Asymptotic representations for importance-sampling estimators of value-at-risk and conditional value-at-risk |
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Authors: | Lihua Sun |
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Institution: | Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China |
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Abstract: | Value-at-risk (VaR) and conditional value-at-risk (CVaR) are important risk measures. They are often estimated by using importance-sampling (IS) techniques. In this paper, we derive the asymptotic representations for IS estimators of VaR and CVaR. Based on these representations, we are able to prove the consistency and asymptotic normality of the estimators and to provide simple conditions under which the IS estimators have smaller asymptotic variances than the ordinary Monte Carlo estimators. |
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Keywords: | Value-at-risk Conditional value-at-risk Importance sampling Asymptotic representation |
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