European pricing options on modified Black-Scholes model

Previous option pricing research typically assumes that the stock volatility and expectation return rate are constant during the life of the option.In this study,we assume the stock volatility and expectation return rate in our option valuation model are function of stock.By the self-financing strategy and Ito formula for Brownian motion,the general Black-Scholes partial differential equations for European claim and pricing formula for European option are obtained.