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Improved estimation of portfolio value‐at‐risk under copula models with mixed marginals

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  • Douglas J. Miller
  • Wei‐Han Liu

Abstract

Portfolio value‐at‐risk (PVAR) is widely used in practice, but recent criticisms have focused on risks arising from biased PVAR estimates due to model specification errors and other problems. The PVAR estimation method proposed in this article combines generalized Pareto distribution tails with the empirical density function to model the marginal distributions for each asset in the portfolio, and a copula model is used to form a joint distribution from the fitted marginals. The copula–mixed distribution (CMX) approach converges in probability to the true marginal return distribution but is based on weaker assumptions that may be appropriate for the returns data found in practice. CMX is used to estimate the joint distribution of log returns for the Taiwan Stock Exchange (TSE) index and the associated futures contracts on SGX and TAIFEX. The PVAR estimates for various hedge portfolios are computed from the fitted CMX model, and backtesting diagnostics indicate that CMX outperforms the alternative PVAR estimators. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:997–1018, 2006

Suggested Citation

  • Douglas J. Miller & Wei‐Han Liu, 2006. "Improved estimation of portfolio value‐at‐risk under copula models with mixed marginals," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(10), pages 997-1018, October.
    • Handle: RePEc:wly:jfutmk:v:26:y:2006:i:10:p:997-1018
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    Cited by:

    1. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    2. Chakraborty, Sandip & Kakani, Ram Kumar & Sampath, Aravind, 2022. "Portfolio risk and stress across the business cycle," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    3. Atilgan, Yigit & Demirtas, K. Ozgur & Simsek, Koray D., 2016. "Derivative markets in emerging economies: A survey," International Review of Economics & Finance, Elsevier, vol. 42(C), pages 88-102.
    4. Nupur Moni Das & Bhabani Sankar Rout & Yashmin Khatun, 2023. "Does G7 Engross the Shock of COVID 19: An Assessment with Market Volatility?," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(4), pages 795-816, December.
    5. Ning Zhang & Yujing Gong & Xiaohan Xue, 2023. "Less disagreement, better forecasts: Adjusted risk measures in the energy futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(10), pages 1332-1372, October.
    6. Fernanda Maria Müller & Marcelo Brutti Righi, 2018. "Numerical comparison of multivariate models to forecasting risk measures," Risk Management, Palgrave Macmillan, vol. 20(1), pages 29-50, February.
    7. Ching-Chung Kuo, 2011. "Optimal assignment of resources to strengthen the weakest link in an uncertain environment," Annals of Operations Research, Springer, vol. 186(1), pages 159-173, June.
    8. Gene C. Lai & Erin P. Lu & Haijun Li & Dennis C. Chen, 2017. "Measuring insurers’ investment risk taking with asymmetric tail dependencies," Risk Management, Palgrave Macmillan, vol. 19(1), pages 1-31, February.

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