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.
Original language | English (US) |
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Pages (from-to) | 667-704 |
Number of pages | 38 |
Journal | International Journal of Numerical Analysis and Modeling |
Volume | 8 |
Issue number | 4 |
State | Published - 2011 |
Keywords
- Barrier options
- Finite-difference scheme
- General stable tempered process
- Jump-diffusion
- Numerical method
- Pricing
- Stochastic skew
- The Green function
ASJC Scopus subject areas
- Numerical Analysis