American Option Pricing Under a Two‐Factor Stochastic Volatility Model With Nonlinear Exogenous Costs

ABSTRACT This paper examines the pricing of American options within a two‐factor stochastic volatility framework, incorporating a stochastic long‐term mean, while accounting for transaction costs that introduce nonlinear effects on option values. These conditions lead to distinct four‐dimensional partial differential equations for both option holders and writers, derived from a dynamic hedging strategy. The equations are solved numerically using an explicit finite‐difference approach due to their high nonlinearity. Additionally, the study investigates the impact of transaction costs and conducts a sensitivity analysis on key parameters. The proposed methodology can be easily extended to price other option types in a multifactor stochastic volatility or stochastic interest rate setting with transaction costs.