Essentially High-Order Compact Schemes with Application to Stochastic Volatility Models on Non-Uniform Grids
Author | : Bertram Düring |
Publisher | : |
Total Pages | : 6 |
Release | : 2016 |
ISBN-10 | : OCLC:1305916111 |
ISBN-13 | : |
Rating | : 4/5 ( Downloads) |
Download or read book Essentially High-Order Compact Schemes with Application to Stochastic Volatility Models on Non-Uniform Grids written by Bertram Düring and published by . This book was released on 2016 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.