Tail approximations in credit portfolios using large deviations techniques

Abstract

In this paper, it is analyzed how Large Deviations (LD) techniques can be used for practical credit portfolio management. Applications include the internal risk management for a large credit portfolio, or the overall need to meet external requirements imposed by Basel II. For this purpose the paper provides fast and reliable methods for the computation of Value at Risk (VaR) and Conditional Value at Risk (CVaR) in general factor models using LD. Recovery rate (RR) is modelled as a random variable, depending on the state of the economy, using different models from the literature. The applicability of LD is shown, above mentioned risk measures are calculated and compared to the case of deterministic RR, demonstrating the need of an adequate modelling of RRs. Optimal portfolios with regard to either VaR or CVaR under portfolio constraints are derived, showing that LD techniques can outperform Monte Carlo (MC) simulations with regard to computational effort without a significant lack of accuracy.