Nonlinear PDE model for pricing European options with transaction costs under the 3/2 non-affine stochastic volatility model

Abstract

In this paper, we study the problem of pricing European options with transaction costs under the 3/2 non-affine stochastic volatility model. First, we derive a nonlinear partial differential equations (PDE) model for pricing European options by using the expectation of transaction costs in a small time interval. It is worth to mention that the nonlinear PDE degenerates into the corresponding pricing PDE under the 3/2 stochastic volatility model when the transaction cost rate is set to zero. Then, we solve the nonlinear PDE numerically by using the finite difference method. Finally, we present numerical simulations and sensitivity analysis to illustrate both the consistency and the impact of transaction costs on option pricing.