Essentially high-order compact schemes with application to stochastic volatility models on non-uniform grids

Dűring, Bertram and Heuer, Christof (2017) Essentially high-order compact schemes with application to stochastic volatility models on non-uniform grids. In: Erhhardt, Matthias, Gunther, Michael and ter Maten, E. Jan W. (eds.) Novel Methods of Computational Finance. The European Consortium of Mathematics in Industry, 25 . Springer International, pp. 313-319. ISBN 978-3-319-61282-9 (Accepted)

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Abstract

We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a non- uniform grid with more grid-points around the strike price. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical convergence study we achieve fourth-order accuracy also for non-zero correlation. A combination of Crank-Nicolson and BDF-4 discretisation is applied in time. Numerical examples confirm that a standard, second-order infinite difference scheme is significantly outperformed.

Item Type: Book Section
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
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Depositing User: Billy Wichaidit
Date Deposited: 04 Sep 2017 08:08
Last Modified: 08 Sep 2017 08:09
URI: http://sro.sussex.ac.uk/id/eprint/69974

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Project NameSussex Project NumberFunderFunder Ref
Novel discretisations of higher-order nonlinear PDEG1603LEVERHULME TRUSTRPG-2015-069