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

Bertram D\"uring and Christof Heuer
Authors registered in the RePEc Author Service: Bertram Düring

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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.

Date: 2016-11
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1611.00316

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