High-Order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Models on Non-Uniform Grids

21 Pages Posted: 19 Jul 2013 Last revised: 25 Apr 2014

See all articles by Bertram Düring

Bertram Düring

University of Warwick - Mathematics Institute

Michel Fournie

Université Paul Sabatier Toulouse III

Christof Heuer

University of Sussex - School of Mathematical and Physical Sciences

Date Written: January 17, 2014

Abstract

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all numerical experiments a comparative standard second-order discretisation is significantly outperformed. We conduct a numerical stability study which indicates unconditional stability of the scheme.

Keywords: option pricing, stochastic volatility, high-order compact finite difference method

JEL Classification: C63, G13

Suggested Citation

Düring, Bertram and Fournie, Michel and Heuer, Christof, High-Order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Models on Non-Uniform Grids (January 17, 2014). Available at SSRN: https://ssrn.com/abstract=2295581 or http://dx.doi.org/10.2139/ssrn.2295581

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

Christof Heuer

University of Sussex - School of Mathematical and Physical Sciences ( email )

Brighton, BN1 9QH
United Kingdom

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