Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models. Issue 1 (February 2014)

• Record Type: Journal Article
• Authors: Pang, Hong-Kui; Sun, Hai-Wei
• Is Part Of: East Asian journal on applied mathematics. Volume 4:Issue 1(2014)
• Page Start: 52
• Page End: 68
• Publication Date: 2014-02
• Subjects: 91B28, -- 62P05, -- 35K15, -- 65F10, -- 65M06, -- 91B70, -- 47B35; Stochastic volatility jump diffusion, -- European option, -- barrier option, -- partial integro-differential equation, -- matrix exponential, -- shift-invert Arnoldi, -- matrix splitting, -- multigrid method; Applied mathematics -- Periodicals; 519.05
• DOI: 10.4208/eajam.280313.061013a
• Languages: English
• ISSNs: 2079-7362

Abstract

Abstract: The stochastic volatility jump diffusion model with jumps in both return and volatility leads to a two-dimensional partial integro-differential equation (PIDE). We exploit a fast exponential time integration scheme to solve this PIDE. After spatial discretization and temporal integration, the solution of the PIDE can be formulated as the action of an exponential of a block Toeplitz matrix on a vector. The shift-invert Arnoldi method is employed to approximate this product. To reduce the computational cost, matrix splitting is combined with the multigrid method to deal with the shift-invert matrix-vector product in each inner iteration. Numerical results show that our proposed scheme is more robust and efficient than the existing high accurate implicit-explicit Euler-based extrapolation scheme.