Nontraded asset valuation with portfolio constraints: a binomial approach

We provide a simple binomial framework to value American-stylederivatives subject to trading restrictions. The optimal investmentof liquid wealth is solved simultaneously with the early exercisedecision of the nontraded derivative. No-short-sales constraintson the underlying asset manifest themselves in the form of animplicit dividend yield in the risk-neutralized process forthe underlying asset. One consequence is that American calloptions may be optimally exercised prior to maturity even whenthe underlying asset pays no dividends. Applications to executivestock options (ESO) are presented: it is shown that the valueof an ESO could be substantially lower than that computed usingthe Black-Scholes model. We also analyze nontraded payoffs basedon a price that is imperfectly correlated with the price ofa traded asset.