Numerical Issues of Stochastic Volatility Models

Abstract

In this chapter we address various numerical issues associated with stochastic volatility models. The sophisticated numerical implementation of stochastic volatility models is crucial for a sound performance of the pricing engine and the model calibration, and includes some different aspects: the numerical integration of (inverse) Fourier transform, the computation of functions of complex number, especially the logarithm of complex number, the calculation of Greeks as well as the simulation of stochastic volatility process. Each of these issues has been already extensively discussed in financial literature. Here we present a comprehensive and compact treatment of these numerical issues from the point of view of practitioners. The discussion on the efficient simulations of stochastic volatility models is left in the next chapter.