Importance Sampling for Calculating the Value-at-Risk and Expected Shortfall of the Quadratic Portfolio with t-Distributed Risk Factors

In the banking industry, the calculation of regulatory capital by the Basel accords is directly related to the values of the Value-at-Risk (VaR) and expected shortfall (ES). The Monte Carlo simulation approach for calculating the VaR and ES is preferred, because it is able to incorporate a wide range of realistic models. Motivated by the gigantic size of the derivatives market, we consider the quadratic portfolio with t-distributed risk factors. To overcome the slow convergence of the Monte Carlo simulation approach, we propose a novel importance sampling scheme, which is applicable to the calculation of the VaR and ES. Numerical experiments confirm the superiority of our method in terms of substantial reduction in variance and computing time, particularly in calculating the ES.