High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:271

Article

Duering, Bertram¹  Fournie, Michel^2,3  Heuer, Christof¹ 

[1] Univ Sussex, Dept Math, Brighton BN1 9QH, E Sussex, England

[2] Univ Toulouse, Inst Math Toulouse, Toulouse, France

[3] CNRS, UMR 5219, F-75700 Paris, France

关键词: High-order compact finite difference method;    Partial differential equation;    Mixed derivatives;    Option pricing;   

DOI  :  10.1016/j.cam.2014.04.016

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free