Abstract: By using fractional Girsanov formula and fractional Wick-Itô-Skorohod integral, based on a linear combination of Brownian motion, fractional Brownian motion and Poisson process, a new market pricing model is built. Under the conditions of Merton assumptions, we analyze the Cauchy initial problem of stochastic parabolic partial differential equations. Then the pricing Merton-formula of European option meets the pricing model for the European fixed strike and floating strike price of the lookback option. Finally the pricing formulas of fixed strike and floating strike lookback call option and lookback put option are proved. Numerical simulations illustrate that our model are valid and accurate.

Key words: mixed jump-diffusion fractional Brownian motion, Merton assumptions, fractional Wick-Itô-Skorohod integral, European lookback option