A rotationally invariant technique for rare event simulation

Because of their low probability, including extreme events in Monte Carlo calculations of the value-at-risk of a credit-risky portfolio requires many simulations. Here, Susanne Klöppel, Ranja Reda and Walter Schachermayer demonstrate a geometrically simple change of measure technique that dramatically reduces computation time

The estimation of credit default risk is often based on credit portfolio models (Boegelein et al, 2002, Gupton, Finger & Bhatia, 1997), which try to capture dependencies between obligors in the portfolio. These models should reflect diversification and concentration effects accurately. The most important output of such credit portfolio models is the portfolio loss distribution, from which very popular credit risk management measures such as value-at-risk or expected shortfall (ES) can be derived