Valuation of Contingent Claims — MCQs

Ardent Medical Systems, a US-based manufacturer whose functional currency is USD, has sold diagnostic equipment to a customer in the eurozone. The customer will pay a fixed EUR amount in three months. Because Ardent reports and budgets in USD, a depreciation of the EUR against the USD before collection would reduce the receivable's USD value. All exchange rates in the case are quoted as USD per EUR, making EUR the base currency and USD the price currency. Treasurer Samuel Lee evaluates three alternatives: leaving the receivable unhedged, selling EUR under a three-month forward contract, or purchasing a three-month European put on EUR. The forward has no initial premium and requires physical delivery of EUR at maturity. The put permits Ardent to sell EUR at the exercise price but does not require exercise. The quoted option premium is paid today in USD per EUR of notional. For the requested option comparison, financing on the premium is explicitly ignored. Lee expects the expiration spot rate to be below the put's exercise price. He nevertheless distinguishes the expected outcome from the guaranteed minimum outcome. The unhedged strategy provides neither a floor nor a fixed conversion rate. The forward fixes Ardent's conversion rate but eliminates participation in any appreciation of the EUR. The put provides a floor after deducting its premium while allowing Ardent to benefit if the expiration spot rate exceeds the exercise price. Management states that, for one decision, its sole objective is to obtain the highest certain minimum USD proceeds; it assigns no value to retaining favorable currency upside. Ardent also has access to exchange-traded EUR futures and asks Lee to calculate a minimum-variance hedge. The futures and the receivable have the same three-month horizon, and futures contracts are available only in whole numbers. The hedge ratio must be calculated as the correlation between spot and futures price changes multiplied by the ratio of their standard deviations. Because Ardent will receive EUR, a hedge should gain value when the EUR depreciates. Margin liquidity and basis risk are acceptable within Ardent's risk policy. The exposure, quotations, option terms, contract size, and statistical inputs are provided in Exhibits 1 and 2.