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Estimating value-at-risk and expected shortfall using the intraday low and range data

Taylor, James and Meng, Xiaochun Estimating value-at-risk and expected shortfall using the intraday low and range data. European Journal of Operational Research. (Accepted)

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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.

Item Type: Article
Keywords: management science, finance, value -at-risk, expected shortfall, intraday low, joint scoring functions
Subject(s): Management science
Date Deposited: 17 Jul 2019 13:22
Last Modified: 17 Jul 2019 13:22
Funders: n/a

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