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Option Pricing using Realized Volatility

Author

Listed:
  • Lars Stentoft

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract
In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate dynamics to be used for option pricing purposes in this framework, and we show that our model explains some of the mispricings found when using traditional option pricing models based on interdaily data. We then show explicitly that a Generalized Autoregressive Conditional Heteroskedastic model with Normal Inverse Gaussian distributed innovations is the corresponding benchmark model when only daily data is used. Finally, we perform an empirical analysis using stock options for three large American companies, and we show that in all cases our model performs significantly better than the corresponding benchmark model estimated on return data alone. Hence the paper provides evidence on the value of using high frequency data for option pricing purposes.

Suggested Citation

  • Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers 2008-13, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2008-13
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    File URL: https://repec.econ.au.dk/repec/creates/rp/08/rp08_13.pdf
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Masato Ubukata & Toshiaki Watanabe, 2014. "Pricing Nikkei 225 Options Using Realized Volatility," The Japanese Economic Review, Japanese Economic Association, vol. 65(4), pages 431-467, December.
    2. Qi Wang & Zerong Wang, 2021. "VIX futures and its closed‐form pricing through an affine GARCH model with realized variance," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(1), pages 135-156, January.
    3. Phan, Dinh Hoang Bach & Sharma, Susan Sunila & Narayan, Paresh Kumar, 2016. "Intraday volatility interaction between the crude oil and equity markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 40(C), pages 1-13.
    4. 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.
    5. Masato Ubukata & Toshiaki Watanabe, 2013. "Pricing Nikkei 225 Options Using Realized Volatility," Global COE Hi-Stat Discussion Paper Series gd12-273, Institute of Economic Research, Hitotsubashi University.
    6. Julien Chevallier & Benoît Sévi, 2009. "On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting," Working Papers hal-04140871, HAL.
    7. repec:dau:papers:123456789/4598 is not listed on IDEAS
    8. Sergii Pypko, 2015. "Volatility Forecast in Crises and Expansions," JRFM, MDPI, vol. 8(3), pages 1-26, August.
    9. J. Piplack & M. Beine & B. Candelon, 2009. "Comovements of Returns and Volatility in International Stock Markets: A High-Frequency Approach," Working Papers 09-10, Utrecht School of Economics.
    10. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.
    11. Christoffersen, Peter & Feunou, Bruno & Jeon, Yoontae, 2015. "Option valuation with observable volatility and jump dynamics," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 101-120.
    12. Takeuchi-Nogimori, Asuka, 2017. "An Empirical Analysis of Nikkei 225 Options Using Realized GARCH Models," Economic Review, Hitotsubashi University, vol. 68(2), pages 97-113, April.
    13. Asuka Takeuchi-Nogimori, 2012. "An Empirical Analysis of the Nikkei 225 Put Options Using Realized GARCH Models," Global COE Hi-Stat Discussion Paper Series gd12-241, Institute of Economic Research, Hitotsubashi University.
    14. repec:ipg:wpaper:2014-053 is not listed on IDEAS
    15. Christoffersen, Peter & Feunou, Bruno & Jacobs, Kris & Meddahi, Nour, 2014. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(3), pages 663-697, June.
    16. Feunou, Bruno & Okou, Cédric, 2019. "Good Volatility, Bad Volatility, and Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 54(2), pages 695-727, April.
    17. Sévi, Benoît, 2014. "Forecasting the volatility of crude oil futures using intraday data," European Journal of Operational Research, Elsevier, vol. 235(3), pages 643-659.
    18. Ubukata, Masato & Watanabe, Toshiaki, 2015. "Evaluating the performance of futures hedging using multivariate realized volatility," Journal of the Japanese and International Economies, Elsevier, vol. 38(C), pages 148-171.
    19. Contreras, Javier & Rodríguez, Yeny E., 2014. "GARCH-based put option valuation to maximize benefit of wind investors," Applied Energy, Elsevier, vol. 136(C), pages 259-268.
    20. Allen, David E. & McAleer, Michael & Scharth, Marcel, 2011. "Monte Carlo option pricing with asymmetric realized volatility dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1247-1256.
    21. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.
    22. Harry Vander Elst & David Veredas, 2017. "Smoothing it Out: Empirical and Simulation Results for Disentangled Realized Covariances," Journal of Financial Econometrics, Oxford University Press, vol. 15(1), pages 106-138.
    23. Yow-Jen Jou & Chih-Wei Wang & Wan-Chien Chiu, 2013. "Is the realized volatility good for option pricing during the recent financial crisis?," Review of Quantitative Finance and Accounting, Springer, vol. 40(1), pages 171-188, January.

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    More about this item

    Keywords

    Option Pricing; Realized Volatility; Stochastic Volatility; GARCH;
    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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