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Estimating Value-at-Risk and Expected Shortfall using the intraday low and range data

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  • Meng, Xiaochun
  • Taylor, James W.

Abstract

Value-at-Risk (VaR) is a popular measure of market risk. To convey information regarding potential exceedances beyond the VaR, Expected Shortfall (ES) has become the risk measure for trading book bank regulation. However, the estimation of VaR and ES is challenging, as it requires the estimation of the tail behaviour of daily returns. In this paper, we take advantage of recent research that develops joint scoring functions for VaR and ES. Using these functions, we present a novel approach to estimating the two risk measures based on intraday data. We focus on the intraday range, which is the difference between the highest and lowest intraday log prices. In contrast to intraday observations, the intraday low and high are widely available for many financial assets. To alleviate the challenge of modelling extreme risk measures, we propose the use of the intraday low series. We draw on a theoretical result for Brownian motion to show that a quantile of the daily returns can be estimated as the product of a constant term and a less extreme quantile of the intraday low returns, which we define as the difference between the lowest log price of the day and the log closing price of the previous day. In view of this, we use estimates of the VaR and ES of the intraday low returns to estimate the VaR and ES of the daily returns. We provide empirical support for the new proposals using data for five stock indices and five individual stocks.

Suggested Citation

  • Meng, Xiaochun & Taylor, James W., 2020. "Estimating Value-at-Risk and Expected Shortfall using the intraday low and range data," European Journal of Operational Research, Elsevier, vol. 280(1), pages 191-202.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:1:p:191-202
    DOI: 10.1016/j.ejor.2019.07.011
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    Citations

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    Cited by:

    1. Brenda Castillo-Brais & Ángel León & Juan Mora, 2022. "Estimating Value-at-Risk and Expected Shortfall: Do Polynomial Expansions Outperform Parametric Densities?," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    2. Mercadier, Mathieu & Strobel, Frank, 2021. "A one-sided Vysochanskii-Petunin inequality with financial applications," European Journal of Operational Research, Elsevier, vol. 295(1), pages 374-377.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. Gao, Lingbo & Ye, Wuyi & Guo, Ranran, 2022. "Jointly forecasting the value-at-risk and expected shortfall of Bitcoin with a regime-switching CAViaR model," Finance Research Letters, Elsevier, vol. 48(C).
    5. Le-Yu Chen & Yu-Min Yen, 2021. "Estimations of the Local Conditional Tail Average Treatment Effect," Papers 2109.08793, arXiv.org, revised May 2024.
    6. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    7. Fiszeder, Piotr & Fałdziński, Marcin & Molnár, Peter, 2023. "Modeling and forecasting dynamic conditional correlations with opening, high, low, and closing prices," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 308-321.
    8. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    9. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    10. Fritzsch, Simon & Timphus, Maike & Weiß, Gregor, 2024. "Marginals versus copulas: Which account for more model risk in multivariate risk forecasting?," Journal of Banking & Finance, Elsevier, vol. 158(C).
    11. Chiranjit Dutta & Kara Karpman & Sumanta Basu & Nalini Ravishanker, 2023. "Review of Statistical Approaches for Modeling High-Frequency Trading Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-48, May.
    12. Man Wang & Yihan Cheng, 2022. "Forecasting value at risk and expected shortfall using high‐frequency data of domestic and international stock markets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1595-1607, December.
    13. Md Akhtaruzzaman & Ramzi Benkraiem & Sabri Boubaker & Constantin Zopounidis, 2022. "COVID‐19 crisis and risk spillovers to developing economies: Evidence from Africa," Journal of International Development, John Wiley & Sons, Ltd., vol. 34(4), pages 898-918, May.
    14. Guanghui Cai & Zhimin Wu & Lei Peng, 2021. "Forecasting volatility with outliers in Realized GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 667-685, July.
    15. Sreekha Pullaykkodi & Rajesh H. Acharya, 2024. "The Effects of Overnight Events on Daytime Return: A Market Microstructure Analysis of Market Quality," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(3), pages 497-542, September.

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