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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: A new class of analytically tractable processes with applications to option pricing

Workshop: Concluding Workshop

Time: Wed, December 03, 2008, 14:30-15:00

Speaker: Christa Cuchiero

Abstract

We introduce a class of Markov processes called $m$-polynomial, for which the calculation of (mixed) moments up to order $m$ only requires the computation of matrix exponentials. This class contains affine processes, processes with quadratic squared diffusion coefficient as well as Levy-driven SDEs with affine vector fields. Thus, many popular models such as the classical Black-Scholes, exponential Levy or affine models are covered by this setting. The applications range from statistical GMM estimation to option pricing. For instance, the easy computation of moments can successfully be used for variance reduction techniques in Monte Carlo simulations.

Presentation slides (pdf, 477 KB)

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