Jumps Without Tears: A New Splitting Technology for Barrier Options

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.