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

Düring, Bertram, Fournié, Michel and Heuer, Christof (2014) High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. Journal of Computational and Applied Mathematics, 271. pp. 247-266. ISSN 0377-0427

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[img] PDF (This is the final accepted version of: B. Düring, M. Fournié, and C. Heuer. High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. J. Comput. Appl. Math. 271 (2014), 247-266.) - Accepted Version
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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.

Item Type: Article
Keywords: High-order compact finite difference method; partial differential equation; mixed derivatives; option pricing
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Bertram During
Date Deposited: 11 Feb 2016 10:42
Last Modified: 07 Sep 2017 10:06
URI: http://sro.sussex.ac.uk/id/eprint/59616

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