407CHAPTER 28 CREDIT RISK Jeremy Graveline and Michael KokalariThis review provides a comprehensive survey of recent quantitative research on the pricing of credit risk. It also explores two types of models commonly used for pric- ing credit risk structural models and reduced - form models. The authors review the contract details and pricing of such popular credit derivatives as credit default swaps, collateralized debt obligations (CDOs), and basket default swaps. They dis- cuss models for correlated default risk and supply an example of pricing a CDO using Monte Carlo analysis. The global market for credit derivatives has exploded in recent years; the International Swaps and Derivatives Association released a midyear 2006 report giving $ 26 trillion as the notional amount of credit derivatives outstanding. In conjunction with the development of credit derivatives markets, research on credit risk has also increased. The objective of this literature review is to provide an introduction to recent quantitative research on the modeling and pric- ing of credit risk. WHAT ARE CREDIT DERIVATIVES? Credit derivatives are contracts in which the payout depends on the default behavior of a company or a portfolio of companies. For example: A corporate bond portfolio manager may want to protect his portfolio against the extreme event that more than three companies in his portfolio go bankrupt over the next five years. A credit derivatives contract could insure against such a loss in the same way that an out -of - the - money put option could insure an equity portfolio manager against catastrophic losses. Copyright 2006, 2008, 2010, The Research Foundation of CFA Institute. Modified with permission. CH028.indd 407CH028.indd 4078/28/10 8:38:41 PM8/28/10 8:38:41 PM408 Part III: Managing RiskCredit RiskThe credit risk manager at a commercial bank is concerned about her bank s level of exposure to a particular corporate customer, but the lending officer wants to maintain a good relationship with this customer. Credit derivatives would allow the bank to reduce its credit exposure to that one customer with an off - balance - sheet transaction. The equity derivatives analogy is selling a forward contract against one stock in a portfolio, which eliminates the risk but keeps the physical transaction on the books. A medium - size commercial bank has concentrated credit risk in a small group of indus- tries (say, manufacturing), but almost no customer exposure and no credit risk exposure to another group of industries (say, consumer products). Credit derivatives allow the bank to reduce its concentrated credit risk and gain exposure to the other sectors. A portfolio manager would like to invest in a group of bonds but is restricted from doing so because of the bonds low credit rating. A credit derivative can repackage the cash flows from these low - rated bonds and offer the portfolio manager an investment with a higher credit rating. Many dimensions of credit risk affect the prices of credit derivatives and corporate debt. For example, there is the risk that an issuer will default. If an issuer defaults, the payout on its bonds or a related credit derivative is uncertain. Even though an issuer may not default, its credit quality may change, and hence, the price of its bonds can also change. Researchers have proposed quantitative models that address all of these risks. This literature review begins with a discussion of models for predicting default. We discuss two types of models commonly used for pricing credit risk: structural models and reduced - form models. We then review the contract details and pricing of such popular credit derivatives as credit default swaps (CDS), collateralized debt obligations (CDOs), 1 and basket default swaps. We conclude with a discussion of models for correlated default risk and an example of pricing a CDO using Monte Carlo analysis. PREDICTING DEFAULT Companies are generally considered to default when they miss a debt payment or file for Chapter 7 or Chapter 11 bankruptcy. 2Altman (1968) developed one of the first quantita- tive models for predicting bankruptcy. His Z - score model formalized the more qualitative analysis of default risk provided by ratings agencies such as Standard and Poor s and Moody s Investors Service. Altman identified five key financial ratios and computed a weighted aver- age of those ratios to arrive at the company s “ Z - score. ” Companies with low Z - scores are more likely to default than companies with high Z - scores. Altman used statistical techniques to determine the best weights to put on each ratio. The most significant financial ratio for predicting default is earnings before income and taxes divided by total assets. The next most significant financial ratio is sales to total assets. Altman s Z - score model does not incorporate the fact that the characteris