A Two-Factor Hazard-Rate Model for Pricing Risky Debt and the Term Structure of Credit Spreads

This paper proposes a two-factor hazard-rate model, in closed-form, to price risky debt. The likelihood of default is captured by the firm's non-interest sensitive assets and default-free interest rates. The distinguishing features of the model are threefold. First, impact of capital structure changes on credit spreads can be analyzed. Second, the model allows stochastic interest rates to impact current asset values as well as their evolution. Finally, the proposed model is in closed form enabling us to undertake comparative statics analysis, compute parameter deltas of the model, calibrate empirical credit spreads and determine hedge positions. Credit spreads generated by our model are consistent with empirical observations.

Pricing the Risks of Default

This paper characterizes the risk neutral jump process of default in terms of two entities, i) an instantaneous arrival rate of default and ii) a conditional density of the magnitude of the proportionate reduction in the value of creditors claims. The authors propose models for default arrival and magnitude risks as functions of evolving economic information. These two default components are then explicitly priced in the futures market with the spot price of risky debt being derived as a consequence. The resulting models for default arrival and magnitude risks are estimated on monthly data for rates on certificates of deposit offered by institutions in the Savings and Loan Industry. The data period is January 1987 to December 1991. The default arrival rate is modeled as responsive to abnormal equity returns, while default magnitude risk is modeled to be sensitive to the level of core deposits and the yield on low grade bonds. The authors' empirical results for the arrival and magnitude risk models provide strong support for the hypothesis that uninsured depositors place market discipline on the depository institutions by demanding compensation for both forms of the firm's default risks.

Pricing the Risk of Recovery in Default with APR Violation

This paper proposes a simple approach to infer the risk neutral density of recovery rates implied by the prices of the debt securities of a firm. The proposed approach is independent of modeling default arrival rates and allows for the violation of absolute priority rule (APR). The paper demonstrates that a new statistic, the adjusted relative spread, captures risk neutralrecovery information in debt prices. Interest rates and firm tangible assets are shown to be significant determinants of the price of recovery. An application illustrates the pricing of credit derivatives written on the realized recovery rate.Recovery rates; APR violation; Risky debt pricing; Credit risk; Credit deriva-tives

A Simple Approach to Estimate Recovery Rates with APR Violation from Debt Spreads

This paper proposes a simple approach to estimate the implied recovery rates embedded in the prices of the debt securities of a firm that differ in priority at time of default. The approach allows for a complex capital structure setting assuming that the absolute priority rule (APR) can be violated. The paper demonstrates that a new statistic, the adjusted relative spread, captures recovery information in debt prices. Model implied recovery rates from corporate bond prices are observed to be consistent with the findings of Altman and Kishore (1996). Interest rates and firm tangible assets are shown to be significant determinants of recovery rates.