High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Models

23 Pages Posted: 23 Jul 2010 Last revised: 2 Feb 2012

See all articles by Bertram Düring

Bertram Düring

University of Warwick - Mathematics Institute

Michel Fournie

Université Paul Sabatier Toulouse III

Date Written: July 22, 2010

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.

Keywords: Option pricing, compact finite difference discretizations, mixed derivatives, high-order scheme

JEL Classification: C63, G13

Suggested Citation

Düring, Bertram and Fournie, Michel, High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Models (July 22, 2010). Available at SSRN: https://ssrn.com/abstract=1646885 or http://dx.doi.org/10.2139/ssrn.1646885

Bertram Düring (Contact Author)

University of Warwick - Mathematics Institute ( email )

Zeeman Building
Coventry, CV4 7AL
United Kingdom

Michel Fournie

Université Paul Sabatier Toulouse III ( email )

118 Route de Narbonne
Toulouse cedex 9, F-31062
France

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