ABSTRACT
There are also limitations with the popular portfolio credit derivatives models mentioned above. One of the major drawbacks of the survival-time copula approach for CDOs is that it does not constitute a proper dynamic model. The implication is that although this kind of models can be used to price CDO tranches, options on spread, of either single name or portfolio, cannot be priced under such models (e.g., exponential-copula model of Giesecke [2003]). With the Gaussian copula model, the market standard, default-time correlations are injected after the default times are mapped into normal random variables. There is, however, no economic intuition on how to input the correlations for these normal random variables. This problem is mitigated in the structural model of Hull et al. (2005), where a default is triggered when the value of a firm breaches a barrier (Black and Cox, 1976). However, structural models are difficult to use, as a number of model parameters are needed to be specified, including drifts, volatility, and correlations of the firm values, as well as default barriers. Given that firm values are not observable, a proper specification of the model is a daunting task by itself. In addition, firm-value based structural models do not naturally take the price information like credit spreads and implied spread volatilities from the single-name credit derivatives markets as inputs, hence the structural models do not ensure price consistency across the single-name and portfolio credit markets.
