Numerical methods for pricing options under stochastic volatility models.

Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps. In this talk, we consider the numerical approximation of such models. On one hand, due to the non-local nature of the integral term, we propose to use Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher order accuracy schemes under weak stability time-step restrictions. On the other hand, we propose a hybrid tree-finite difference method to approximate the Heston model, possibly in the presence of jumps. Numerical tests are presented to show the computational efficiency of the approximation.