Volatility measures and Value-at-Risk

W.F.M. Bams, G. Blanchard, T. Lehnert

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We evaluate and compare the abilities of the implied volatility and historical volatility models to provide accurate Value-at-Risk forecasts. Our empirical tests on the S&P 500, Dow Jones Industrial Average and Nasdaq 100 indices over long time series of more than 20 years of daily data indicate that an implied volatility based Value-at-Risk cannot beat, and tends to be outperformed by, a simple GJR-GARCH based Value-at-Risk. This finding is robust to the use of the likelihood ratio, the dynamic quantile test or a statistical loss function for evaluating the Value-at-Risk performance.

The poor performance of the option based Value-at-Risk is due to the volatility risk premium embedded in implied volatilities. We apply both non-parametric and parametric adjustments to correct for the negative price of the volatility risk. However, although this adjustment is effective in reducing the bias, it still does not allow the implied volatility to outperform the historical volatility models.

These results are in contrast to the volatility forecasting literature, which favors implied volatilities over the historical volatility model. We show that forecasting the volatility and forecasting a quantile of the return distribution are two different objectives. While the implied volatility is useful for the earlier objective function, it is not for the latter, due to the non-linear and regime changing dynamics of the volatility risk premium. (C) 2017 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)848-863
Number of pages16
JournalInternational Journal of Forecasting
Volume33
Issue number4
DOIs
Publication statusPublished - 2017

Fingerprint

Value at risk
Implied volatility
Volatility models
Historical volatility
Volatility risk premium
Quantile
Loss function
Nasdaq
Objective function
Return distribution
GJR-GARCH Model
Volatility risk
Volatility forecasting
Likelihood ratio
Empirical test

Keywords

  • CONDITIONAL DENSITY
  • CURRENCY VOLATILITY
  • FORECASTS
  • GARCH models
  • IMPLIED VOLATILITY
  • INFORMATION-CONTENT
  • MARKET
  • MODELS
  • OPTION PRICES
  • Option implied volatility
  • REGRESSION QUANTILES
  • Time-series
  • VARIANCE
  • Value-at-Risk
  • Volatility risk premium

Cite this

Bams, W.F.M. ; Blanchard, G. ; Lehnert, T. / Volatility measures and Value-at-Risk. In: International Journal of Forecasting. 2017 ; Vol. 33, No. 4. pp. 848-863.
@article{1e2079732e9c43c99933f8ed43a47786,
title = "Volatility measures and Value-at-Risk",
abstract = "We evaluate and compare the abilities of the implied volatility and historical volatility models to provide accurate Value-at-Risk forecasts. Our empirical tests on the S&P 500, Dow Jones Industrial Average and Nasdaq 100 indices over long time series of more than 20 years of daily data indicate that an implied volatility based Value-at-Risk cannot beat, and tends to be outperformed by, a simple GJR-GARCH based Value-at-Risk. This finding is robust to the use of the likelihood ratio, the dynamic quantile test or a statistical loss function for evaluating the Value-at-Risk performance.The poor performance of the option based Value-at-Risk is due to the volatility risk premium embedded in implied volatilities. We apply both non-parametric and parametric adjustments to correct for the negative price of the volatility risk. However, although this adjustment is effective in reducing the bias, it still does not allow the implied volatility to outperform the historical volatility models.These results are in contrast to the volatility forecasting literature, which favors implied volatilities over the historical volatility model. We show that forecasting the volatility and forecasting a quantile of the return distribution are two different objectives. While the implied volatility is useful for the earlier objective function, it is not for the latter, due to the non-linear and regime changing dynamics of the volatility risk premium. (C) 2017 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.",
keywords = "CONDITIONAL DENSITY, CURRENCY VOLATILITY, FORECASTS, GARCH models, IMPLIED VOLATILITY, INFORMATION-CONTENT, MARKET, MODELS, OPTION PRICES, Option implied volatility, REGRESSION QUANTILES, Time-series, VARIANCE, Value-at-Risk, Volatility risk premium",
author = "W.F.M. Bams and G. Blanchard and T. Lehnert",
year = "2017",
doi = "10.1016/j.ijforecast.2017.04.004",
language = "English",
volume = "33",
pages = "848--863",
journal = "International Journal of Forecasting",
issn = "0169-2070",
publisher = "Elsevier",
number = "4",

}

Volatility measures and Value-at-Risk. / Bams, W.F.M.; Blanchard, G.; Lehnert, T.

