Toward a Better Estimation of Wrong-way Credit Exposure

May 1, 2000

In credit risk management for swaps, forwards, and other derivative contracts, most applications of credit exposure measures suffer from the assumption that counterparty default is independent of the amount exposed. We introduce conditional measures which account for "wrong way" exposures, but fit naturally into current applications.

Introduction

The market upheavals of 1998 brought greater attention to market and credit risk management alike. On the credit side, last year's events pointed out that as crucial as monitoring the credit quality of counterparties is the seemingly simple task of monitoring the amounts actually exposed to these counterparties. Exposure estimation, while straightforward for traditional credit products, becomes more complex when the exposure is contingent on a market factor (e.g. an exchange rate) and, as we will see in this article, more complex still when there is a dependency between counterparty credit quality and the relevant market factor.

Regulators have explicitly recognized the uncertain future credit exposure on swaps, forwards, and other derivative contracts. The Basle Capital Accord requires regulatory capital for current exposure – roughly, the amount which would be lost should the counterparty default today – plus additional "add-on" capital to account for the potential future exposure – the cost of replacing a contract some time in the future – due to moves in the underlying market factor. As to estimating and monitoring exposure, sophistication among practioners has varied greatly. To address these discrepancies, twelve large commercial and investment banks formed the Counterparty Risk Management Policy Group (CRMPG) in January 1999, and produced a report in June 1999. Fifth of the group's twelve recommendations was that financial intermediaries "should upgrade their ability to monitor and, as appropriate, set limits for various exposure measures".

The CRMPG report also highlights four issues that complicate the analysis of credit exposure. The issues read like a list of risk management themes in general. Liquidity, event, and operational concerns are the first three issues. The fourth is the typical assumption that the credit quality of the counterparty is independent of the market factors that underlie the exposure to the counterparty. In fact, the report is not the first criticism of this assumption. Duffee (1996) investigates the assumption empirically, and concludes that over the period 1971-1992, corporate defaults in the U.S. tended to cluster in periods of falling interest rates. For the receive fixed side of U.S. interest rate swaps, this produced a significant positive correlation between exposure size and counterparty default. In Duffee's example, an exposure measure that accounts for the correlation was on average 65% greater than a comparable measure that maintains the independence assumption.

To address the independence assumption, the CRMPG report proposes stress tests that simultaneously shock the market factors underlying exposure amounts and the credit factors influencing default. Unfortunately, it is difficult to reconcile stress measures of exposures with the common applications of exposure measures today. In this article, we will examine a number of current applications of exposure measures, and show that it is possible to relax the independence assumption and extend the standard measures in a natural way. The extension allows us to begin with any assumption about the distribution of the underlying risk factor, and to account for dependency between credit quality and market moves without resorting to stress tests.

The remainder of this article is structured as follows: in the Section 2, we define a number of standard measures of credit exposure and discuss their applications; in Section 3, we develop a framework to extend these measures by considering the dependency between counterparty credit quality and the underlying market factor; in Section 4, we present an example exposure calculation using this framework; in Section 5, we discuss a technique to calibrate the parameters of the model; lastly, we summarize and conclude.