Cross-Hedging Ambiguous Exchange Rate Risk

Abstract

This paper examines the behavior of an exporting firm that sells its output to two foreign countries, only one of which has futures and options available for its currency. The firm possesses smooth ambiguity preferences and faces multiple sources of ambiguous exchange rate risk. We show that the separation theorem fails to hold in that the firm's production and export decisions depend on the firm's attitude towards ambiguity and on the incident to the underlying ambiguity. Given that the random spot exchange rates are first-order independent with respect to each plausible subjective distribution, we derive necessary and sufficient conditions under which the full-hedging theorem applies to the firm's cross-hedging decisions. When these conditions are violated, we show that the firm includes options in its optimal hedge position. This paper as such offers a rationale for the hedging role of options under smooth ambiguity preferences and cross-hedging of ambiguous exchange rate risk.