Nonlinear PDE model for European options with transaction costs under Heston stochastic volatility

Abstract

In this work, we formulate a pricing model for European options with transaction costs under Heston-type stochastic volatility. The resulting pricing partial differential equations (PDEs) are a pair of nonlinear convection-diffusion-reaction equations with mixed derivative terms, for the writing and holding prices, respectively. The equations are solved numerically by the explicit Euler method. Numerical experiments are presented to illustrate the order of convergence and the effect of the transaction costs on option prices.