a technique introduced by Lewis (2001) for equity options, the payo?s and the stochastic dynamics of intere- rate derivatives are transformed separately. This not only simpli?es the - plication of the residue calculus but improves the e?ciency of numerical ev- uation schemes considerably. Dr. Bouziane introduces a re?ned Fractional InverseFastFourierTransformationalgorithmwhichisabletocalculateth- sands of prices within seconds for a given strike range. The potential of this method is demonstrated for several one- and two-dimensional models. Asaresulttheapplicationofjump-enhancedshortratemodelsforintere- ratederivativesisontheagendaagain. Ihope, Dr. Bouziane’smonographwill stimulate further research in this direction. T¨ ubingen, November 2007 Rainer Sch¨ obel Acknowledgements This book is based on my Ph. D. thesis titled ”Pricing Interest-Rate Deri- tives with Fourier Transform Techniques” accepted at the Eberhard Karls University of Tubing ¨ en, Germany. Writing the dissertation, I am indebted to many people which contributed academic and personal development.