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Rev Fin 1999; 12:835-872
© 1999 the Society for Financial Studies

Article

Nontraded asset valuation with portfolio constraints: a binomial approach

J Detemple and S Sundaresan
McGill University and CIRANO, Canada
Columbia University, USA
Correspondence to: J Detemple, Faculty of Management, McGill University, 1001 Sherbrooke Street West, Montréal, Quebec, Canada H3A 1G5
e-mail: detemple@management.mcgill.ca

Abstract

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.


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