Efficient Simulation of Value at Risk with Heavy-Tailed Risk Factors

Simulation of small probabilities has important applications in many disciplines. The probabilities considered in value-at-risk (VaR) are moderately small. However, the variance reduction techniques developed in the literature for VaR computation are based on large-deviations methods, which are good...

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Bibliographic Details
Published in:Operations research 2011-11, Vol.59 (6), p.1395-1406
Main Authors: Fuh, Cheng-Der, Hu, Inchi, Hsu, Ya-Hui, Wang, Ren-Her
Format: Article
Language:English
Subjects:
Analysis
Applied sciences
Approximation
component VaR
distribution
Distribution theory
Estimators
Exact sciences and technology
importance sampling
Investment analysis
Investment risk
Mathematical models
Mathematical vectors
Mathematics
moderate deviation
Monte Carlo methods
Monte Carlo simulation
multivariate
Objective functions
Operational research and scientific management
Operational research. Management science
Portfolio performance
Portfolio theory
Predisposing factors
Probability and statistics
Probability theory and stochastic processes
Quadratic approximation
Random variables
Risk assessment
Risk management
Risk theory. Actuarial science
Sciences and techniques of general use
Simulation
Simulation methods
Studies
t
Technology application
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Summary:Simulation of small probabilities has important applications in many disciplines. The probabilities considered in value-at-risk (VaR) are moderately small. However, the variance reduction techniques developed in the literature for VaR computation are based on large-deviations methods, which are good for very small probabilities. Modeling heavy-tailed risk factors using multivariate t distributions, we develop a new method for VaR computation. We show that the proposed method minimizes the variance of the importance-sampling estimator exactly, whereas 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.
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1110.0993