Essays on credit derivatives.

摘要

Credit derivatives securities are insurance contracts that protect investors from the credit risk associated with defaultable assets. This dissertation values two credit derivatives with a stable Paretian distribution for the derivatives' underlying risk factors. The valuation is consistent with empirical observations that defaultable assets have returns that exhibit stochastic properties of skewness, leptokurtosis, stochastic volatility and long range dependence. The valuation framework focuses on the first three statistical properties. Traditionally credit derivative valuation frameworks employ Gaussian-based models, i.e. Brownian motion, to capture the stochastic behavior of the underlying risk factors. This project demonstrates the inadequacy of Gaussian-based models in capturing the aforementioned statistical properties with implications for pricing and risk management of credit-sensitive assets.; A reduced form model is used to value the credit derivatives where the underlying security is a Baa rated bond index. In this class of models, given an assumption for the recovery rate for the defaultable asset, the underlying risk factors for the bond index are the risk-free spot rate and the credit spread process. Following Duffie and Singleton [1999], we employ the fractional recovery of market value. Thus, valuing the Baa bond index is identical to valuing a default-free bond using standard term structure models. I propose to use the two-factor Hull-White [1994] term structure model for the risk-free spot rate and the credit spread process extending it however to include stable Paretian distributions following Rachev and Mittnik [2000]. In addition to this I employ a copula function that models the dependence structure between the risk factors to accurately account for their association. This valuation is implemented employing a trinomial tree algorithm. I find that values for both credit derivatives increase significantly in the stable Paretian framework relative to the Gaussian framework. As the stable Paretian framework accounts for the empirical statistical properties of the risk factors, the valuation framework developed is an empirically consistent one. Chapter 1 discusses the literature on credit risk modeling and risk management. Chapter 2 values a credit default swap and Chapter 3 values a credit spread put option in the framework described earlier.