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Estimating value-at-risk via Markov switching ARCH models - an empirical study on stock index returns

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  • Ming-Yuan Leon Li
  • Hsiou-wei William Lin

Abstract

This paper estimates the Value-at-Risk (VaR) on returns of stock market indexes including Dow Jones, Nikkei, Frankfurt Commerzbank index, and FTSE via Markov Switching ARCH (SWARCH) models. It is conjectured that structural changes contribute to non-normality in stock return distributions. SWARCH models, which admit parameters based on various states to control structural changes in the estimating periods, may thus help mitigate kurtosis, tail-fatness and skewness problems in estimating VaR. Significant kurtosis and skewness in return distributions of Dow Jones, Nikkei, FCI and FTSE and significant tail-fatness (tail-thinness) in the 1% (5%) region critical probability are documented. Moreover, it is shown that the more generalized SWARCH outshines both ARCH and GARCH in capturing non-normalities with respect to both in- and out-sample VaR violation rate tests.

Suggested Citation

  • Ming-Yuan Leon Li & Hsiou-wei William Lin, 2004. "Estimating value-at-risk via Markov switching ARCH models - an empirical study on stock index returns," Applied Economics Letters, Taylor & Francis Journals, vol. 11(11), pages 679-691.
    • Handle: RePEc:taf:apeclt:v:11:y:2004:i:11:p:679-691
    DOI: 10.1080/1350485042000236539
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    5. Huang Dashan & Yu Baimin & Lu Zudi & Fabozzi Frank J. & Focardi Sergio & Fukushima Masao, 2010. "Index-Exciting CAViaR: A New Empirical Time-Varying Risk Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-26, March.
    6. Blazej Mazur & Mateusz Pipien, 2012. "On the empirical importance of periodicity in the volatility of financial time series," NBP Working Papers 124, Narodowy Bank Polski.
    7. Laura Garcia‐Jorcano & Alfonso Novales, 2021. "Volatility specifications versus probability distributions in VaR forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 189-212, March.
    8. Eduardo Roca & Victor Wong & Gurudeo Tularam, 2010. "The Market Sensitivity of Australian Superannuation Socially Responsible Investment Funds. Evidence from a Markov Regime Switching Approach," Discussion Papers in Finance finance:201012, Griffith University, Department of Accounting, Finance and Economics.
    9. John Cotter, 2005. "Extreme risk in futures contracts," Applied Economics Letters, Taylor & Francis Journals, vol. 12(8), pages 489-492.
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    11. Javier Ojea-Ferreiro, 2021. "Deconstructing Systemic Risk: A Reverse Stress Testing Approach," Springer Books, in: Marco Corazza & Manfred Gilli & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 369-375, Springer.
    12. Abdollahi, Hooman, 2020. "A novel hybrid model for forecasting crude oil price based on time series decomposition," Applied Energy, Elsevier, vol. 267(C).
    13. Panos Pouliasis & Ioannis Kyriakou & Nikos Papapostolou, 2017. "On equity risk prediction and tail spillovers," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 22(4), pages 379-393, October.
    14. Chang, Kuang-Liang, 2010. "House price dynamics, conditional higher-order moments, and density forecasts," Economic Modelling, Elsevier, vol. 27(5), pages 1029-1039, September.
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    16. Negin Entezari & José Alberto Fuinhas, 2024. "Quantifying the Impact of Risk on Market Volatility and Price: Evidence from the Wholesale Electricity Market in Portugal," Sustainability, MDPI, vol. 16(7), pages 1-21, March.
    17. Humberto Valencia-Herrera & Francisco López-Herrera, 2018. "Markov Switching International Capital Asset Pricing Model, an Emerging Market Case: Mexico," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 17(1), pages 96-129, April.
    18. Emrah İ. Çevik & Turhan Korkmaz & Erdal Atukeren, 2012. "Business confidence and stock returns in the USA: a time-varying Markov regime-switching model," Applied Financial Economics, Taylor & Francis Journals, vol. 22(4), pages 299-312, February.
    19. Venus Khim-Sen Liew & Terence Tai-leung Chong, 2005. "Autoregressive Lag Length Selection Criteria in the Presence of ARCH Errors," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-5.
    20. Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(2), pages 95-116, June.
    21. Emrah Çevik & Erdal Atukeren & Turhan Korkmaz, 2013. "Nonlinearity and nonstationarity in international art market prices: evidence from Markov-switching ADF unit root tests," Empirical Economics, Springer, vol. 45(2), pages 675-695, October.
    22. Liu, Lu, 2014. "Extreme downside risk spillover from the United States and Japan to Asia-Pacific stock markets," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 39-48.
    23. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.

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