Simulation of Nonlinear Portfolio Value-at-Risk by Monte Carlo and Quasi-Monte Carlo Methods

Y. Lai (Canada) and K.S. Tan (Canada & PRC)


Portfolio Value-at-Risk; Options; Monte Carlo and Quasi Monte Carlo simulation methods; Multivariate Student-t distributions; Multivariate normal distributions.


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 ap proximated by the delta-gamma-theta or quadratic method. Under the assumptions of multivariate normal and multi variate Student t distributions for the changes of the risk factors, the coverage probabilities related to Value-at-Risk are transformed into integral representations. By compar ing the relative magnitude of the estimated variance, the test results demonstrate that the lattice rule based quasi Monte Carlo method signi´Čücantly outperforms the pseudo random number based Monte Carlo method.

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