Ebook A Tree Implementation Of A Credit Spread Model For Credit Derivatives
In this paper we present a tree model for defaultable bond prices which can be used for the pricing of credit derivatives. The model is based upon the two-factor Hull-White (1994) model for default-free interest rates, where one of the factors is taken to be the credit spread of the defaultable bond prices. As opposed to the tree model of Jarrow and Turnbull (1992), the dynamics of default-free interest rates and credit spreads in this model can have any desired degree of correlation, and the model can be fitted to any given term structures of default-free and defaultable bond prices, and to the term structures of the respective volatilities.
Further more the model can accommodate several alternative models of default recovery, including the fractional recovery model of Duffie and Singleton (1994) and recovery in terms of equivalent default-free bonds (see e.g. Lando (1998)). Although based on a Gaussian setup, the approach can easily be extended to non-Gaussian processes that avoid negative interest-rates or credit spreads.
The model contributes to the existing literature in two respects: First, it provides an implementation framework for most of the existing intensity-based credit risk models, and second, it enables a quantitative comparison of the properties of these models and the relative importance of input parameters like recovery rates, volatility of credit spreads and the correlation between credit spreads and interest rates.
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