Financial Update (January-March 1999)
Models for Valuing Default-Risky Securities
any financial institutions hold large amounts of defaultable securities in their portfolios, so it is important that these institutions have a reliable estimate of the resulting credit exposure. But the contractual complexities of defaultable securities and the uncertainties surrounding future cash flows make these securities difficult to value. Valuing them requires formal models that take these complexities and uncertainties into account.
In an article in the Atlanta Fed's Economic Review (Fourth Quarter 1998), senior economist Saikat Nandi reviews the developments in valuation models for defaultable securities dating back to the classic model developed by Robert Merton in 1974.
Nandi discusses two classes of models for valuing defaultable securities. Structural models require the use of an imprecisely observed quantity (or quantities), such as a firm's value or variables related to it, in the valuation formula. In contrast, reduced-form models do not need firm-value-related variables and so may hold more promise.
The valuation formulas of reduced-form models are often very similar to those used for valuing the corresponding default-free securities, the only difference being that the discounting factor is adjusted upward to account for the probability of default and the fraction of value lost upon default. Therefore, many of the existing results for valuing default-free securities can be used to price default-risky securities. This advantage is significant because some models for valuing default-free securities are analytically and computationally easier to use. Some of the reduced-form models can also incorporate the historical probabilities of credit-rating changes and defaults, information that can be crucial for pricing instruments whose payoffs are explicitly linked to credit events, such as credit upgrades or downgrades.
However, because only limited work has been done so far in validating the efficacy of various reduced-form models, caution is warranted in using these models for pricing and hedging defaultable securities.
Nandi finds that although researchers have improved considerably on the basic Merton framework, problems remain. For example, many of the institutional features of bankruptcy and defaults, such as rescheduling of debts, cannot be readily incorporated into the models discussed without making the models intractable. The next generation of valuation models, Nandi concludes, should incorporate at least some institutional features and be able to use the historical probabilities of defaults and credit-rating changes without making unnecessarily strong assumptions.