Efficient Computation of Value at Risk with Heavy-Tailed Risk Factors
24 Pages Posted: 25 Aug 2009
Date Written: August 24, 2009
The probabilities considered in value-at-risk (VaR) are typically of moderate deviations. However, the variance reduction techniques developed in the literature for VaR computation are based on large deviations methods. Modeling heavy-tailed risk factors using multivariate $t$ distributions, we develop a new moderate-deviations method for VaR computation. We show that the proposed method solves the corresponding optimization problem exactly, while 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.
Keywords: Importance sampling, moderate deviation, multivariate t distribution, quadratic approximation, component VaR
JEL Classification: C15, C63, D30
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