Ebook Credit Risk And Risk Neutral Default Probabilities: Information About Rating Migrations And Defaults
Fixed income markets are the largest capital markets in the world. In the United States, the fixed income markets are about two to three times as large as the equity markets. In most other countries, equity markets are even smaller relative to fixed income. Risks in fixed income (and other) markets are sometimes characterized as market risk and credit risk, although the two are not unrelated since changes in either risk are associated with security price changes. However, market risk is generally considered to be the risk associated with changes in prices of traded securities, usually bond prices, stock prices, foreign exchange prices, and commodity prices. Credit risk is the risk that the issuer of a fixed income security does not meet the security’s promised obligations and thus defaults. For example, default could happen if the value of the issuer’s assets falls below the value of the promised payments. Thus, credit risk is dynamic and is related to market risk because credit risk changes with variations in the value of the issuer’s assets. While credit risk is important to all fixed income markets (including the sovereign risk of government bond markets), this paper is primarily concerned with corporate credit risk.
Today in most developed financial markets, derivative securities can be used to control the various forms of so-called market risk in a firm’s balance sheet. For most firms, these balance sheet risks include equity risk, currency risk, interest rate risk, commodity price risk, and asset price risk. However, until recently few derivative securities were available to help hedge credit risk. This is now changing with the advent of credit derivatives, considered by some as the derivative market’s new frontier. Default probabilities and changes in expected default frequencies are important to both the structure and pricing of credit derivatives.
Default is literally defined as failure to meet a required or contractual obligation. As noted, in financial markets this usually implies the corporate issuer failed to make a promised payment on its debt securities. When one considers the large number of corporations issuing fixed income securities and the relatively small number of actual defaults, one might regard default as a rare event. However, all corporate issuers have some positive probability of default. This default probability should change continuously with changes in the firm’s stock price and thus its leverage. The value of most fixed income securities is typically inversely related to the probability of default. Investors are concerned about changes in the value of their fixed income securities due to changes in the probability of default, even though the actual default seldom occurs. In fact, fixed income investors may be more concerned with changes in the perceived credit quality of their bond holdings than with actual default. Rating migrations, which offer one reflection of changes in perceived quality of bonds, occur much more frequently than defaults.
Rating agencies regularly measure the historical default frequency of both US and non US corporate issuers. While these historical default frequencies are interesting, they are not forward-looking. Option models can provide a forward-looking, risk neutral default probability. Changes in this risk neutral default probability might provide leading information about changes in the credit quality of a debt issuer, and thus about either an impending rating change or default.
From a theoretical perspective, default risk has been modeled in a variety of ways. Using diffusion processes to describe changes in the value of the firm, Merton (1974) was the first to demonstrate that a firm’s default option could be modeled with the Black and Scholes (1973) methodology. He showed that stock could be considered as a call option on the firm with the strike price equal to the face value of a single payment debt issue. Geske (1977, 1979) extended Merton’s analysis by showing that multiple default options for coupons, sinking funds, junior debt, safety covenants, or other payment obligations could be treated as compound options.
The basic Merton model has been extended in many ways. Black and Cox (1977) allow for safety covenants, subordination arrangements, and limits on refinancing. Turnbull (1979) includes corporate taxes and bankruptcy costs. In order to study the interaction of default risk and interest rate risk, Kim, Ramaswamy, and Sundaresan (1993) allow the riskless interest rate to follow a square root process which is correlated with the firm value. They showed that default risk is not particularly sensitive to the volatility of interest rates but is sensitive to interest rate expectations. Longstaff and Schwartz (1995) also have stochastic interest rates correlated with the firm process, an exogenous early default and an exogenous recovery rate. Leland (1995) endogenizes the bankruptcy decision while accounting for taxes and bankruptcy costs.
Altman (1977, 1986) took a different approach using z-scores and discriminant analysis to examine risky corporate debt. Another approach has been to model default as a rare event, or Poisson process. Mason and Bhattachayra (1981) allowed the firm to follow a discontinuous Poisson process with more complex boundary conditions. Jarrow and Turnbull (1995) model default as a Poisson event when pricing derivatives with credit risk . Duffie and Singleton (1997), when considering the term structure of defaultable bonds or swaps, model the default event as an inaccessible stopping time, such as a Poisson arrival. They argue that this is appropriate because when defaults do occur, they are rarely anticipated even a short time before the event. However, here we show that this is not necessarily the case.
The focus of this research is the properties of risk neutral default probabilities, especially their estimation, their size as an upperbound on actual default probabilities, their sensitivities, their term structure, and the information embedded within them about credit risk. The market has an interest in estimates and properties of default probabilities, both actual and risk neutral, in order to learn more about credit risk. We could also focus on default spreads from option models or on converting risk neutral default probabilities to actual default probabilities, but those topics are left for future research.
In this paper we use the option models of Merton (1974) and Geske (1977) to estimate a monthly time series of risk neutral default probabilities over approximately 10 years, from 1987 to 1996. We then examine the changes in these default probabilities before the event of a rating migration or default. There appears to be significant leading information about rating migrations and about defaults in these forward looking risk neutral probabilities of default. The term structure of default probabilities from the Geske model appears to contain additional information. The short term probability of default from the Geske model appears to contain significant information about both the default event and the shape of the term structure of default probabilities prior to the actual default. It appears this short term default probability is able to distinguish impending cash flow problems for the firm.
Furthermore, rating migrations and defaults do not appear to be a surprise to the market since they can be detected months in advance by either model. Thus, the diffusion approach to credit migrations and default may be as, or more, appropriate than the Poisson approach.
In section 2 of the paper we present a brief description of the models and the derivations of each model’s risk neutral default probabilities. Section 3 describes our data sources and construction, section 4 presents our results, and section 5 offers some conclusions.
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