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Sensitivity estimation of conditional value at risk using randomized quasi-Monte Carlo

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  • He, Zhijian

Abstract

Conditional value at risk (CVaR) is a popular measure for quantifying portfolio risk. Sensitivity analysis of CVaR is common in risk management and gradient-based optimization algorithms. In this paper, we study the infinitesimal perturbation analysis estimator for CVaR sensitivity using randomized quasi-Monte Carlo (RQMC) simulation. RQMC has proved valuable in financial option pricing with a better rate of convergence compared to Monte Carlo sampling, but theoretical guarantees for this new application of RQMC shall be studied. To this end, we first prove that the RQMC-based estimator is strongly consistent under very mild conditions. Under some technical conditions, RQMC yields a mean error rate of O(n−1/2−1/(4d−2)+ϵ) for arbitrarily small ϵ>0, where d represents the dimension of RQMC points and n is the sample size. Some typical applications of CVaR sensitivity estimation are conducted to both show how the theoretical results can be applied, as well as to provide numerical results documenting the superiority of the RQMC estimator.

Suggested Citation

  • He, Zhijian, 2022. "Sensitivity estimation of conditional value at risk using randomized quasi-Monte Carlo," European Journal of Operational Research, Elsevier, vol. 298(1), pages 229-242.
    • Handle: RePEc:eee:ejores:v:298:y:2022:i:1:p:229-242
    DOI: 10.1016/j.ejor.2021.11.013
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    References listed on IDEAS

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    1. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129, January.
    2. Guangwu Liu & Liu Jeff Hong, 2009. "Kernel estimation of quantile sensitivities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 511-525, September.
    3. Weng, Chengfeng & Wang, Xiaoqun & He, Zhijian, 2016. "An auto-realignment method in quasi-Monte Carlo for pricing financial derivatives with jump structures," European Journal of Operational Research, Elsevier, vol. 254(1), pages 304-311.
    4. Michael C. Fu & L. Jeff Hong & Jian-Qiang Hu, 2009. "Conditional Monte Carlo Estimation of Quantile Sensitivities," Management Science, INFORMS, vol. 55(12), pages 2019-2027, December.
    5. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    6. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    7. Chaojun Zhang & Xiaoqun Wang, 2020. "Quasi-Monte Carlo-based conditional pathwise method for option Greeks," Quantitative Finance, Taylor & Francis Journals, vol. 20(1), pages 49-67, January.
    8. Vali Asimit & Liang Peng & Ruodu Wang & Alex Yu, 2019. "An efficient approach to quantile capital allocation and sensitivity analysis," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1131-1156, October.
    9. L. Jeff Hong & Sandeep Juneja & Jun Luo, 2014. "Estimating Sensitivities of Portfolio Credit Risk Using Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 848-865, November.
    10. Hui Dong & Marvin K. Nakayama, 2017. "Quantile Estimation with Latin Hypercube Sampling," Operations Research, INFORMS, vol. 65(6), pages 1678-1695, December.
    11. Xie, Fei & He, Zhijian & Wang, Xiaoqun, 2019. "An importance sampling-based smoothing approach for quasi-Monte Carlo simulation of discrete barrier options," European Journal of Operational Research, Elsevier, vol. 274(2), pages 759-772.
    12. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    13. Xiaoqun Wang & Ken Seng Tan, 2013. "Pricing and Hedging with Discontinuous Functions: Quasi-Monte Carlo Methods and Dimension Reduction," Management Science, INFORMS, vol. 59(2), pages 376-389, July.
    14. Guangxin Jiang & Michael C. Fu, 2015. "Technical Note—On Estimating Quantile Sensitivities via Infinitesimal Perturbation Analysis," Operations Research, INFORMS, vol. 63(2), pages 435-441, April.
    15. L. Jeff Hong & Guangwu Liu, 2009. "Simulating Sensitivities of Conditional Value at Risk," Management Science, INFORMS, vol. 55(2), pages 281-293, February.
    16. Athanassios N. Avramidis & James R. Wilson, 1998. "Correlation-Induction Techniques for Estimating Quantiles in Simulation Experiments," Operations Research, INFORMS, vol. 46(4), pages 574-591, August.
    17. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
    18. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
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