An Importance Sampling Method to Evaluate Value-at-Risk for Assets with Jump Risks

Risk management is an important issue when there is a catastrophic event that affects asset price in the market such as a sub-prime financial crisis or other financial crisis. By adding a jump term in the geometric Brownian motion, the jump diffusion model can be used to describe abnormal changes in asset prices when there is a serious event in the market. In this paper, we propose an importance sampling algorithm to compute the Value-at-Risk for linear and nonlinear assets under a multi-variate jump diffusion model. To be more precise, an efficient computational procedure is developed for estimating the portfolio loss probability for linear and nonlinear assets with jump risks. And the titling measure can be separated for the diffusion and the jump part under the assumption of independence. The simulation results show that the efficiency of importance sampling improves over the naive Monte Carlo simulation from 7 times to 285 times under various situations. We also show the robustness of the importance sampling algorithm by comparing it with the EVT-Copula method proposed by Oh and Moon (2006).