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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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    References listed on IDEAS

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    1. Arturo Estrella & Darryll Hendricks & John Kambhu & Soo Shin & Stefan Walter, 1994. "Options positions: risk management and capital requirements," Research Paper 9415, Federal Reserve Bank of New York.
    2. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc.
    3. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
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    Cited by:

    1. Eduardo Roca & Victor Wong, 2008. "An analysis of the sensitivity of Australian superannuation funds to market movements: a Markov regime switching approach," Applied Financial Economics, Taylor & Francis Journals, vol. 18(7), pages 583-597.
    2. Nomikos, Nikos K. & Pouliasis, Panos K., 2011. "Forecasting petroleum futures markets volatility: The role of regimes and market conditions," Energy Economics, Elsevier, vol. 33(2), pages 321-337, March.
    3. Li, Ming-Yuan Leon, 2009. "Could the jump diffusion technique enhance the effectiveness of futures hedging models?," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3076-3088.
    4. 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.
    5. 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, Economic Research Department.
    6. 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.
    7. 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, CEJEME, vol. 4(2), pages 95-116, June.
    8. John Cotter, 2005. "Extreme risk in futures contracts," Applied Economics Letters, Taylor & Francis Journals, vol. 12(8), pages 489-492.
    9. 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.
    10. 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.
    11. 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.
    12. Chang, Kuang-Liang, 2010. "House price dynamics, conditional higher-order moments, and density forecasts," Economic Modelling, Elsevier, vol. 27(5), pages 1029-1039, September.
    13. repec:ebl:ecbull:v:3:y:2005:i:19:p:1-5 is not listed on IDEAS

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