Efficient Simulation of Value at Risk with Heavy-Tailed Risk Factors

Simulation of small probabilities has important applications in many disciplines. The probabilities considered in value-at-risk (VaR) are moderately small. However, the variance reduction techniques developed in the literature for VaR computation are based on large-deviations methods, which are good for very small probabilities. Modeling heavy-tailed risk factors using multivariate t distributions, we develop a new method for VaR computation. We show that the proposed method minimizes the variance of the importance-sampling estimator exactly, whereas previous methods produce approximations to the exact solution. Thus, the proposed method consistently outperforms existing methods derived from large deviations theory under various settings. The results are confirmed by a simulation study.