Two essays played on the credit triangle: Implied Recovery Rates and Implied Ratings

Local Volatility and the Recovery Rate of Corporate Bonds: The credit default swap (CDS) spread can be decomposed into the product of the probability of default and the loss given default. It is necessary to implement some structure on either the probability or the loss given default to disentangle them. With the help of a hybrid binomial tree for equities and a recovery function, Das and Hanouna (2009) found accurate estimates for the CDS spreads by fitting the model to historical equity volatilities (or at-the-money volatilities). We extend their approach by including the full implied volatility surface, developing an implied binomial tree with a jump to default based on the Derman and Kani (1994) tree. We then evaluate the effect of including the full volatility surface on the recovery rate of bonds.

CDS Implied Credit Ratings: Rating agencies cluster companies in rating categories to signal their creditworthiness. The rating is based on qualitative and quantitative factors and often is a mix between public and private information. Market prices, either asset swap spreads or credit default swap premia reflect the market perception on creditworthiness (default probability) and loss given default. Assuming a recovery rate, we use the (risk-neutral) default probabilities to cluster them in (rating) groups. We use the well-developed technique of regime switching to cluster issuers into categories. We test the model over the period 2004-2014 on issues such as in-sample likelihood, forecasting accuracy and rating stability. The model allows market participants to rate a company’s credit risk directly complimentary to ratings issued by credit rating agencies.