Third Order Approximation to the Price of Perpetual American Lookback Option with a Mean-Reverting Stochastic Volatility

Abstract

This paper is a research for a perpetual American lookback option introduced in Dai \cite{dai2000closed, dai2005american} under a stochastic volatility model. We derive the formula in closed form for the price of the perpetual American lookback option under the mean-reverting stochastic volatility introduced by Fouque et al. \cite{fouque2000derivatives}. As this work is a direct extension of the work of Lee \cite{lee2018pricing} where the zero and first order terms are derived, we focus on improving accuracy in an asymptotic series expansion. Based on the second order approach used in Fouque et al. \cite{fouque2016second}, we extend the approximation by incorporating the third order asymptotics for the stochastic volatility.