No-Arbitrage Approach to Pricing Credit Spread Derivatives

Abstract

Among the new credit-based derivatives are options on the yield spread between a credit-sensitive instrument and a comparable riskless bond. Valuation requires considering the behavior of both the risk-free interest rate and the credit spread, which may be correlated. A challenge in implementing valuation models for such derivatives is the need to match observed market pricing for both riskless and risky securities. In this article, Chu and Kwok show how a pricing model for credit spread options can be constructed and calibrated to the market, while maintaining its ability to produce option prices in closed form. The two correlated processes are assumed to follow the “extended Vasicek” model developed by Hull and White for arbitrage-free modeling of the interest rate. The article also shows how models of the Black-Karasinski and Heath-Jarrow-Morton type may also be fitted, though not in closed form.