AMERICAN FRACTIONAL LOOKBACK OPTIONS: VALUATION AND PREMIUM DECOMPOSITION

This paper deals with valuation and premium decomposition of American fractional lookback options written on dividend-paying assets, for which exact formulas are unknown except for the perpetual case. Via a PDE approach, we derive Laplace transforms of the values of lookback call and put options, which can be decomposed into the associated European values plus the early exercise premiums. Using Abelian theorems of Laplace transforms, we characterize asymptotic behaviors of the early exercise boundaries at a time to close to expiration and at infinite time to expiration. Based on the Gaver-Stehfest inversion method combined with the Newton method, we develop a fast and accurate algorithm for computing both the option value and the early exercise boundary. Numerical analysis reveals some notable features of the American fractional lookback options.