派发股息美式期权的一个解析公式

Analytic formula of American option with paying dividends

一般的美式期权难以用解析公式求解,而带有分红股息的资产却是一个例外.如果当前市场收益优于股息派发日的收益,美式期权可以在期权到期之前提前执行.应用扩展的Roll-Geske-Whaley模型并利用n重复合期权,在资产派发n次股息n>2时,得到了一个派发股息的美式买权解析公式,并进行了数值仿真.

In general,American options cannot be solved by closed-form formulas.However,the asset with paying dividend is an exception.American call option will be implemented before the expire date of the option only when the current market return is better than the return of paying dividend on paying dividend date.An analytic formula of American call option is derived using extended Roll-Geske-Whaley model and the theory of the n-fold compound options when the asset has pay divided n times (n>2).Finally a numerical example is presented.