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Volatility Regimes For The Vix Index

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  • JACINTO MARABEL ROMO

    (University of Alcalá)

Abstract

This article presents a Markov chain framework to characterize the behavior of the CBOE Volatility Index (VIX index). Two possible regimes are considered: high volatility and low volatility. The specification accounts for deviations from normality and the existence of persistence in the evolution of the VIX index. Since the evolution of the VIX index seems to indicate that its conditional variance is not constant over time, I consider two different versions of the model. In the first one, the variance of the index is a function of the volatility regime, whereas the second version includes ARCH and GARCH specifications for the conditional variance of the index. The empirical results show that the model adjusts quite well to the vola - ti lity regimes corresponding to the VIX index. The information provided by the model may be a useful tool for investment decisions, as well as for hedging purposes regarding the volatility of a certain asset.

Suggested Citation

  • Jacinto Marabel Romo, 2012. "Volatility Regimes For The Vix Index," Revista de Economia Aplicada, Universidad de Zaragoza, Departamento de Estructura Economica y Economia Publica, vol. 20(2), pages 111-134, Autumn.
    • Handle: RePEc:rev:reveca:v:20:y:2012:i:2:p:111-134
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    1. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    2. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Do Call Prices and the Underlying Stock Always Move in the Same Direction?," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 549-584.
    3. Toby Daglish & John Hull & Wulin Suo, 2007. "Volatility surfaces: theory, rules of thumb, and empirical evidence," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 507-524.
    4. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February.
    5. Dueker, Michael J, 1997. "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 26-34, January.
    6. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    7. Grunbichler, Andreas & Longstaff, Francis A., 1996. "Valuing futures and options on volatility," Journal of Banking & Finance, Elsevier, vol. 20(6), pages 985-1001, July.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    10. John Y. Campbell & Albert S. Kyle, 1993. "Smart Money, Noise Trading and Stock Price Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 1-34.
    11. Jérôme Detemple & Carlton Osakwe, 2000. "The Valuation of Volatility Options," Review of Finance, European Finance Association, vol. 4(1), pages 21-50.
    12. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
    13. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
    14. Yingzi Zhu & Marco Avellaneda, 1997. "An E-ARCH model for the term structure of implied volatility of FX options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(2), pages 81-100.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    16. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    17. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    18. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    19. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    20. Franks, Julian R & Schwartz, Eduardo S, 1991. "The Stochastic Behaviour of Market Variance Implied in the Prices of Index Options," Economic Journal, Royal Economic Society, vol. 101(409), pages 1460-1475, November.
    21. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    22. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
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    Cited by:

    1. Oscar V. De la Torre-Torres & Francisco Venegas-Martínez & Mᵃ Isabel Martínez-Torre-Enciso, 2021. "Enhancing Portfolio Performance and VIX Futures Trading Timing with Markov-Switching GARCH Models," Mathematics, MDPI, vol. 9(2), pages 1-22, January.
    2. Jyothi Chittineni,, 2017. "Regime switching behavior of Indian VIX and its time dependent correlation with select developed economies," Business and Economic Horizons (BEH), Prague Development Center, vol. 13(5), pages 666-675, December.

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    More about this item

    Keywords

    VIX index; Markov chain; realized volatility; implied volatility; volatility regimes;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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