Hedging~interest Rate Risk with Options on Average Interest Rates

MARCH 1995 Hedging interest rate risk has become one of the most common and important types of a financial manager's risk management activities. A classic example is for a firm to hedge its cost of funds by using an interest rate cap to place an upper bound on its borrowing costs. The hedge typically consists of a sequence of individual call options on the interest rate, with option expiration dates options coinciding with the borrower's interest payment dates. By purchasing an interest rate cap, the borrower can insure that the net interest cost for each individual payment is less than or equal to the cap rate. Some firms may find it optimal to hedge the cost of individual interest payments. Most firms, however, would view their objective as hedging their average cost of funds during an accounting cycle, rather than hedging individual payments. For these firms, there are potential hedging vehicles that could prove far more cost-effective than a standard interest rate cap. We describe one such hedging vehicle: a cap on the average interest rate during a period. Using a simple term structure model, we derive closed-form expressions for caps on average interest rates, illustrate their pricing and hedging properties, and contrast these properties with those of standard interest rate caps. We show that a cap on the average rate can cost far less than a conventional cap. This is consistent with Merton [1973], who shows that an option on an average is worth less than a portfolio of options. What is different here, however, is that mean reversion and the slope of the term structure play an additional role in determining the relation between the two prices. We also show that caps on the average rate are generally less sensitive to changes in