Polynomial processes and their applications to mathematical finance

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Christa Cuchiero - , Universität Wien (Autor:in)
  • Martin Keller-Ressel - , Technische Universität Berlin (Autor:in)
  • Josef Teichmann - , ETH Zurich (Autor:in)

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.

Details

OriginalspracheEnglisch
Seiten (von - bis)711-740
Seitenumfang30
FachzeitschriftFinance and stochastics
Jahrgang16
Ausgabenummer4
PublikationsstatusVeröffentlicht - Okt. 2012
Peer-Review-StatusJa
Extern publiziertJa

Externe IDs

ORCID /0000-0003-0913-3363/work/167706916

Schlagworte

Schlagwörter

  • Affine processes, Analytic tractability, Diffusions with jumps, Hedging, Markov processes, Pricing