An Efficient Numerical Scheme for the Solution of a Stochastic Volatility Model Including Contemporaneous Jumps in Finance

Abstract

The model of stochastic volatility with contemporaneous jumps is written for pricing under a partial integro-differential equation (PIDE) having a double integral and a nonsmooth initial value. To tackle this problem, first, a new radial basis function (RBF) as a convex combination of two known RBFs is given. Second, the weighting coefficients of the RBF generated finite difference (FD) method are contributed and the associated error equations are derived. To deal with the integral part, the new idea is to apply an estimate for the unknown function for every cell and do an integration of the density function. The contributed approach is competitive and reduces both the calculational efforts and elapsed time.