Spread Risk and Default Intensity Models

This chapter discusses credit spreads, the difference between risk-free and default-risky interest rates, and estimates of default probabilities based on credit spreads. Credit spreads are the compensation the market offers for bearing default risk. They are not pure expressions of default risk, though. Apart from the probability of default over the life of the security, credit spreads also contain compensation for risk. The spread must induce investors to put up not only with the uncertainty of credit returns, but also liquidity risk, the extremeness of loss in the event of default, for the uncertainty of the timing and extent of recovery payments, and in many cases also for legal risks: Insolvency and default are messy.

Most of this chapter is devoted to understanding the relationship between credit spreads and default probabilities. We provide a detail example of how to estimate a risk neutral default curve from a set of credit spreads. The final section discusses spread risk and spread volatility.


Just as risk-free rates can be represented in a number of ways—spot rates, forward rates, and discount factors—credit spreads can be represented in a number of equivalent ways. Some are used only in analytical contexts, while others serve as units for quoting prices. All of them attempt to decompose bond interest into the part of the interest rate that is compensation for credit and liquidity risk and the part ...

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