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Erschienen in:
2017 | OriginalPaper | Buchkapitel
17. Essentially High-Order Compact Schemes with Application to Stochastic Volatility Models on Non-Uniform Grids
verfasst von : Bertram Düring, Christof Heuer
Erschienen in: Novel Methods in Computational Finance
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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 finite difference scheme is significantly outperformed.