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

Xiaochun Meng, James W. Taylor

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28 Citations (SciVal)


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.

Original languageEnglish
Pages (from-to)191-202
Number of pages12
JournalEuropean Journal of Operational Research
Issue number1
Early online date19 Jul 2019
Publication statusPublished - 1 Jan 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


  • Expected Shortfall
  • Finance
  • Intraday low
  • Joint scoring functions
  • Value-at-Risk

ASJC Scopus subject areas

  • General Computer Science
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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