Black-Scholes期权定价模型的拓展

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.

Expansion of Black-Scholes Option Pricing Model

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 differenti...