Optimal Static Hedging of Currency Risk Using FX Forwards

Abstract

An exporter is invariably exposed to a currency risk due to unpredictable fluctuations in the exchange rates, and it is of paramount importance to minimize risk emanating from these forex exposures.

In this paper, we present optimal static currency hedging strategies in which Forward FX contracts are used as hedging instruments. First, we introduce a static trading strategy and present the analytical expressions for different risk measures such as Value-at-
Risk (VaR), Conditional Value-at-Risk (CVaR), Probability of Loss, and Conditional Expectation of Loss. The results presented here make no implicit assumptions about the underlying probability distribution. Next, using the expressions for risk measures we derive optimal static hedginging strategies to minimize these risk measures. Finally, we illustrate the results by specializing the underlying model to the case of geometric Brownian motion.