Optimal international hedging in commodity and currency forward markets

This paper derives optimal hedging and production rules for an exporting firm which faces both commodity-price and foreign- exchange-rate uncertainty. The size of the commodity hedge is independent of the properties of the foreign-exchange market. However, the optimal foreign-exchange hedge depends on the commodity hedge and the properties of the commodity forward market. The firm's production decision is independent of its objective function if both forward markets exist, but depends on the consumption beta of the unhedgeable risks in the absence of one or both of the markets.     

Non-marketability and the value of employee stock options

We adapt the Benninga et al. (2005) framework to value employee stock options (ESOs). The model quantifies non-diversification effects, is computationally simple, and provides an endogenous explanation of ESO early-exercise. Using a proprietary dataset of ESO exercise events we measure the non-marketability ESO discount. We find that the ESO value on the grant date is approximately 45% of a similar plain vanilla Black–Scholes value. The model is aligned with empirical findings of ESOs, gives an exercise boundary of ESOs and can serve as an approximation to the fair value estimation of share-based employee and executive compensation. Using the model we give a numerical measure of non-diversification in an imperfect market.     

Heterogeneity and Option Pricing

An economy with agents having constant yetheterogeneous degrees of relative risk aversion prices assetsas though there were a single decreasing relative risk aversion``pricing representative' agent. The pricing kernel has fattails, and option prices do not conform to the Black-Scholesformula. Implied volatility exhibits a ``smile.' Heterogeneityas the source of non-stationary pricing fits Rubenstein's (1994)interpretation of the ``over-pricing' as an indication of ``crash-o-phobia'.Rubinstein's term suggests that those who hold out-of-the moneyput options have relatively high risk aversion (or relativelyhigh subjective probability assessments of low market outcomes).The essence of this explanation is investor heterogeneity.