A Unified Credit and Interest Rate Arbitrage-Free Contingent Claim Model

Abstract

The authors have used an interest rate stochastic movement model, or the Ho–Lee model, to evaluate interest contingent claims. Once the interest rate binomial process can be specified under the condition that there are no arbitrage opportunities in the binomial process, any interest contingent claims can be evaluated in a manner similar to the pricing of stock-related options from the binomial stock process. This article extends such an arbitrage-free interest rate model to incorporate credit risk. By this extension, the contingent claims, which depend on interest rate risk as well as credit risk, can be evaluated. The main issue of the unified Ho–Lee model is that there should be no arbitrage opportunities from each stochastic process. The unified Ho–Lee model is useful because the model can show that interest rate risk and default risk are essentially the same in the sense that the discount function and the survival function can represent the interest rate and the hazard rate, respectively, and the two functions share similar characteristics. The authors have used the unified model to simulate the value of a coupon bond, a callable bond, and a make-whole bond when the bonds are subject to interest risk as well as credit risk. Since the authors measure the nonlinearity of an interest rate and credit option by the behavior of the surface of the performance profile, they use the principal curvature and principal direction.