The Innovation Of The Stock Option Pricing Method And The Analysis Of Incentive Strength Under Equity Incentives Mechanism

It is well known that in the definition of the incentive strength introduced by many scholars from home and abroad, the stock option price is just Black-Scholes op-tion price. While in the classical Black-Scholes model, the dynamic process of stock price is considered as the geometric Brownian Motion. But in practice, its sample path is not necessarily continuous, there are some jumps taking place sometimes with the stocks limit moves, and hence it is of great significance both in theory and prac-tice to discuss the stock option pricing method by under a price process with jumps. Consequently, in this paper we describe the stock price process by the geometric Brow-nian Motion with some special random jumps. Under this assumption, we apply the no-speculation theorem to improve and to extend the stock option pricing formula under equity incentives mechanism. Meanwhile, we can compute the probability for the fallling underwater of the stock option by this improved option pricing formula. The results obtained show that the probability for the fallling underwater of the stock option is positive correlation to the jump intensity, but is negative correlation to the drift parameter.Additionally, we use the improved stock option pricing formula to redefine the incentive strength, based on which we further extend the equity incentive effect model of Hall and Knox (2002), and employ the panel data with variable coefficients to em-pirically research part of the listed companies having carried out the equity incentive since 2008. The empirical results indicate that not only in the bull market, but also in the bear market, once the quoted company give up putting equity incentives into force, its corresponding incentive strength will trail off, which fully shows the utility of the equity incentives. on the other hand, in the implementation procedure of the equity incentive, the incentive strength has a gradual decline trend, which can reflect that in our country there are some flaws in this implementation procedure. Therefore, we should try to make the equity incentive mechanism be being prefected in the future.