A Credit Risk Toolbox

This paper describes the use of counterparty loss distributions for credit risk management and capital allocation in derivative portfolios. We describe the data requirements, theory and simulation procedure for estimating such a distribution and highlight the important effects using simple examples. Moreover, we investigate techniques that yield an analytical expression for the loss distribution under restricted assumptions. Given that such simulations are generally highly time-consuming, two Monte Carlo acceleration techniques are described that can reduce the simulation time significantly. One technique is based upon importance sampling. The second technique is based upon a restricted analytical expression for the true loss distribution that can be used as a control variate.