Bulletin of the
Korean Mathematical Society BKMS

In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By using the asymptotic analysis introduced by Fouque et al. [17] and the Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.

Keywords: American lookback options, stochastic volatility, Laplace-Carson transform, Monte-Carlo simulation

MSC numbers: 60H30, 91G15, 91G20

Supported by: The research of J.-H. Yoon was supported by the National Research Foundation of Korea grants funded by the Korean government (NRF-2019R1A2C108931011).