Estimating and evaluating Value‐at‐Risk forecasts based on realized variance: empirical evidence from ICE Brent Crude oil futures

• Author: Erik Haugom,Gudbrand Lien,Steinar Veka,Sjur Westgaard
• Published date: 01 December 2014
• DOI: http://doi.org/10.1111/opec.12024
• Date: 01 December 2014

Estimating and evaluating Value-at-Risk

forecasts based on realized variance:

empirical evidence from ICE Brent Crude

oil futures

Erik Haugom,*,** Steinar Veka,***,**** Gudbrand Lien***** and

Sjur Westgaard******

*Associate Professor, Faculty of Economics and Organization Science, Lillehammer University College,

NO-2624 Lillehammer, Norway. Email: erik.haugom@hil.no

**Postdoctoral Student, Department of Industrial Economics and TechnologyManagement, Norwegian

University of Science and Technology,NO-7491 Trondheim, Norway. Email: erik.haugom@hil.no

***PhD Student, Faculty of Economics and Organization Science, Lillehammer University College,

NO-2624 Lillehammer, Norway

****PhD Student, Department of Industrial Economics and TechnologyManagement, Norwegian

University of Science and Technology,NO-7491 Trondheim, Norway

*****Professor, Faculty of Economics and Organization Science, Lillehammer University College,

NO-2624 Lillehammer, Norway

******Professor, Department of Industrial Economics and TechnologyManagement, Norwegian

University of Science and Technology,NO-7491 Trondheim, Norway

Abstract

This paper is the first to use the concept of realized volatility to forecastValue-at-Risk (VaR)for ICE

Brent Crude oil futures. We examine sensitivities in the VaR forecasts across intra-dailysampling

frequency used to calculate realized volatility.We evaluatethe VaR forecasts using Christoffersen’s

test for conditional coverage on quantiles of particular interest. Additionally, we examine a

percentile–percentile plot of the VaRforecasts for all percentiles. The main empirical results show

that very good VaR forecasts can be obtained using Gaussian critical values in combination with

volatility forecasts based on realized volatility.An examination of the sampling frequency suggests

that the most accurate VaR forecasts are obtained with a sampling frequency of between 1 and

10 min. This has important implications for practitioners operating in the financial oil sector.

1. Introduction

Recent advances in financial econometrics have led some researchers to argue that more

accurate volatility estimates can be obtained by using high-frequency intra-daily data

(Andersen et al., 2003).1In these cases the daily variance is calculated as the sum of a

Supplemental materials: Online appendix availableat: http://sveka.net/varoil/

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certain amount of finely sampled intra-daily squared returns. This measure has become

known as realizedvariance and is by now well established in the literature. However,while

the concept of realized variance has been studied thoroughly for many markets, the focus

on practical usage for assessing the day-by-dayexposure to risk using this high-frequency

framework has been relatively scarce, especially so in the oil sector.

Previous studies examining oil price fluctuations orValue-at-Risk (VaR) modelling for

such prices, or both, either use daily data (Giot and Laurent, 2003; Aloui, 2008; Hung

et al., 2008; Mabrouk 2011) or examine only one intra-daily sampling frequency when

using high-frequency data without doing any VaR modelling or forecasting (Wang et al.,

2008). This article extends previous work on risk calculations and forecasting within the

financial oil sector and makes several contributions.

Firstly, the paper is one of the first using the concept of realized volatility and the

Heterogenous Autoregressive (HAR) model of Corsi (2009) to forecast VaR in general,

and certainly so for oil futures trades at the ICE. Secondly,to the best of our knowledge, no

previous studies have evaluatedthe sensitivities in VaRforecasts directly across sampling

frequencies for calculating realized volatility.Thirdly, we implement a recent method by

Hansen and Lunde (2005) to calculate the variance for the wholeday when high-frequency

price data are unavailable for part of the day. This method has not been tested on energy

commodities previously. Finally, we suggest using a PP-plot approach for the evaluationof

VaRforecasts for all percentiles.

Our main results show that reliable VaR forecasts can be obtained using quantile

values from the Gaussian distribution based on accurate volatility estimates.2This

makes the proposed model easy to implement and accessible as it resembles the

RiskMetrics framework with a more sophisticated volatility estimation and a slightly

different model for prediction. However, VaR forecasts are sensitive to the choice of

sampling frequency used for calculating realized volatility.The best VaR forecasts using

the HAR-model of Corsi (2009) are obtained with a sampling frequency of between 1

and 10 min for oil futures traded at ICE. This result is important because it differs from

the optimal sampling frequency one would suggest by just examining a signature plot of

realized volatility itself.

The empirical results also show that betterVaR predictions are obtained for the whole

day compared with business hours only. This suggests that optimally combining the two

variance measures (realized variance and overnightvariance), as presented by Hansen and

Lunde (2005), provides more information about the total variation than the two variance

measures do individually.

The rest of this article is structured as follows. The next section providesa theoretical

framework ofVaR, the concept of realized variance and methods for evaluatingVaR fore-

casts. Section 3 describes the data and presents some preliminary analyses. Section 4 pre-

sents the results, and Section 5 ends the article with some concluding remarks.

E. Haugom et al.374

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