Executive basket stock option pricing with stochastic exercise date

An executive basket stock option with stochastic exercise dates is designed. It rearranges the profit structure of the executive stock option, eliminates some low-income risk under the deterministic exercise dates. To some extent, such an option can prevent the executive's short-term behavior. Under the equivalent martingale, the paper also improves the stock option pricing model with deterministic exercise dates, builds up a stock option pricing model with stochastic exercise dates and gives the close form solution. Numerical calculation and analysis are conducted. The conclusion shows that to encourage the executive, besides the profit amount the profit time should also be emphasized. The proper time arrangement can improve the encouraging effect.