Simulating Confidence Intervals for Conditional Value-at-Risk via Least-Squares Metamodels

Qidong Lai (), Guangwu Liu (), Bingfeng Zhang () and Kun Zhang ()
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Qidong Lai: Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon, Hong Kong
Guangwu Liu: Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon, Hong Kong
Bingfeng Zhang: SAFE Investment Company Limited, Central, Hong Kong
Kun Zhang: Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China

INFORMS Journal on Computing, 2025, vol. 37, issue 4, 1087-1105

Abstract: Metamodeling techniques have been applied to approximate portfolio loss as a function of financial risk factors, thus producing point estimates of various measures of portfolio risk based on Monte Carlo samples. Rather than point estimates, this paper focuses on the construction of confidence intervals (CIs) for a widely used risk measure, the so-called conditional value-at-risk (CVaR), when the least-squares method (LSM) is employed as a metamodel in the point estimation. To do so, we first develop lower and upper bounds of CVaR and construct CIs for these bounds. Then, the lower end of the CI for the lower bound and the upper end of the CI for the upper bound together form a CI of CVaR with justifiable statistical guarantee, which accounts for both the metamodel error and the noises of Monte Carlo samples. The proposed CI procedure reuses the samples simulated for LSM point estimation, thus requiring no additional simulation budget. We demonstrate via numerical examples that the proposed procedure may lead to a CI with the desired coverage probability and a much smaller width than that of an existing CI in the literature.

Keywords: simulation; conditional value-at-risk; confidence interval; portfolio risk measurement (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:37:y:2025:i:4:p:1087-1105

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