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Information Management Network

 
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Pricing Models For Credit Derivatives

These days, it's possible to call up five or six dealers and get a price quote for the credit structure of your choice. But do you need your own special pricing models to evaluate those prices?

Most major dealers argue that it is possible to evaluate credit derivatives by simply considering the price of their underlying assets. But dealers go beyond this when they price deals themselves. "All the major dealers have their own proprietary models for pricing credit products," admits one New York credit derivatives dealer. If the dealers can benefit from this sort of modeling, why can't end-users?

There are several good reasons why a theoretical method of pricing credit would help anyone in the credit derivatives market. A theoretical model allows people to evaluate dealer prices, and to ascertain how much of the price they pay is really extra cash for their dealers. A model could also be the first step toward running risk management simulations on a portfolio of credit derivatives; in these simulations, users might stress various market factors and see how their portfolio performs. Finally, a theoretical pricing model for common types of credit derivatives would make the pricing of these products more transparent.

The problem is that there is no industry-standard way to price credit. So far, only two companies have been working on the problem long enough to make any headway: San Francisco-based KMV Associates and Tokyo-based Kamakura. KMV Associates, founded in 1990, offers off-the-shelf software capable of estimating default probabilities and managing portfolios of default risk; this software is in production at many large international banks. Kamakura, meanwhile, is a risk management consulting and software development firm that is now developing a credit pricing module.

These two companies, however, have quite different philosophies in terms of the relationship between fluctuating interest rates and default probabilities, whether or not this relationship can be reliably calculated given the data now available on secondary credit markets-and, in fact, whether or not credit can be accurately priced at all given data-related constraints.

Kamakura, which has yet to offer an over-the-counter credit pricing module, is developing software based largely on the research of Robert Jarrow, the firm's head of research and a professor at Cornell University's Johnson Graduate School of Management. Jarrow, in conjunction with professor Stuart Turnbull of Queens University in Canada, published an early version of the Jarrow-Turnbull model in 1993 that described a general methodology for pricing credit and credit-based structures. Later, in 1995, Jarrow and Turnbull published an extended version of the earlier model, which used historical data to estimate specific parameters in the model.

According to Jarrow, the Jarrow-Turnbull model incorporates multifactor interest rate analysis, and attempts to quantify the relationship between interest rate fluctuations and default probability over time. He emphasizes that this cross-market relationship is important to capture accurately the value of a credit-based instrument. For example, rising interest rates are known to cause problems for highly leveraged companies. Certainly, the way a credit investment might perform under a different interest rate environment is valuable information for the potential investor.

"Assuming that interest rates are constant is a heroic assumption," says Don Van Deventer, president of Kamakura, who cites an analogy from the mortgage market. According to a recent study by the Federal Reserve, much of the seemingly irrational behavior of home borrowers who did not refinance under favorable interest rate conditions was, in fact, a result of the asset value of their homes. If the value of the house was less than the balance of the mortgage, then borrowers would not refinance. According to Van Deventer, similar principles are at work in the corporate borrowing market-the asset valuation of the corporation in question and the level of interest rates are both critical to refinancing decisions. He emphasizes that both factors must be taken into consideration in order to accurately value credit derivatives.

However, Stephen Kealhofer, one of KMV's founding directors, says, "At a conceptual level there may well be an important relationship between interest rates and default probabilities, but the empirical evidence for it is weak." Kealhofer explains that KMV uses equity prices as a key input to its model for estimating default; according to KMV's research, interest rate effects are to a great extent embedded in these equity prices.

Over the past few years, KMV has attempted to boost the accuracy of its software by testing methods that include an explicit interest rate factor in addition to equity prices. However, the results were less than encouraging. He says, "We have not been able to find much of any consistent relationship between interest rates and default risk after taking equity prices into account."

And, adds Kealhofer, the extent of interest rate effects on default probabilities may be relatively mild. He says, "The corporate capital structure consists of interest-sensitive assets and liabilities, which in many cases create a natural hedge against interest rate fluctuations." And, at the asset level, KMV's research has found that most firms' assets exhibit only a modest level of interest rate sensitivity. Still, KMV's software does incorporate a correlation factor that represents the relationship between interest rate fluctuations and asset value.

What KMV does not endorse, however, is the value of correlations between interest rates and credit quality based on incomplete data. According to KMV vice president Mac McQuown, known variables that affect credit spreads include default probability, interest rate fluctuations and time. Likewise, there may be other dimensions, such as liquidity, which have yet to be adequately quantified. "Interpreting motion across three dimensions-default, interest rates and time-is as much an empirical problem as it is a theoretical one," says McQuown. Using Bridge's (formerly EJV) indicated credit spread data-which is arguably one of the best such data sets in existence today-in research efforts over the past year, KMV has concluded that even this data is "too noisy" to allow any firm conclusions on the relationship between credit migrations and interest rates.

So far, KMV does not offer a credit valuation model. Although the firm has developed several prototype models intended to predict future corporate bond prices, none of these models has been deemed "ready for prime time." Adds McQuown, "This topic is very complex, and its resolution depends on the availability of better data."

KMV is currently the only firm actually offering stand-alone credit-pricing software, but other companies are busy developing modules for their systems as well as trying to build effective credit-valuation models. "Our methodology is in production at many large financial institutions today," notes McQuown. "There are many things that have to happen after a model is published in academic journals before it can be judged as appropriate for use in a live trading environment." We'll just have to wait and see.

-K.S.

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