On the Estimation of Credit Exposures Using Regression-Based Monte Carlo Simulation

In this paper we tackle one of the problems that arises in the broad area of credit risk management. We seek a scenario consistent way of modeling the future credit exposure of complex products that do not admit an analytical (closed-form) solution. We present a technique for calculating future credit exposures that relies on least squares Monte Carlo simulation. Whereas the pricing of instruments is done under the risk-neutral probability measure used in front- office pricing models, the dynamical evolution of future prices should be captured using the historical (physical) probability measure used for risk management objectives. Therefore, we extend existing least squares Monte Carlo approaches used for pricing purposes to allow for modeling of future credit exposures. We apply the established technique to several product examples (such as American options, convertible bonds, cancelable interest rate swaps and variance swaps) and benchmark the algorithm to products that allow closed-form representations