New model for executive stock option pricing

A new type of stock option is defined, which takes the arithmetic mean of stock price in the exercise period as maturity price and takes the indexed stock price as strike price. The stochastic processes that stock price and stock price index follow are assumed. Based on the options theory and no-arbitrage analysis, the value equation of the new model is set up. Using the exchange option pricing formula, the approximate analytic solution of value equation is derived. Numerical results show how the parameters interact to determine the option price. Finally, a simulated demonstration is carried on to compare the incentive effects of our model with the others. Our model ensures that a manager with good performance gains incentives from the executive stock options; and the more a company excels its competitors in business, the more profits its manager earns.