High-order compact finite difference scheme for option pricing in stochastic volatility models

Authors:
Bertram DüRing;Michel Fournié
Affiliations:
Department of Mathematics, University of Sussex, Pevensey II, Brighton, BN1 9QH, United Kingdom;Institut de Mathématiques de Toulouse, Université de Toulouse et CNRS (UMR 5219), France
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the analysis becomes too involved we validate our findings by a numerical study. Numerical experiments for the European option pricing problem are presented. We observe fourth order convergence for non-smooth payoff.