Black-Scholes期权定价模型的拓展  

Expansion of Black-Scholes Option Pricing Model

作　　者：郭翱[1] 徐丙振[1] 于利伟[1] 

机构地区：[1]宁波大学理学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2010年第2期52-56,共5页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(10774080)

摘　　要：假定动态风险资产价格遵从扩散-跳跃复合泊松过程,无风险利率、股票收益率、市场波动率、股票红利等均为自适应过程,利用随机微分方程和鞅方法,得到了资产投资组合贴现过程鞅成立的条件.在相同测度下,考虑到交易费用和红利支付,对经典Black-Scholes方程进行了修正,得到了不同条件下的欧式看涨期权的定价方程,使得期权定价公式更加符合市场实际,拓展了鞅方法的使用范围和意义.Based upon the hypothesis that the price of dynamic and risky assets complies with the processes of compound jump-diffusion,and riskless interest rate,stock yield rate,market volatility and dividends can be described with a self-adaptive process,the result of discounted portfolio is obtained,which is a martingale with the same measure of the martingale.Also obtained is a new corrected function of Black-Scholes European call option,which is well adapted to the real security market using stochastic differential equations and the measure of equivalent martingale under the condition of the existence of dealing fees and dividends.Moreover,the approach of martingale is extended,resulting with more meaningful and general applications.

关 键 词：扩散-跳跃复合泊松过程 鞅方法 随机微分方程 期权定价 贴现过程 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]