SIMULATION OF NONLINEAR PORTFOLIO VALUE-AT-RISK BY MONTE CARLO AND QUASI-MONTE CARLO METHODS

摘要

This paper considers Monte Carlo and quasi-Monte Carlo simulations of Value-at-Risk for portfolios with nonlinear relations to the market risk factors. The loss function is approximated by the delta-gamma-theta or quadratic method. Under the assumptions of multivariate normal and multivariate Student t distributions for the changes of the risk factors, the coverage probabilities related to Value-at-Risk are transformed into integral representations. By comparing the relative magnitude of the estimated variance, the test results demonstrate that the lattice rule based quasi-Monte Carlo method significantly outperforms the pseudorandom number based Monte Carlo method.