THIRD ORDER APPROXIMATION TO THE PRICE OF PERPETUAL AMERICAN LOOKBACK OPTION WITH A MEAN-REVERTING STOCHASTIC VOLATILITY

THIRD ORDER APPROXIMATION TO THE PRICE OF PERPETUAL AMERICAN LOOKBACK OPTION WITH A MEAN-REVERTING STOCHASTIC VOLATILITY

This paper is a research for a perpetual American lookback option introduced in Dai [3, 4] 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. [6]. As this work is a direct extension of the work of Lee [11] 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. [8], we extend the approximation by incorporating the third order asymptotics for the stochastic volatility.