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

2016/11/01 by Bertram Düring, Düring, Bertram, Christof Heuer +1
Economics, Econometrics and Finance · #65M06 #91B28 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1611.00316

openalex publication_date 2016/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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