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The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation

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  • Simon Lalancette
  • Jean†Guy Simonato

Abstract

The CBOE VIX index is a widely recognised benchmark measure of expected stock market volatility. As shown in the literature, probability distributions other than Gaussian are key features required to describe the dynamics of the S&P 500, the variable that ultimately determines the VIX index level. As such, it is important to assess if deviations from the Gaussian distribution have important impacts on the VIX index level. We examine herein how a model articulated over a time†varying non†Gaussian distribution with conditional skewness and kurtosis can contribute to the overall explanation of the VIX dynamics.

Suggested Citation

  • Simon Lalancette & Jean†Guy Simonato, 2017. "The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation," European Financial Management, European Financial Management Association, vol. 23(2), pages 325-354, March.
    • Handle: RePEc:bla:eufman:v:23:y:2017:i:2:p:325-354
    DOI: 10.1111/eufm.12096
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    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Becker, Ralf & Clements, Adam E. & McClelland, Andrew, 2009. "The jump component of S&P 500 volatility and the VIX index," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1033-1038, June.
    4. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    5. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
    6. Jeff Fleming & Chris Kirby, 2003. "A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 1(3), pages 365-419.
    7. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, Department of Economics and Business Economics, Aarhus University.
    8. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    9. Kanniainen, Juho & Lin, Binghuan & Yang, Hanxue, 2014. "Estimating and using GARCH models with VIX data for option valuation," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 200-211.
    10. Yingzi Zhu & Jin E. Zhang, 2007. "Variance Term Structure And Vix Futures Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 111-127.
    11. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    12. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    13. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    14. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
    15. Duan, Jin-Chuan & Yeh, Chung-Ying, 2010. "Jump and volatility risk premiums implied by VIX," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2232-2244, November.
    16. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-317, July.
    17. K. Hsieh & P. Ritchken, 2005. "An empirical comparison of GARCH option pricing models," Review of Derivatives Research, Springer, vol. 8(3), pages 129-150, December.
    18. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 399-421.
    19. Kaeck, Andreas & Alexander, Carol, 2012. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 3110-3121.
    20. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    21. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    22. Dimitris Psychoyios & George Skiadopoulos, 2006. "Volatility options: Hedging effectiveness, pricing, and model error," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(1), pages 1-31, January.
    23. Markku Lanne & Saikkonen Pentti, 2007. "Modeling Conditional Skewness in Stock Returns," The European Journal of Finance, Taylor & Francis Journals, vol. 13(8), pages 691-704.
    24. Jinji Hao & Jin E. Zhang, 2013. "GARCH Option Pricing Models, the CBOE VIX, and Variance Risk Premium," Journal of Financial Econometrics, Oxford University Press, vol. 11(3), pages 556-580, June.
    25. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
    26. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    27. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    28. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    29. Jean-Guy Simonato & Lars Stentoft, 2015. "Which pricing approach for options under GARCH with non-normal innovations?," CREATES Research Papers 2015-32, Department of Economics and Business Economics, Aarhus University.
    30. Dotsis, George & Psychoyios, Dimitris & Skiadopoulos, George, 2007. "An empirical comparison of continuous-time models of implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3584-3603, December.
    31. Gonzalez-Perez, Maria T., 2015. "Model-free volatility indexes in the financial literature: A review," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 141-159.
    32. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
    33. Kaeck, Andreas & Alexander, Carol, 2013. "Continuous-time VIX dynamics: On the role of stochastic volatility of volatility," International Review of Financial Analysis, Elsevier, vol. 28(C), pages 46-56.
    34. Jen S. Shang & Pandu R. Tadikamalla, 2004. "Modeling Financial Series Distributions: A Versatile Data Fitting Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 231-251.
    35. Pierre Collin-Dufresn & Robert S. Goldstein & J. Spencer Martin, 2001. "The Determinants of Credit Spread Changes," Journal of Finance, American Finance Association, vol. 56(6), pages 2177-2207, December.
    36. Simonato, Jean-Guy, 2012. "GARCH processes with skewed and leptokurtic innovations: Revisiting the Johnson Su case," Finance Research Letters, Elsevier, vol. 9(4), pages 213-219.
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    3. Ouandlous, Arav & Barkoulas, John T. & Alhaj-Yaseen, Yaseen, 2018. "Persistence and discontinuity in the VIX dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 333-344.
    4. León, Ángel & Ñíguez, Trino-Manuel, 2020. "Modeling asset returns under time-varying semi-nonparametric distributions," Journal of Banking & Finance, Elsevier, vol. 118(C).
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    8. Qiao, Gaoxiu & Yang, Jiyu & Li, Weiping, 2020. "VIX forecasting based on GARCH-type model with observable dynamic jumps: A new perspective," The North American Journal of Economics and Finance, Elsevier, vol. 53(C).
    9. León, Ángel & Ñíguez, Trino-Manuel, 2021. "The transformed Gram Charlier distribution: Parametric properties and financial risk applications," Journal of Empirical Finance, Elsevier, vol. 63(C), pages 323-349.

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