IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1311.5036.html
   My bibliography  Save this paper

Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data

Author

Listed:
  • Kyungsub Lee

Abstract

We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S\&P 500 index high frequency data, the realized versions of the moment variations is used for the estimation of a stochastic volatility model. We propose a simple estimation method of a stochastic volatility model using the sample averages of the variations and ARMA estimation. In addition, we compare the results with a generalized method of moments estimation based on the successive relation between realized moments and their lagged values.

Suggested Citation

  • Kyungsub Lee, 2013. "Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data," Papers 1311.5036, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1311.5036
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1311.5036
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    2. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    3. 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.
    4. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    5. Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
    6. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, September.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Anthony Neuberger, 2012. "Realized Skewness," The Review of Financial Studies, Society for Financial Studies, vol. 25(11), pages 3423-3455.
    10. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    11. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    12. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
    13. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    14. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    15. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Oxford University Press, vol. 3(3), pages 399-421.
    16. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    17. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    18. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    19. Leon, Angel & Rubio, Gonzalo & Serna, Gregorio, 2005. "Autoregresive conditional volatility, skewness and kurtosis," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 599-618, September.
    20. Roman Kozhan & Anthony Neuberger & Paul Schneider, 2013. "The Skew Risk Premium in the Equity Index Market," The Review of Financial Studies, Society for Financial Studies, vol. 26(9), pages 2174-2203.
    21. 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.
    22. Geon Ho Choe & Kyungsub Lee, 2013. "High moment variations and their application," Papers 1311.4973, arXiv.org.
    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. Kyungsub Lee & Byoung Ki Seo, 2017. "Performance of Tail Hedged Portfolio with Third Moment Variation Swap," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 447-471, October.

    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. Geon Ho Choe & Kyungsub Lee, 2013. "High moment variations and their application," Papers 1311.4973, arXiv.org.
    2. Kyungsub Lee & Byoung Ki Seo, 2017. "Performance of Tail Hedged Portfolio with Third Moment Variation Swap," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 447-471, October.
    3. Lee Kyungsub, 2016. "Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(1), pages 19-36, February.
    4. Bruno Feunou & Mohammad R. Jahan-Parvar & Roméo Tédongap, 2016. "Which parametric model for conditional skewness?," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1237-1271, October.
    5. Chang, Bo Young & Christoffersen, Peter & Jacobs, Kris, 2013. "Market skewness risk and the cross section of stock returns," Journal of Financial Economics, Elsevier, vol. 107(1), pages 46-68.
    6. Lim, Kian Guan & Chen, Ying & Yap, Nelson K.L., 2019. "Intraday information from S&P 500 Index futures options," Journal of Financial Markets, Elsevier, vol. 42(C), pages 29-55.
    7. Amaya, Diego & Christoffersen, Peter & Jacobs, Kris & Vasquez, Aurelio, 2015. "Does realized skewness predict the cross-section of equity returns?," Journal of Financial Economics, Elsevier, vol. 118(1), pages 135-167.
    8. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    9. Prosper Dovonon, 2013. "Conditionally Heteroskedastic Factor Models With Skewness And Leverage Effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1110-1137, November.
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    11. DeMiguel, Victor & Plyakha, Yuliya & Uppal, Raman & Vilkov, Grigory, 2013. "Improving Portfolio Selection Using Option-Implied Volatility and Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(6), pages 1813-1845, December.
    12. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    13. Yang (Greg) Hou & Mark Holmes, 2020. "Do higher order moments of return distribution provide better decisions in minimum-variance hedging? Evidence from US stock index futures," Australian Journal of Management, Australian School of Business, vol. 45(2), pages 240-265, May.
    14. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
    15. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 154-183.
    16. Sylvia J. Soltyk & Felix Chan, 2023. "Modeling time‐varying higher‐order conditional moments: A survey," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 33-57, February.
    17. Bruno Feunou & Mohammad R Jahan-Parvar & Cédric Okou, 2018. "Downside Variance Risk Premium," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 341-383.
    18. Yoann Potiron & Per Mykland, 2020. "Local Parametric Estimation in High Frequency Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 679-692, July.
    19. Lin, Yuehao & Lehnert, Thorsten & Wolff, Christian, 2019. "Skewness risk premium: Theory and empirical evidence," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 174-185.
    20. Hou, Yang & Holmes, Mark, 2017. "On the effects of static and autoregressive conditional higher order moments on dynamic optimal hedging," MPRA Paper 82000, University Library of Munich, Germany.

    More about this item

    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:arx:papers:1311.5036. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.