Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach
提出一个二叉树框架，用于评估存在交易限制的美式衍生品，同时求解流动性财富的最优投资和非交易衍生品的提前行权决策。研究发现，对标的资产的卖空限制会以隐含股息收益率的形式表现出来，导致即使标的资产不支付股息，美式看涨期权也可能提前行权。应用于高管股票期权时，其价值可能远低于布莱克-舒尔斯模型的计算结果。
We provide a simple binomial framework to value American-style derivatives subject to trading restrictions. The optimal investment of liquid wealth is solved simultaneously with the early exercise decision of the nontraded derivative. No-short-sales constraints on the underlying asset manifest themselves in the form of an implicit dividend yield in the risk-neutralized process for the underlying asset. One consequence is that American call options may be optimally exercised prior to maturity even when the underlying asset pays no dividends. Applications to executive stock options (ESO) are presented: it is shown that the value of an ESO could be substantially lower than that computed using the Black–Scholes model. We also analyze nontraded payoffs based on a price that is imperfectly correlated with the price of a traded asset.