Year: 2011
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 4 : pp. 667–704
Abstract
The market pricing of OTC FX options displays both stochastic volatility and stochastic skewness in the risk-neutral distribution governing currency returns. To capture this unique phenomenon Carr and Wu developed a model (SSM) with three dynamical state variables. They then used Fourier methods to value simple European-style options. However, pricing exotic options requires numerical solution of 3D unsteady PIDE with mixed derivatives which is expensive. In this paper to achieve this goal we propose a new splitting technique. Being combined with another method of the authors, which uses pseudo-parabolic PDE instead of PIDE, this reduces the original 3D unsteady problem to a set of 1D unsteady PDEs, thus allowing a significant computational speedup. We demonstrate this technique for single and double barrier options priced using the SSM.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-IJNAM-706
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 4 : pp. 667–704
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Barrier options pricing stochastic skew jump-diffusion finite-difference scheme numerical method the Green function general stable tempered process.