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.

On the American style futures contracts

“…Note that the limit above is zero due to Lemma 1. We can easily check that function (14) achieves its maximum namely for c given by formula (11) and it leads to price (12).…”

“…The other class of American derivatives leads to an optimal region consisting of two parts -thus a first exit from a strip arises. Such instruments are the straddle options, [1,9], their extensions named strangles, [6,12,14,15,21,22,32], cancelable American options, also known as Israeli or game options, [8,16,18,24,31,30], etc.…”

American strangle options with arbitrary strikes

“…Also, Abdou and Moraux (2016) use an EEP method for pricing and hedging. Recently, Jeon and Kim (2022) derive an analytic valuation formula under mean-reversion assumptions.…”