Optimal Exercise Strategy Of A Bermuda Executive Stock Option

Executive stock options are call options granted by a traded company to anemployee on the stock of the company. These options are part of the remunerationpackage of the employee so as to encourage him to work hard. Study on the Executivestock options is of vital significance on issuing executive stock option efciently andaccounting the cost of executive stock option for a company.In our paper we study an optimal exercise strategy problem of a two-date Bermu-da executive stock option.Suppose executive options are only exercised at two dates:t1and t2,0<t1<t2=T§T is the expiration.The employee always wishes to maxi-mize the expected utility from exercising his options,so at date t=0the value ofeach executive option is in addition,Stis the stock price process,K is the knock price of option,β is thediscounting rate of employee,U(x)=xγ(0<γ <1) is the utility function ofemployee.M is a set composed of all the random variables whose value is chosenfrom0and1. m∈M is called the exercise strategy. If m∈M makes thesupremum on the right side of equation available when m=m,m is called theoptimal exercise strategy.In our paper, we study the optimal exercise strategy m of problem in a strictmathematica framework. Suppose the stock price process follows Brownian motion,when T t1are high enough and low enough we have strictly proved some depen-dency relationship among the optimal exercise strategy m and related parametersand discussed the financial meaning of the results.