Pricing Asian options in a stochastic volatility model with jumps

We consider the problem of pricing arithmetic Asian options in the presence of stochastic volatility. By performing a change of numeraire introduced by Vĕcĕr, we derive a partial integro-differential equation (PIDE) for Asian options within Barndorff-Nielsen and Shephard (BNS) model framework. Then, a finite difference discretization is proposed for dealing with the terms containing the partial derivatives and a simple trapezoidal rule is used for the integral term due to jumps. Numerical experiments confirm that the developed methods are very efficient.