具有时滞效应的股票期权定价

Stock option pricing with time delay

主要研究标的股票价格满足随机微分延迟方程(stochastic differential delay equation,SDDE)时欧式期权的定价公式,采用倒向随机微分方程(backward stochastic differential equation,BSDE)方法进行处理,值得注意的是得到的财富方程与经典的BSDE有差异,该方程为时滞BSDE。利用时滞BSDE与超前随机微分方程(advanced stochastic differential equations,ASDE)的对偶关系,给出股票价格具有时滞的欧式看涨期权的定价公式。

In this article,we mainly develop an formula for pricing European option when stock price follows a stochastic differential delay equation（SDDE）. The backward stochastic differential equation（BSDE） method is used,but it is worth noting that the wealth equation is different from the classical BSDE,and it is delayed BSDE. By the dual relationship of delayed BSDE and advanced stochastic differential equation（ASDE）,we obtain the formula for pricing European call option.