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 finite difference scheme is significantly outperformed.
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Acknowledgements
BD acknowledges support by the Leverhulme Trust research project grant ‘Novel discretisations for higher-order nonlinear PDE’ (RPG-2015-69). CH was partially supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE—Novel Methods in Computational Finance).
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Düring, B., Heuer, C. (2017). Essentially High-Order Compact Schemes with Application to Stochastic Volatility Models on Non-Uniform Grids. In: Ehrhardt, M., Günther, M., ter Maten, E. (eds) Novel Methods in Computational Finance. Mathematics in Industry(), vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-61282-9_17
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DOI: https://doi.org/10.1007/978-3-319-61282-9_17
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