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Value-at-Risk under Lévy GARCH models: Evidence from global stock markets

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  • Slim, Skander
  • Koubaa, Yosra
  • BenSaïda, Ahmed

Abstract

The aim of this paper is to reconsider the evidence on the forecasting ability of GARCH-type models in estimating the Value-at-Risk (VaR) of global stock market indices with improved return distribution. The performance of twenty-one VaR models that are generated by a combination of three conditional volatility specifications including GARCH, GJR and FIGARCH and seven distributional assumptions for return innovations is investigated. We implement stringent backtesting during crisis and post-crisis periods for developed, emerging and frontier markets. Results show that the skewed-t along with heavy-tailed Lévy distributions considerably improve the forecasts of one-day-ahead VaR for long and short trading positions during crisis period, regardless of the volatility model. However, we find no evidence that a given volatility specification outperforms the others across markets. The relevant models show evidence of long memory in developed markets and conditional asymmetry in frontier markets; whereas the standard GARCH is found to be the best suited specification for estimating VaR forecasts in emerging markets. The inclusion of high volatility period in the estimation sample highlights the predictability of VaR during post-crisis period, where even the normal distribution rivals the more sophisticated ones in terms of statistical accuracy and regulatory capital allocation.

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  • Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.
  • Handle: RePEc:eee:intfin:v:46:y:2017:i:c:p:30-53
    DOI: 10.1016/j.intfin.2016.08.008
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    Cited by:

    1. Sobreira, Nuno & Louro, Rui, 2020. "Evaluation of volatility models for forecasting Value-at-Risk and Expected Shortfall in the Portuguese stock market," Finance Research Letters, Elsevier, vol. 32(C).
    2. Slim, Skander & Dahmene, Meriam & Boughrara, Adel, 2020. "How informative are variance risk premium and implied volatility for Value-at-Risk prediction? International evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 22-37.
    3. Paolella, Marc S. & Polak, Paweł & Walker, Patrick S., 2019. "Regime switching dynamic correlations for asymmetric and fat-tailed conditional returns," Journal of Econometrics, Elsevier, vol. 213(2), pages 493-515.
    4. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    5. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    6. Ahmed BenSaïda & Sabri Boubaker & Duc Khuong Nguyen & Skander Slim, 2018. "Value‐at‐risk under market shifts through highly flexible models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(8), pages 790-804, December.

    More about this item

    Keywords

    Value-at-Risk; Risk management; Lévy distributions; GARCH model; Asymmetry; Long memory;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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