Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment

Abstract

This paper investigates the American strangle option in a mean-reversion environment. When the underlying asset follows a mean-reverting lognormal process, an analytic pricing formula for an American strangle option is explicitly provided. To present the pricing formula, we consider the partial differential equation (PDE) for American strangle options with two optimal stopping boundaries and use Mellin transform techniques to derive the integral equation representation formula arising from the PDE. A Monte Carlo simulation is used as a benchmark to validate the formula’s accuracy and efficiency. In addition, the numerical examples are provided to demonstrate the effects of the mean-reversion on option prices and the characteristics of options with respect to several significant parameters.