Term structure of credit spreads

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). 

FIGURE 8.7 The term structure of credit spread for investment- and speculative-grade bonds. 

Leland, H.E., Toft, K.B., 1996. Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads. J. Financ. 51 (3), 987-1019. 

Truck, S., Laub, M., Rachev, S.T., 2004 The terms structure of credit spreads and credit default swaps - an empirical investigation. Working Paper, September. 

In Chapter 8, we described several models to measure the term structure of credit spread and we introduced the model proposed by Longstaff and Schwartz (1995) for pricing fixed-rate debt. The authors propose also a model to valuing floating-rate notes. The equation derived for pricing floating-rate bonds is given by (10.2) ... 

Robert Jarrow and David Lando, A Markov Model for the Term Structure of Credit Spreads, Review of Financial Studies 10 (1997), pp. 481-523 Darrell Duffie and Kenneth Singleton, Modelling Term Structures of Defaultable Bonds, Review of Financial Studies (1997). 

Of these factors, one of the most significant is the term to maturity. The term structure of credit spreads exhibits a number of features. For instance, lower-quality credits trade at a wider spread than higher-quality credits, and longer-dated obligations normally have higher spreads than shorter-dated ones. For example, for a particular sector they may look like this ... 

Jarrow, R.A., Lando, D., Turnbull, S.M., 1997. A Markov model for the term structure of credit ride spreads. Rev. Financ. Stud. 10 (2), 481-523. 

Since credit default swaps are written on the reference entities, their pricing provide information on the default probabilities of the issuer and are not subject to liquidity premia that can be present in the credit spreads of the credit risky bonds. Therefore, the term structure of credit default swap spreads for a particular issuer is used to determine the cumulative default probability of the issuer. 

More complex models for the credit spread process may take into account factors such as the term structure of credit and possible correlation between the spread process and the interest process. 

Moreover, duration will be influenced by the floater s stmcture. In fact, the choice of the reference rate affects the duration depending on how much volatile the index is. The lower the frequency of couptm payments, the greater the price sensitivity between reset dates. Thus, while floating-rate notes have a lower price sensitivity to a change of the reference rate, fixed and floating-rate notes both have a price sensitivity to changes of credit spread reflecting the issuer s creditworthiness. A shift of the credit term structure will determine the decline of the bond s price. 

The credit curves (or default swap curves) reflect the term structure of spreads by maturity (or tenor) in the credit default swap markets. The shape of the credit curves are influenced by the demand and supply for credit protection in the credit default swaps market and reflect the credit quality of the reference entities (both specific and systematic risk). The changing levels of credit curves provide traders and arbitragers with the opportunity to measure relative value and establish credit positions. 

The Das-Tufano (DT) model is an extension of the JLT model. The model aims to produce the risk-neutral transition matrix in a similar way to the JLT model however, this model uses stochastic recovery rates. The final risk neutral transition matrix should be computed from the observable term structures. The stochastic recovery rates introduce more variability in the spread volatility. Spreads are a function of factors that may not only be dependent on the rating level of the credit as in practice, credit spreads may change even though credit ratings have not changed. Therefore, to some extent, the DT model introduces this additional variability into the risk-neutral transition matrix. 

Fortunately for the investment community, there are alternatives to calculating tracking error that give an accurate idea of where a portfolio s risks lie. These methods start with understanding the exposures of a portfolio relative to its benchmark, along several dimensions such as duration, term structure, rating, sector, and issuer. They then create interest rate and credit spread scenarios for different future time periods and perform a what-if analysis on the portfolio and the benchmark for these scenarios. These scenarios should encompass both expected and extreme conditions (best and worst case) in order to generate a return profile, both absolute and relative to the index, as well as to identify key thresholds. 

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