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The Fine Structure of Equity-Index Option Dynamics

Author

Listed:
  • Torben G. Andersen

    () (Northwestern University and CREATES)

  • Oleg Bondarenko

    () (University of Illinois at Chicago)

  • Viktor Todorov

    () (Northwestern University and CREATES)

  • George Tauchen

    () (Duke University)

Abstract

We analyze the high-frequency dynamics of S&P 500 equity-index option prices by constructing an assortment of implied volatility measures. This allows us to infer the underlying fine structure behind the innovations in the latent state variables driving the movements of the volatility surface. In particular, we focus attention on implied volatilities covering a wide range of moneyness (strike/underlying stock price), which load differentially on the different latent state variables. We conduct a similar analysis for high-frequency observations on the VIX volatility index as well as on futures written on it. We find that the innovations in the risk-neutral intensity of the negative jumps in the S&P 500 index over small time scales are best described via non-Gaussian shocks, i.e., jumps. On the other hand, the innovations over small time scales of the diffusive volatility are best modeled as Gaussian with occasional jumps.

Suggested Citation

  • Torben G. Andersen & Oleg Bondarenko & Viktor Todorov & George Tauchen, 2013. "The Fine Structure of Equity-Index Option Dynamics," CREATES Research Papers 2013-52, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2013-52
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    References listed on IDEAS

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    1. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, pages 2249-2276.
    2. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382.
    3. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
    4. Todorov, Viktor, 2013. "Power variation from second order differences for pure jump semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2829-2850.
    5. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    6. Johannes Muhle-Karbe & Marcel Nutz, 2010. "Small-Time Asymptotics of Option Prices and First Absolute Moments," Papers 1006.2294, arXiv.org, revised Jun 2011.
    7. Todorov, Viktor & Tauchen, George, 2010. "Activity signature functions for high-frequency data analysis," Journal of Econometrics, Elsevier, vol. 154(2), pages 125-138, February.
    8. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    9. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    10. Cecilia Mancini, 2009. "Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296.
    11. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    12. Whaley, Robert E, 1986. " Valuation of American Futures Options: Theory and Empirical Tests," Journal of Finance, American Finance Association, vol. 41(1), pages 127-150, March.
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    Cited by:

    1. Chang, Chia-Lin & McAleer, Michael, 2015. "Econometric analysis of financial derivatives: An overview," Journal of Econometrics, Elsevier, vol. 187(2), pages 403-407.
    2. Chang, C-L. & McAleer, M.J., 2014. "Econometric Analysis of Financial Derivatives," Econometric Institute Research Papers EI 2015-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Hounyo, Ulrich & Varneskov, Rasmus T., 2017. "A local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation," Journal of Econometrics, Elsevier, vol. 198(1), pages 10-28.

    More about this item

    Keywords

    VPIN; high-frequency data; implied volatility; jump activity; Kolmogorov-Smirnov test; stable process; stochastic volatility; VIX index;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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