10. Stochastic Skew Model

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, P. Carr and L. Wu developed a so-called stochastic-skew model (SSM) with three dynamical state variables that is highly tractable. Hence, they were able to value simple European-style options using Fourier methods. However, pricing exotic options under this model requires numerical solution of a three-dimensional PIDE with mixed derivatives, which is computationally expensive if one uses the standard approaches considered in the introduction to Chapter 5 Therefore, in this chapter, to achieve this goal, we propose a new splitting technique, which, combined with MPsDO, reduces the solution of the original three-dimensional PIDE to the solution of a set of one-dimensional PDEs, thus allowing a significant computational speedup. Following (Itkin and Carr, Int. J. Numer. Anal. Model. 8(4):667–704, 2011), we demonstrate this technique for single and double barrier options priced using the SSM.