Valuation Models for Default-Risky Securities: An Overview

by Saikat Nandi of the Federal Reserve Board of Atlanta

Q4 1998

Beginning Paragraphs: Valuing financial securities often assumes that the contractual obligations of the security are going to be honored. However, frequently a party to a contract will default on its obligations. An issuer of a corporate bond may be unable to make is promised coupon and principal payments, and a party to a derivatives contract such as an interest rate swap may default on the periodic payments of the swap contract.

Because the contractual features of defaultable securities are usually complex and it may be difficult to find comparable securities for which to observe prices, valuation based on simple rules of thumb is often infeasible. For example, one may have to value an interest rate swap subject to termination if one of the parties has its credit downgraded, and there are no comparable swaps that one can look up for a reference price (see the glossary for a definition of a swap and of other terms used throughout this discussion). Hence it becomes necessary to resort to formal models that can value a defaultable security on the basis of expected future cash flows, taking into account the contractual features of the defaultable security and the uncertainties surrounding the future cash flows. Many financial institutions hold large amounts of default-risky securities of various degrees of complexity in their portfolios, and it is important that these institutions have a reliable estimate of the resulting credit exposure. Estimating the credit exposure often involves knowing the possible values of the defaultable security at various times in the future. Therefore, under-standing the different valuation models of default-risky securities and the strengths and drawbacks of various modeling approaches (see Table 1) is also important for implementing prudent risk-management policies to manage credit exposures.

This article discusses some of the models for valuing financial instruments that are subject to default risk, the implications of these models, and the difficulties that might be encountered in implementing them. The focus is on the valuation of default-risky bonds and swaps, although the general principles of valuation can be applied to other related instruments. The first section explains the classic Merton (1974) model for valuing a default-risky bond. Subsequently, the text discusses some of the more recent models for valuing such bonds. These models differ in terms of how predictable the degree of default is and whether the firm's value is needed as an input in the valuation formula. Next, some of the valuation models for default-risky swaps are considered, including ones in which both parties to a swap can default. The discussion concludes with a review of the strengths and drawbacks of different valuation models and some thoughts for future research.

Keywords: Econometric models, Financial markets, Securities.

Published in: Economic Review, (Q4 1998), pp. 22-35.

Download paper (199K PDF) 14 pages