We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed-form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model.

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This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data. This model is useful for pricing and hedging corporate debt with imbedded options, for pricing and hedging OTC derivatives with counterparty risk, for pricing and hedging (foreign) government bonds subject to default risk (e.g., municipal bonds), for pricing and hedging credit derivatives, and for risk management

We derive a closed form solution for the valuation of risky discount debt when interest rates are stochastic. We extend Merton's [1974] approach to risky discount debt valuation under constant interest rates to the stochastic interest rate environment of Vasicek [1977]. Business risk is modelled as a geometric Brownian motion that is correlated with interest rates. We derive and explore the relationship between the credit premium and the term premium of corporate debt. In a banking environment, the results can also be applied to analyze (a) the allocation of capital to banking activities of varying credit risk and interest rate risk, (b) the measurement of relative capital adequacy when compared to peer banks, and (c) the interest rate risk-minimizing funding strategy.