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Optimization models for foreign exchange rate hedging using currency options

Currency options provide a convenient means for multinational corporations to hedge future revenues and liabilities against exchange rate risk. While, ideally, companies would prefer to hedge their entire exposure at a single favorable strike price (exchange rate), it is frequently too expensive to do so. Moreover, a fully hedged position is usually unnecessary to adequately eliminate down side risk. Instead, the optimal strategy lies somewhere between the two extremes of a fully hedged and an unhedged position. In general, the optimal hedging strategy will be comprised of a package of currency options of various strike prices, each covering a portion of the exposure. We refer to the problem of deciding which strike prices to buy the options at, and the percentage of the exposure that each covers, as the options hedging problem. This thesis explores three sets of mathematical models to evaluate the options hedging problem. The first set of models uses a probabilistic approach to the problem and describes how a currency options package changes the shape of the efficient market forecast of exchange rates to create a new distribution of what we call the effective exchange rate. The second set of models relaxes the notion of market efficiency and describes how best to take advantage of differences between the market's forecast and one's own. Finally, the third set of models explores how one can apply linear and stochastic programming methodologies to the problem. In this final section, we extend the scope of the decision process by allowing multi-period, multi-objective decision criteria. Additionally, applying mathematical programming to the problem allows us to account for constraints that may be specific to each company, such as budgetary requirements and cash flow needs. Thesis Supervisor: Jeremy F. Shapiro Title: Professor of Operations Research and Management