Modeling credit exposure for collateralized counterparties

Michael Pykhtin

Abstract

ABSTRACT

Modeling the credit exposure of a financial institution to a counterparty usually requires a Monte Carlo simulation of values of the trades in the portfolio at future time points. For collateralized counterparties, collateral at any simulation time point depends on the portfolio value at an earlier time point because of the margin period of risk. Thus, in order to simulate collateralized exposure at a single (primary) time point, one needs to simulate the trade values at two time points: the primary and the look-back, resulting in a doubling of the total simulation time. In this paper we present a semi-analytical method for calculating expected exposure for collateralized counterparties that does not require the simulation of the trade values at the look-back time points. This method can be easily implemented with an existing system that simulates uncollateralized exposure, without a noticeable increase in the simulation time. Potential applications of the method include the pricing and hedging of counterparty credit risk and the calculation of economic and regulatory capital.