Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

A new frame work for pricing the American fractional look back option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using It (o) over cap formula and Wick-It (o) over cap -Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.