CVA and Wrong-Way Risk

Abstract

The authors propose a simple model for incorporating wrong-way and right-way risk into the Monte Carlo simulation that is used to calculate credit value adjustment (CVA). The model assumes a relationship between the hazard rate of a counterparty and variables whose values are generated, or can be generated, as part of the Monte Carlo simulation. The authors present numerical results for portfolios of 25 instruments dependent on five underlying market variables.Credit value adjustment, or CVA, is the reduction in the value of a dealer’s portfolio of derivative transactions with a counterparty to reflect the possibility that the counterparty will default. DVA (debit or debt value adjustment) is the increase in the value of the portfolio due to the possibility of a default by the dealer. In this article, we explain the way CVA and DVA calculations are carried out. For CVA calculations, it is necessary to divide the remaining life of the derivative portfolio into a number of time steps and to calculate (1) the probability of a counterparty default during each time step and (2) the expected exposure of the dealer to the counterparty at the midpoint of each time step. The probabilities of default are estimated from credit spreads. The expected exposure is calculated by carrying out a Monte Carlo simulation of the market variables on which the value of the portfolio depends.The simplest assumption in CVA calculations is that the probability of a counterparty default at a point in time is independent of the exposure at that time. Wrong-way risk arises from a positive correlation between probability of default and exposure, and right-way risk arises from a negative correlation between probability of default and exposure. Most approaches for taking account of wrong-way and right-way risk make adjustments to the expected exposure. Specifically, the expected exposure conditional on default is assumed to be different from the unconditional expected exposure.We use a different approach. We assume that the counterparty’s hazard rate at a particular time (which is a measure of its default probability) depends on the values of variables that are included, or could be included, in the Monte Carlo simulation of the underlying market variables. There are a number of alternative ways in which these variables can be chosen. For example, for a gold producer, it may make sense to relate the hazard rate to the price of gold. In other circumstances, the hazard rate could be related to a company’s stock price. Yet another possibility is to relate the hazard rate to the value of the dealer’s portfolio with the counterparty. The nature of the relationship between the hazard rate and the chosen variable (or variables) can be estimated subjectively or by using historical data. We explain how the relationship can be chosen so that it is consistent with the initial term structure of credit spreads.We present numerical results for the case in which the hazard rate is assumed to depend on the value of the dealer’s portfolio with the counterparty. We considered portfolios of 25 instruments dependent on five underlying market variables and found that wrong-way risk and right-way risk have a significant effect on the variables used to calculate CVA as well as on CVA itself. We also found that the percentage effect depends on the collateral arrangements.

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