Credit Spread Option Valuation under GARCH

Abstract

Understanding the stochastic behavior of credit spreads and devising models for derivatives with credit spreads as underliers grows increasingly important every day. Mean reversion in spreads is clearly evident in the data, as is time-varying volatility. In this paper, Tahani models credit spreads using a mean-reverting GARCH framework. Adopting Heston and Nandi's GARCH specification allows closed-form option valuation formulas to be obtained by inversion of the characteristic function. Moreover, Tahani's model contains the Longstaff-Schwartz spread model as a special case. The model is then taken to the data, by fitting it to the credit spreads between Moody's Aaa and Baa bond yields and U.S. Treasuries. The GARCH specification fits that data well, and the GARCH option model calibrated to the bond yields exhibits the same kinds of unusual behavior (e.g., option prices below intrinsic values, in some cases) as Longstaff and Schwartz found with their more restricted model.