Polynomial processes and their applications to mathematical Finance

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Cuchiero, Christa
Keller-Ressel, Martin
Teichmann, Josef
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Abstract
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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 diffusion coefficients, as well as L\'evy-driven SDEs with affine vector fields. Thus, many popular models such as exponential L\'evy models or affine models are covered by this setting. The applications range from statistical GMM estimation procedures to new techniques for option pricing and hedging. For instance, the efficient and easy computation of moments can be used for variance reduction techniques in Monte Carlo methods.
Comment: revised and extended version, accepted for publication in Finance and Stochastics
Keywords
Mathematics - Probability, Mathematics - Numerical Analysis, 60J25, 91B70
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