Option Pricing with Transaction Costs and Stochastic Interest Rate

Abstract

In the case when transaction costs are associated with trading assets the option pricing problem is known to lead to solving nonlinear partial differential equations even when the underlying asset is modelled using a simple geometric Brownian motion. The nonlinear term in the resulting PDE corresponds to the presence of transaction costs. We generalize this model to a stochastic one-factor interest rate model. We show that the model follows a nonlinear parabolic type partial differential equation. Under certain assumption we prove the existence of classical solution for this model.