Practice Leader, ERM and Structured Products Advisory, Promontory Financial, New York
In this issue we present four full-length research papers. We are pleased to include papers coauthored by two very prominent contributors in the field, Robert Jarrow and John Hull, in this issue. The first paper, "An implied multi-factor model for bespoke collateralized debt obligation tranches and other portfolio credit derivatives", is by Igor Halperin. Practitioners have largely relied on first-generation models based on the single-factor Gaussian copula framework to value collateralized debt obligations (CDOs). Such models have well-documented practical and theoretical inadequacies. Recently, more sophisticated, second-generation models have been developed. This paper presents one such technique. The author provides a novel methodology, which essentially combines the implied factor approach to valuing CDOs with some tools from the top-down loss distribution models and with some optimization tools. While the methodology and the example are largely presented for the static case, the paper demonstrates how to simultaneously match the full term structure of observed prices. It is also more generally applicable to a dynamic multi-step setting.
In the second paper, “Pricing and hedging collateralized loan obligations with implied factor models”, the authors Jovan Nedeljkovic, Dan Rosen and David Saunders propose an innovative and parsimonious framework for pricing collateralized loan obligation (CLO) tranches under consistent dynamics across capital structure that provides an alternative to the current industry standard base correlation approach. The authors point out limitations of the base correlation and related copula approaches and propose a method that, unlike those methods, requires a single correlation parameter across the entire capital structure of a CLO. The model involves generating, via Monte Carlo methods, a distribution of systematic factors whose dynamics are calibrated to observable market prices. The dynamics of the model includes stochastic loan prepayments and recovery values in default, both of which are dependent on the same systematic factor. Furthermore, the model incorporates the empirically observed negative correlation between default rate and recovery value in default. Prepayment speed and recovery value are both critical considerations underlying reliable CLO prices. In addition to the modeling framework, the paper presents a practical algorithm for calibrating the model and provides several numerical examples to demonstrate the behavior of the model under various conditions.
The third paper, “The valuation of correlation-dependent credit derivatives using a structural model”, is by John Hull, Mirela Predescu and Alan White. In this paper, the authors first extend the Merton-type structural model framework into the risk-neutral setting, whereby model parameters are estimated from credit default swap (CDS) spreads, and then extend the work of Zhou to model default correlations among multiple obligors based on a single systematic factor affecting asset prices. They then go on to extend the framework to multi-factor correlation. Finally, the authors apply the model to pricing CDS tranches. Along the way they show how the model can be extended to handle correlations among asset values (or, equivalently, correlations among defaults), they demonstrate the rough equivalence between their modified Merton model and copula models in regard to joint defaults, and they add stochastic correlation, stochastic recovery rates and stochastic volatility to the model.
In the last paper, “Credit rating accuracy and incentives”, Robert Jarrowand Liheng Xu develop a signaling equilibrium model of the credit rating process. A conflict of interest arises because issuers pay the rating agency a share of the issuer’s future profits if they are rated good and nothing if they are rated bad. This creates an incentive for the rating agency to overstate credit quality and leads to inaccurate ratings. Investors find inaccurate ratings useful as they provide an imperfect signal of the issuer’s profits, which are costly for investors to learn on their own. As the number of issuers in the model increases, the incentive to overstate credit quality falls and ratings become more accurate. The paper demonstrates that an imperfect signal (inaccurate ratings) makes investors better off and that the incentive to overstate credit quality can correlate with the business cycle (more bad firms are rated good in a boom).
An implied multi-factor model for bespoke collateralized debt obligation tranches and other portfolio credit derivatives