Long term exchange rate risk and hedging with quantity uncertainty in a market that only provides short term futures contracts

This paper analyzes the problem faced by an investor expecting to receive an uncertain amount of cash flow in a foreign currency on a certain future date T. The investor is also assumed to be exposed to long-term exchange rate risk, and has access only to short-term futures contracts to hedge. A closed form solution for both the optimal hedging strategy and the quality of the hedging are identified. Next, we explored how those solutions depend on some key factors such as the volatility of the exchange rate, the volatility of the amount of foreign currency to be received and the degree of correlation between all the stochastic variables considered.