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Simulating Sensitivities of Conditional Value at Risk

Author

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  • L. Jeff Hong

    (Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Guangwu Liu

    (Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

Abstract

Conditional value at risk (CVaR) is both a coherent risk measure and a natural risk statistic. It is often used to measure the risk associated with large losses. In this paper, we study how to estimate the sensitivities of CVaR using Monte Carlo simulation. We first prove that the CVaR sensitivity can be written as a conditional expectation for general loss distributions. We then propose an estimator of the CVaR sensitivity and analyze its asymptotic properties. The numerical results show that the estimator works well. Furthermore, we demonstrate how to use the estimator to solve optimization problems with CVaR objective and/or constraints, and compare it to a popular linear programming-based algorithm.

Suggested Citation

  • L. Jeff Hong & Guangwu Liu, 2009. "Simulating Sensitivities of Conditional Value at Risk," Management Science, INFORMS, vol. 55(2), pages 281-293, February.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:2:p:281-293
    DOI: 10.1287/mnsc.1080.0901
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    References listed on IDEAS

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