Pricing Options on Stocks Driven by a Geometric Fractional Brownian Motion

The pricing European option on a stock whose price process is driven by geometric fractional Brownian motion is considered.Existing arbitrage opportunities for these process shows that option pricing is not possible with traditional financial asset pricing methods,such as capital asset pricing model,arbitrage pricing theory,dynamic equitable pricing theory.In this paper,the formulas of the pricing European option are obtained by insurance actuary pricing without any other market assumption.Then,the expand formulas are discussed under payment of a given stock dividends and stock yields during the effective date.