Several Extended CAViaR Models and Their Applications to the VaR Forecasting of the Security Markets

Xiaorong Yang; Chun He; Jie Chen

doi:10.20965/jaciii.2016.p0590

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JACIII Vol.20 No.4 pp. 590-596

doi: 10.20965/jaciii.2016.p0590

(2016)

Paper:

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Several Extended CAViaR Models and Their Applications to the VaR Forecasting of the Security Markets

Xiaorong Yang, Chun He, and Jie Chen

College of Statistics & Mathematics, Zhejiang Gongshang University
Hangzhou 310018, China

Received:

January 18, 2016

Accepted:

April 21, 2016

Published:

July 19, 2016

Keywords:

CAViaR, VaR, conditional quantile, volatility

Abstract

The conditional autoregressive Value-at-Risk (CAViaR) model, as a conditional autoregressive specification for calculating the Value-at-Risk (VaR) of the security market, has been receiving more and more attentions in recent years. As asymmetry may have a significant influence on the markets and the returns may have an autoregressive mean, this study proposes some extended CAViaR models, including asymmetric indirect threshold autoregressive conditional heteroskedasticity (TARCH) model and indirect generalized autoregressive conditional heteroskedasticity (GARCH) model with an autoregressive mean. We also present two types of CAViaR-Volatility models by adding the volatility term as an exogenous explanatory variable. Our empirical results indicate that extended models perform more effectively on out-of-sample predictions, as both forecasting effect and model stability have been improved. In addition, we find that the forecasting effect is better at the lower quantile (1%) than at the higher quantile (5%); a possible explanation is that extreme market information has more impact on VaR. In addition, there is negative correlation between volatility and VaR; VaR decreases as volatility increases.

Cite this article as:

X. Yang, C. He, and J. Chen, “Several Extended CAViaR Models and Their Applications to the VaR Forecasting of the Security Markets,” J. Adv. Comput. Intell. Intell. Inform., Vol.20 No.4, pp. 590-596, 2016.

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References

[1] Basel Committee on Banking Supervison (BCBS), Basel I: Market Risk Amendment to the Capital Accord, Bank for Int. Settlements, 1996.
[2] R. F. Engle and S. Manganelli, “CAViaR: Conditional autoregressive value at risk byregression quantiles,” J. of Business & Economoc Statistics. Vol.22, No.4: pp. 367-381 2004.
[3] X. Wang and X. Song, “Measure Market Risk Based on Bayesian Quantile Regression Model,” J. of System and Management, Vol.18, No.1, 2009.
[4] D. Huang, B. Yu, Z. Lu, F. J. Fabozzi, S. Focardi, and M. Fukushima, “Index-exciting CAViaR: A new empirical time-varying risk model,” Studies in Nonlinear Dynamics & Econometrics, Vol.14, No.2, pp. 1-27, 2010.
[5] C. W. S. Chen, R. Gerlach, B. B. K. Hwang, and M. McAleer, “Forecasting value-at-risk using nonlinear regression quantiles and intra-day range,” Department of Economics and Finance College of Business and Economics University of Canterbury, Private Bag 4800, Christchurch, New Zealand, Working paper, 2011.
[6] J. Schaumburg, “Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory,” Computational Statistics and Data Analysis, Vol.56, pp. 4081-4096, 2012.
[7] K. Kuester, S. Mittnik, and M. S. Paolella, “Value-at-risk prediction: A comparison of alternative strategies,” J. of Financial Econometrics, Vol.4, pp. 53-89, 2006.
[8] J. Zakoian, “Threshold heteroskedastic models,” J. of Economic Dynamicsand Control, Vol.18, No.5, pp. 931-955 1994.
[9] R. Koenker, and J. G. Bassett, “Regression quantiles, Econometrica” J. of the Econometric Society, pp. 33-50 1978.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] Basel Committee on Banking Supervison (BCBS), Basel I: Market Risk Amendment to the Capital Accord, Bank for Int. Settlements, 1996.

[2] [2] R. F. Engle and S. Manganelli, “CAViaR: Conditional autoregressive value at risk byregression quantiles,” J. of Business & Economoc Statistics. Vol.22, No.4: pp. 367-381 2004.

[3] [3] X. Wang and X. Song, “Measure Market Risk Based on Bayesian Quantile Regression Model,” J. of System and Management, Vol.18, No.1, 2009.

[4] [4] D. Huang, B. Yu, Z. Lu, F. J. Fabozzi, S. Focardi, and M. Fukushima, “Index-exciting CAViaR: A new empirical time-varying risk model,” Studies in Nonlinear Dynamics & Econometrics, Vol.14, No.2, pp. 1-27, 2010.

[5] [5] C. W. S. Chen, R. Gerlach, B. B. K. Hwang, and M. McAleer, “Forecasting value-at-risk using nonlinear regression quantiles and intra-day range,” Department of Economics and Finance College of Business and Economics University of Canterbury, Private Bag 4800, Christchurch, New Zealand, Working paper, 2011.

[6] [6] J. Schaumburg, “Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory,” Computational Statistics and Data Analysis, Vol.56, pp. 4081-4096, 2012.

[7] [7] K. Kuester, S. Mittnik, and M. S. Paolella, “Value-at-risk prediction: A comparison of alternative strategies,” J. of Financial Econometrics, Vol.4, pp. 53-89, 2006.

[8] [8] J. Zakoian, “Threshold heteroskedastic models,” J. of Economic Dynamicsand Control, Vol.18, No.5, pp. 931-955 1994.

[9] [9] R. Koenker, and J. G. Bassett, “Regression quantiles, Econometrica” J. of the Econometric Society, pp. 33-50 1978.