We proposed a new model to price employee stock options （ESOs）. The model is based on nonparametric statistical methods with market data. It incorporates the kernel estimator and employs a three-step method to modif...We proposed a new model to price employee stock options （ESOs）. The model is based on nonparametric statistical methods with market data. It incorporates the kernel estimator and employs a three-step method to modify Black- Scholes formula. The model overcomes the limits of Black-Scholes formula in handling option prices with varied volatility. It disposes the effects of ESOs self-characteristics such as non-tradability, the longer term for expiration, the eady exercise feature, the restriction on shorting selling and the employee＇s risk aversion on risk neutral pricing condition, and can be applied to ESOs valuation with the explanatory variable in no matter the certainty case or random case.展开更多
Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs si...Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs since 2004. The main difficulty of ESO valuation lies in the uncertain timing of exercises, and a number of contractual restrictions of ESOs further complicate the problem. We present a valuation framework that captures the main characteristics of ESOs. Specifically, we incorporate the holder＇s risk aversion, and hedging strategies that include both dynamic trading of a correlated asset and static positions in market-traded options. Their combined effect on ESO exercises and costs are evaluated along with common features like vesting periods, job termination risk and multiple exercises. This leads to the study of a joint stochastic control and optimal stopping problem. We find that ESO values are much less than the corresponding Black-Scholes prices due to early exercises, which arise from risk aversion and job termination risk; whereas static hedges induce holders to delay exercises and increase ESO costs.展开更多
基金Funded by the No. 12 Project of Joint Research Projects of Shanghai Stock Exchange with Chongqing University.
文摘We proposed a new model to price employee stock options （ESOs）. The model is based on nonparametric statistical methods with market data. It incorporates the kernel estimator and employs a three-step method to modify Black- Scholes formula. The model overcomes the limits of Black-Scholes formula in handling option prices with varied volatility. It disposes the effects of ESOs self-characteristics such as non-tradability, the longer term for expiration, the eady exercise feature, the restriction on shorting selling and the employee＇s risk aversion on risk neutral pricing condition, and can be applied to ESOs valuation with the explanatory variable in no matter the certainty case or random case.
文摘Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs since 2004. The main difficulty of ESO valuation lies in the uncertain timing of exercises, and a number of contractual restrictions of ESOs further complicate the problem. We present a valuation framework that captures the main characteristics of ESOs. Specifically, we incorporate the holder＇s risk aversion, and hedging strategies that include both dynamic trading of a correlated asset and static positions in market-traded options. Their combined effect on ESO exercises and costs are evaluated along with common features like vesting periods, job termination risk and multiple exercises. This leads to the study of a joint stochastic control and optimal stopping problem. We find that ESO values are much less than the corresponding Black-Scholes prices due to early exercises, which arise from risk aversion and job termination risk; whereas static hedges induce holders to delay exercises and increase ESO costs.
