Counterparty Risk and the Pricing of Defaultable Securities

Motivated by recent financial crises in East Asia and the U.S. where the downfall of a small number of firms had an economy-wide impact, this paper generalizes existing reduced-form models to include default intensities dependent on the default of a counterparty. In this model, firms have correlated defaults due not only to an exposure to common risk factors, but also to firm-specific risks that are termed “counterparty risks.” Numerical examples illustrate the effect of counterparty risk on the pricing of defaultable bonds and credit derivatives such as default swaps. It has been well documented in Moody’s reports on historical default rates of corporate bond issuers that the number of defaults, the number of credit rating downgrades, and credit spreads are all strongly correlated with the business cycle. This has motivated reduced-form models such as Duffie and Singleton (1999) and Lando (1994, 1998), which assume that the intensity of default is a stochastic process that derives its randomness from a set of state variables such as the short-term interest rate. This approach has the convenient features that conditioning on the state variables, defaults become independent events, and default correlation arises due to the common influence of these state variables. On the other hand, a default intensity that depends linearly on a set of smoothly varying macroeconomic variables is unlikely to account for the clustering of defaults around an economic recession. This is evident from a casual inspection of the exhibits in the latest Moody’s report (see Keenan (2000)). Within the usual affine framework, one can model the state variables as jump diffusions (see Duffie, Pan and Singleton (1999)). But presently there is no evidence whether the magnitude of jumps needed to justify the clustering of defaults is consistent with well-defined, observable macroeconomic variables.1 This paper complements the current literature on default risk modeling by introducing the concept of counterparty risk. In our model, each firm has a unique (firm-specific) counterparty structure that arises from its relation with other firms in the economy. Counterparty risk is the risk that the default of a firm’s counterparty might affect its own default probability. This approach has two benefits. First, to the extent that the public is aware of the counterparty relations, the prices of marketed securities will reflect the market’s assessment of the importance of counterparty risk. Relying on the notion of market efficiency, our model allows the extraction of this information, which is potentially important for the pricing of defaultable bonds and credit derivatives, as we demonstrate below. Second, the additional default correlation introduced by counterparty relations makes it straightforward to account for the observed clustering of defaults. For instance, a group of firms can be so highly interdependent that a single default can trigger a cascade of defaults. Because the likelihood of default is higher for all firms during a recession, this cascading effect is much more likely to be observed then. This has important implications for the management of credit risk portfolios, where default correlation needs to be explicitly modeled. Our concept of counterparty risk has been motivated by a series of recent events in which firm-specific risks figure prominently. Several such examples are given below: