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A New Approach for Using Lévy Processes for Determining High‐Frequency Value‐at‐Risk Predictions

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  • Wei Sun
  • Svetlozar Rachev
  • Frank J. Fabozzi

Abstract

A new approach for using Lévy processes to compute value‐at‐risk (VaR) using high‐frequency data is presented in this paper. The approach is a parametric model using an ARMA(1,1)‐GARCH(1,1) model where the tail events are modelled using fractional Lévy stable noise and Lévy stable distribution. Using high‐frequency data for the German DAX Index, the VaR estimates from this approach are compared to those of a standard nonparametric estimation method that captures the empirical distribution function, and with models where tail events are modelled using Gaussian distribution and fractional Gaussian noise. The results suggest that the proposed parametric approach yields superior predictive performance.

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  • Wei Sun & Svetlozar Rachev & Frank J. Fabozzi, 2009. "A New Approach for Using Lévy Processes for Determining High‐Frequency Value‐at‐Risk Predictions," European Financial Management, European Financial Management Association, vol. 15(2), pages 340-361, March.
    • Handle: RePEc:bla:eufman:v:15:y:2009:i:2:p:340-361
    DOI: 10.1111/j.1468-036X.2008.00467.x
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    2. Batten, Jonathan A. & Kinateder, Harald & Wagner, Niklas, 2014. "Multifractality and value-at-risk forecasting of exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 71-81.
    3. Edward W. Sun & Yu-Jen Wang & Min-Teh Yu, 2018. "Integrated Portfolio Risk Measure: Estimation and Asymptotics of Multivariate Geometric Quantiles," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 627-652, August.
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    5. Yi-Ting Chen & Edward W. Sun & Min-Teh Yu, 2018. "Risk Assessment with Wavelet Feature Engineering for High-Frequency Portfolio Trading," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 653-684, August.
    6. Lin, Edward M.H. & Sun, Edward W. & Yu, Min-Teh, 2020. "Behavioral data-driven analysis with Bayesian method for risk management of financial services," International Journal of Production Economics, Elsevier, vol. 228(C).
    7. Yi-Ting Chen & Edward W. Sun & Yi-Bing Lin, 2019. "Coherent quality management for big data systems: a dynamic approach for stochastic time consistency," Annals of Operations Research, Springer, vol. 277(1), pages 3-32, June.
    8. Andrés García Mirantes & Javier Población & Gregorio Serna, 2012. "The Stochastic Seasonal Behaviour of Natural Gas Prices," European Financial Management, European Financial Management Association, vol. 18(3), pages 410-443, June.
    9. Bertrand Groslambert & Devraj Basu & Wan Ni Lai, 2019. "Is tail risk the missing link between institutions and risk?," Economics Bulletin, AccessEcon, vol. 39(2), pages 1435-1448.

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