关键词: 布朗运动, 期权定价, 修正的Black-Scholes模型, 障碍期权

Abstract:

Previous option pricing research typically assumes that the stock volatility is constant during the life of the option. In this study, we assume the stock volatility in our option valuation model is function of stock. By approximate method, the partial differential equation satisfied the down-and-out option and up-and-out option are changed to another partial 
differential equation which can be solved. Finally, the pricing formula for down-and-out option and up-and-out option are obtained. In order to the mathematically rigorous, we supply the error estimation.

Key words: Brownian motion, Option pricing, Modified Black-Scholes model, Barriar option