IDEAS home Printed from https://ideas.repec.org/p/aah/create/2013-52.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/13/rp13_52.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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, vol. 119(7), pages 2249-2276, July.
    4. 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, July.
    5. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    6. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    7. 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.
    8. Viktor Todorov & George Tauchen, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 356-371, July.
    9. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    10. Johannes Muhle-Karbe & Marcel Nutz, 2010. "Small-Time Asymptotics of Option Prices and First Absolute Moments," Papers 1006.2294, arXiv.org, revised Jun 2011.
    11. Todorov, Viktor & Tauchen, George, 2010. "Activity signature functions for high-frequency data analysis," Journal of Econometrics, Elsevier, vol. 154(2), pages 125-138, February.
    12. 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.
    13. 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.
    14. 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, June.
    15. repec:dau:papers:123456789/1392 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Robert Davies & George Tauchen, 2018. "Data-Driven Jump Detection Thresholds for Application in Jump Regressions," Econometrics, MDPI, vol. 6(2), pages 1-25, March.
    2. Hounyo, Ulrich & Varneskov, Rasmus T., 2020. "Inference for local distributions at high sampling frequencies: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 215(1), pages 1-34.
    3. Chang, Chia-Lin & McAleer, Michael, 2015. "Econometric analysis of financial derivatives: An overview," Journal of Econometrics, Elsevier, vol. 187(2), pages 403-407.
    4. Zhenzhen Fan & Juan M. Londono & Xiao Xiao, 2019. "US Equity Tail Risk and Currency Risk Premia," International Finance Discussion Papers 1253, Board of Governors of the Federal Reserve System (U.S.).
    5. 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.
    6. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.
    7. Ronald Gallant, A. & Tauchen, George, 2018. "Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale," Journal of Econometrics, Elsevier, vol. 205(1), pages 140-155.
    8. 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.
    9. Fan, Zhenzhen & Londono, Juan M. & Xiao, Xiao, 2022. "Equity tail risk and currency risk premiums," Journal of Financial Economics, Elsevier, vol. 143(1), pages 484-503.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    2. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
    3. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    4. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2011. "Realized Laplace transforms for estimation of jump diffusive volatility models," Journal of Econometrics, Elsevier, vol. 164(2), pages 367-381, October.
    5. Caporin, Massimiliano & Kolokolov, Aleksey & Renò, Roberto, 2017. "Systemic co-jumps," Journal of Financial Economics, Elsevier, vol. 126(3), pages 563-591.
    6. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    7. Massimiliano Caporin & Aleksey Kolokolov & Roberto RenoÕ, 2014. "Multi-jumps," "Marco Fanno" Working Papers 0185, Dipartimento di Scienze Economiche "Marco Fanno".
      • Caporin, Massimiliano & Kolokolov, Aleksey & Renò, Roberto, 2014. "Multi-jumps," MPRA Paper 58175, University Library of Munich, Germany.
    8. Pierre Bajgrowicz & Olivier Scaillet & Adrien Treccani, 2016. "Jumps in High-Frequency Data: Spurious Detections, Dynamics, and News," Management Science, INFORMS, vol. 62(8), pages 2198-2217, August.
    9. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
    10. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S., 2020. "High-frequency jump tests: Which test should we use?," Journal of Econometrics, Elsevier, vol. 219(2), pages 478-487.
    11. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    12. Yi-Ting Chen & Wan-Ni Lai & Edward W. Sun, 2019. "Jump Detection and Noise Separation by a Singular Wavelet Method for Predictive Analytics of High-Frequency Data," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 809-844, August.
    13. Zhou, Haigang & Zhu, John Qi, 2019. "Firm characteristics and jump dynamics in stock prices around earnings announcements," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    14. Filip Žikeš & Jozef Baruník, 2016. "Semi-parametric Conditional Quantile Models for Financial Returns and Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 185-226.
    15. Xin Zhang & Donggyu Kim & Yazhen Wang, 2016. "Jump Variation Estimation with Noisy High Frequency Financial Data via Wavelets," Econometrics, MDPI, vol. 4(3), pages 1-26, August.
    16. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2017. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    17. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    18. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Econometric modeling of exchange rate volatility and jumps," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 16, pages 373-427, Edward Elgar Publishing.
    19. Bollerslev, Tim & Todorov, Viktor, 2014. "Time-varying jump tails," Journal of Econometrics, Elsevier, vol. 183(2), pages 168-180.
    20. Christensen, Kim & Oomen, Roel & Podolskij, Mark, 2010. "Realised quantile-based estimation of the integrated variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 74-98, November.

    More about this item

    Keywords

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

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2013-52. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.