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- Title
Polynomial processes and their applications to mathematical finance.
- Authors
Cuchiero, Christa; Keller-Ressel, Martin; Teichmann, Josef
- 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.
- Subjects
BUSINESS mathematics; MARKOV processes; POLYNOMIALS; NUMERICAL calculations; MATRIX exponential; MONTE Carlo method
- Publication
Finance & Stochastics, 2012, Vol 16, Issue 4, p711
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-012-0188-x