5

Credit Portfolio Correlations with Dynamic Leverage Ratios

5.1 INTRODUCTION

Default correlations have been an important research area in credit risk analysis. There are a number of approaches to credit risk modeling, for example, the Gaussian copula method, the reduced-form approach and the structural approach. In the structural approach, default happens when the firm value falls below a default threshold. For example the fundamental model of Merton (1974) assumed that default could only happen at the maturity date of the bond. This was later modified by Black and Cox (1976) to allow default before the maturity date. Longstaff and Schwartz (1995) combine the early default mechanism in Black and Cox (1976) and the stochastic interest rate model of Vasicek (1977). Their model also accommodates the complicated liability structures and payoffs by deriving the solution as a function of a ratio of the firm value to the bond payoff value. Instead of using a constant default threshold, Briys and de Varenne (1997) consider a time-dependent default threshold and assume that it depends on the risk-free interest rate.

Later developments by Collin-Dufresne and Goldstein (2001) and Hui et al. (2006) consider the stationary leverage ratio for modeling credit risk. Collin-Dufresne and Goldstein (2001) assume that the default threshold changes dynamically over time, in particular ...

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