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Non-Traded Asset Valuation with Portfolio Constraints: A Binomial Approach

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 non-traded 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 compensation options are presented. We also analyze non-traded payoffs based on a price that is imperfectly correlated with the price of a traded asset.
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