Pricing And Incentive Effect Of Executive Stock Options

On the base of no-arbitrage principle and risk-neutral valuation principle, the pricing formula of executive stock options was derived. And combining with actual cases, we analyze the incentive effects. The main work includes the following contents:a) Derived the pricing formula and analyzed the incentive effects of indexed executive stock options in Geometric Fractional Brownian Motion environment;b) Analyzed the price and incentive effects of purchased option with stochastic exercise date;c) Analyzed the results of actual cases.For the price of indexed executive stock options in Geometric Fractional Brownian Motion environment, we get the pricing formula on the base of risk-neutral valuation principle. Via choosing appropriate data the incentive effects was analyzed. Compared with the traditional indexed stock options, the formula we get is consistent with the traditional one when Hurst parameter equals 0.5.To solve the problem that the standard purchased executive stock options have a fixed exercise date, the pricing formula of purchased option with stochastic exercise date was derived. In order to analyze the incentive effects of the executive options, the sensitivity of the option value to stock price(delta) and the sensitivity of the option value to stock return volatility(vega) were selected. By changing the value of some parameters, the changes of incentive effects were analyzed. According to the numerical result, we found the value of the options with stochastic exercise date is lower than the traditional one. Besides, by changing the value of some parameters, the company can adjust the incentive effects.At last, we analyze the actual case with the help of mathematical model, and we get the pricing formula of executive stock options when the barrier price is stochastic.