Pricing options under the non-affine stochastic volatility models: An extension of the high-order compact numerical scheme

We consider an improvement of a high-order compact finite difference scheme for option pricing in non-affine stochastic volatility models. Upon applying a proper transformation to equate the different coefficients of second-order non-cross derivatives, a high-order compact finite difference scheme is developed to solve the partial differential equation with nonlinear coefficients that the option values satisfied. Based on the local von Neumann stability analysis, a theoretical stability result is obtained under certain restrictions. Numerical experiments are presented showing the convergence and validity of the expansion methods and the important effects of the non-affine coefficient and volatility of volatility on option values.