Defaulted bonds recovery rates

Another reduced model is the one proposed by Duffie and Singleton. In this model, the recovery rate of debt is determined prior to default, that is default and recovery rates are assumed exogenous. The price of bond is given by Equation (8.33) ... 

We set pt as the probability that a bond will default in year t, and is the probability of default up to year t, while is the expected recovery rate on the bond should it default. The default probability is assumed to fluctuate over time, while the recovery rate remains constant. Therefore, the probability that the bond will not have defaulted up to the beginning of year t is given by ... 

Fons (1994) studied the term structure of credit risk based on the historical default probabilities, ratings and recovery rates. In fact, he proposes a bond pricing model in which the value depends on the probability of default and average recovery rate. The model presented is based on the following assumptions ... 

The research compares the model spread to the one observed in the market. In order to determine the term structure of credit spread. Eons uses historical probabilities by Moody s database, adopting a recovery rate of 48.38%. The empirical evidence is that bonds with high investment grade have an upward credit spread curve. Therefore, the spread between defaultable and default-free bonds increases as maturity increases. Conversely, speculative-grade bonds have a negative or flat credit yield curve (Figure 8.7). 

Recovery rates for individual obligors differ by issuer and industry classification. Rating agencies publish data on the average prices of all defaulted bonds, and generally analysts will construct a database of recovery rates by industry and credit rating for use in modelling the expected recovery rates of assets in the collateral portfolio. 

In practice, the spread information from the CDS market is used to imply the probability of default and the hazard rate for the underlying reference entity. The recovery rate is an input when the calculation of implied probabilities takes place. It is common to assume a recovery rate that reflects the rate on the cheapest to deliver deliverable obligation. Credit derivative traders will monitor the prices of the cheapest to deliver bonds (i.e., deliverable obligations with the lowest recovery), when constructing hedges. 

Recovery rates on bonds vary by the position in the reference entity s capital structure and the level of security offered to the bond holders. Determining the appropriate recovery rate is not a trivial process and requires careful analysis into the traded prices of deliverable obligations for the reference credit. In practice there is limited historical information on the recovery rates experienced for credit default swaps. 

Given this new landscape, in 2001, Fitch Ratings created a par based default index specific to the European high-yield market. The objective of this chapter is to compare and contrast default and recovery patterns across the two markets in order to give global bond investors and European investors, in particular, historical and current benchmarks for measuring credit risk. 

What is noteworthy is that the recovery rates for telecommunication defaults were nearly parallel in the two markets. They averaged 11.5% and 13.7% of par in the United States in 2001 and 2002, respectively, and 8% and 12% of par in Europe. Since the cable sector in Europe shared many of the same characteristics of the beleaguered telecommunication sector, the average recovery rate on defaulted cable bonds in Europe was also low at 15% of par. (In contrast, recovery rates on cable bonds in the United States were 53% and 41% in 2001 and 2002, respectively.) Considering that the overwhelming volume of defaults in Europe came from the two sectors, it is therefore apparent that the primary reason for the low recovery rates in Europe was this industry concentration. 

Here we demonstrate that the credit spread is related to risk of default (as represented by the hazard rate) and the level of recovery of the bond. We assume that a zero-coupon risky bond maturing in a small time element At where ... 

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