In: International Journal of Forecasting, Vol. 33, No. 4, 2017, p. 848-863.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Volatility measures and Value-at-Risk

AU - Bams, W.F.M.

AU - Blanchard, G.

AU - Lehnert, T.

PY - 2017

Y1 - 2017

N2 - We evaluate and compare the abilities of the implied volatility and historical volatility models to provide accurate Value-at-Risk forecasts. Our empirical tests on the S&P 500, Dow Jones Industrial Average and Nasdaq 100 indices over long time series of more than 20 years of daily data indicate that an implied volatility based Value-at-Risk cannot beat, and tends to be outperformed by, a simple GJR-GARCH based Value-at-Risk. This finding is robust to the use of the likelihood ratio, the dynamic quantile test or a statistical loss function for evaluating the Value-at-Risk performance.The poor performance of the option based Value-at-Risk is due to the volatility risk premium embedded in implied volatilities. We apply both non-parametric and parametric adjustments to correct for the negative price of the volatility risk. However, although this adjustment is effective in reducing the bias, it still does not allow the implied volatility to outperform the historical volatility models.These results are in contrast to the volatility forecasting literature, which favors implied volatilities over the historical volatility model. We show that forecasting the volatility and forecasting a quantile of the return distribution are two different objectives. While the implied volatility is useful for the earlier objective function, it is not for the latter, due to the non-linear and regime changing dynamics of the volatility risk premium. (C) 2017 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

AB - We evaluate and compare the abilities of the implied volatility and historical volatility models to provide accurate Value-at-Risk forecasts. Our empirical tests on the S&P 500, Dow Jones Industrial Average and Nasdaq 100 indices over long time series of more than 20 years of daily data indicate that an implied volatility based Value-at-Risk cannot beat, and tends to be outperformed by, a simple GJR-GARCH based Value-at-Risk. This finding is robust to the use of the likelihood ratio, the dynamic quantile test or a statistical loss function for evaluating the Value-at-Risk performance.The poor performance of the option based Value-at-Risk is due to the volatility risk premium embedded in implied volatilities. We apply both non-parametric and parametric adjustments to correct for the negative price of the volatility risk. However, although this adjustment is effective in reducing the bias, it still does not allow the implied volatility to outperform the historical volatility models.These results are in contrast to the volatility forecasting literature, which favors implied volatilities over the historical volatility model. We show that forecasting the volatility and forecasting a quantile of the return distribution are two different objectives. While the implied volatility is useful for the earlier objective function, it is not for the latter, due to the non-linear and regime changing dynamics of the volatility risk premium. (C) 2017 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

KW - CONDITIONAL DENSITY

KW - CURRENCY VOLATILITY

KW - FORECASTS

KW - GARCH models

KW - IMPLIED VOLATILITY

KW - INFORMATION-CONTENT

KW - MARKET

KW - MODELS

KW - OPTION PRICES

KW - Option implied volatility

KW - REGRESSION QUANTILES

KW - Time-series

KW - VARIANCE

KW - Value-at-Risk

KW - Volatility risk premium

U2 - 10.1016/j.ijforecast.2017.04.004

DO - 10.1016/j.ijforecast.2017.04.004

M3 - Article

VL - 33

SP - 848

EP - 863

JO - International Journal of Forecasting

JF - International Journal of Forecasting

SN - 0169-2070

IS - 4

ER -