Valuing Credit Derivatives

by Francis A. Longstaff of the University of California, Los Angeles, and
Eduardo S. Schwartz of the University of California, Los Angeles

June 1995

Abstract: Credit Derivatives are potentially one of the most important new types of financial products introduced during the past decade. Many investors have portfolios with values that are highly sensitive to shifts in the spread between risky and riskless yields, and credit derivatives offer these investors are important new tool for managing and hedging their exposure to this type of risk.

In this article, we develop a simple framework for valuing derivatives on credit spreads. It captures the major empirical properties of observed credit spreads in that it allows for spreads to be stationary and mean-reverting. We then use this framework to derive simple closed-form solutions for the prices of call and put options on the credit spread.

These closed-form solutions have a number of interesting implications for the pricing and hedging properties of credit derivatives. We show that calls can have negative convexity, and that the delta of the call can be higher for out-of-the-money and at-the-money calls than for in-the-money calls. In addition, we show that the deltas of both calls and puts converge to zero as the time until expiration increases, which implies that long-term credit derivatives may have little ability to hedge against current shifts in credit spreads.

Published in: Journal of Fixed Income, Vol. 5, No. 1, (June 1995), pp. 6-12.

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