Abstract:

The mixed jump-diffusion fractional Brownian motion model under the Itó formula and fractional diffusion process with non-homogeneous Poisson process was proposed. By using the iterative method, the Cauchy initial problem of stochastic differential equations were estimated under the conditions of Merton assumptions. Then the pricing Mertonformula of European option that meets the pricing model for the European floating strike price of the lookback option was obtained. Finally the pricing formulas of floating strike lookback call option and lookback put option were proofed.

Key words: mixed jump-diffusion fractional Brownian motion; Merton assumptions; iterative method; European lookback option