Polynomial processes and their applications to mathematical finance

Christa Cuchiero (), Martin Keller-Ressel () and Josef Teichmann ()

Finance and Stochastics, 2012, vol. 16, issue 4, 740 pages

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 diffusion coefficients, as well as Lévy-driven SDEs with affine vector fields. Thus, many popular models such as exponential Lévy 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. Copyright Springer-Verlag 2012

Keywords: Markov processes; Diffusions with jumps; Affine processes; Analytic tractability; Pricing; Hedging; 60J25; 91B70; C02; G12 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s00780-012-0188-x

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