IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v146y2023ics0378426622002989.html
   My bibliography  Save this article

GARCH option pricing with volatility derivatives

Author

Listed:
  • Oh, Dong Hwan
  • Park, Yang-Ho

Abstract

This paper studies benefits of joint estimations for GARCH option pricing that utilize both stock returns and volatility derivatives. The proposed estimations not only provide realistic volatility term structures but also generate flat skewness term structures much like those seen in the S&P 500 index (SPX) options data. In particular, the estimated GARCH models yield a highly persistent volatility component, which allows the leverage effect to hold up until long horizons. Such a persistent volatility component is key to modeling long-term tail risk and pricing long-term put options. Overall, our exercise highlights the usefulness of volatility derivatives in GARCH option valuation.

Suggested Citation

  • Oh, Dong Hwan & Park, Yang-Ho, 2023. "GARCH option pricing with volatility derivatives," Journal of Banking & Finance, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:jbfina:v:146:y:2023:i:c:s0378426622002989
    DOI: 10.1016/j.jbankfin.2022.106718
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426622002989
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2022.106718?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    2. Park, Yang-Ho, 2020. "Variance disparity and market frictions," Journal of Econometrics, Elsevier, vol. 214(2), pages 326-348.
    3. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    4. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    5. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    6. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    7. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    8. 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.
    9. 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.
    10. 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.
    11. Amengual, Dante & Xiu, Dacheng, 2018. "Resolution of policy uncertainty and sudden declines in volatility," Journal of Econometrics, Elsevier, vol. 203(2), pages 297-315.
    12. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    13. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
    14. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    15. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    16. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    17. Torben G. Andersen & Oleg Bondarenko & Maria T. Gonzalez-Perez, 2015. "Exploring Return Dynamics via Corridor Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 28(10), pages 2902-2945.
    18. Giovanni Barone Adesi & Robert F. Engle & Loriano Mancini, 2014. "A GARCH Option Pricing Model with Filtered Historical Simulation," Palgrave Macmillan Books, in: Giovanni Barone Adesi (ed.), Simulating Security Returns: A Filtered Historical Simulation Approach, chapter 4, pages 66-108, Palgrave Macmillan.
    19. Aït-Sahalia, Yacine & Amengual, Dante & Manresa, Elena, 2015. "Market-based estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 187(2), pages 418-435.
    20. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    21. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
    22. 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.
    23. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
    24. Pacati, Claudio & Pompa, Gabriele & Renò, Roberto, 2018. "Smiling twice: The Heston++ model," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 185-206.
    25. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
    26. Egloff, Daniel & Leippold, Markus & Wu, Liuren, 2010. "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(5), pages 1279-1310, October.
    27. Aït-Sahalia, Yacine & Karaman, Mustafa & Mancini, Loriano, 2020. "The term structure of equity and variance risk premia," Journal of Econometrics, Elsevier, vol. 219(2), pages 204-230.
    28. 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.
    29. 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.
    30. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    31. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    32. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    33. Majewski, Adam A. & Bormetti, Giacomo & Corsi, Fulvio, 2015. "Smile from the past: A general option pricing framework with multiple volatility and leverage components," Journal of Econometrics, Elsevier, vol. 187(2), pages 521-531.
    34. Tianyi Wang & Yiwen Shen & Yueting Jiang & Zhuo Huang, 2017. "Pricing the CBOE VIX Futures with the Heston–Nandi GARCH Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(7), pages 641-659, July.
    35. 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.
    36. Song‐Ping Zhu & Guang‐Hua Lian, 2012. "An analytical formula for VIX futures and its applications," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(2), pages 166-190, February.
    37. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    38. Papantonis, Ioannis, 2016. "Volatility risk premium implications of GARCH option pricing models," Economic Modelling, Elsevier, vol. 58(C), pages 104-115.
    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. Sharif Mozumder & Bakhtear Talukdar & M. Humayun Kabir & Bingxin Li, 2024. "Non-linear volatility with normal inverse Gaussian innovations: ad-hoc analytic option pricing," Review of Quantitative Finance and Accounting, Springer, vol. 62(1), pages 97-133, January.
    2. Wu, Xinyu & Zhao, An & Liu, Li, 2023. "Forecasting VIX using two-component realized EGARCH model," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).

    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. Wang, Qi & Wang, Zerong, 2020. "VIX valuation and its futures pricing through a generalized affine realized volatility model with hidden components and jump," Journal of Banking & Finance, Elsevier, vol. 116(C).
    2. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.
    3. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    4. Zhuo Huang & Chen Tong & Tianyi Wang, 2019. "VIX term structure and VIX futures pricing with realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 72-93, January.
    5. Wenjun Zhang & Jin E. Zhang, 2020. "GARCH Option Pricing Models and the Variance Risk Premium," JRFM, MDPI, vol. 13(3), pages 1-21, March.
    6. Huang, Hung-Hsi & Lin, Shin-Hung & Wang, Chiu-Ping, 2019. "Reasonable evaluation of VIX options for the Taiwan stock index," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 111-130.
    7. Papantonis, Ioannis, 2016. "Volatility risk premium implications of GARCH option pricing models," Economic Modelling, Elsevier, vol. 58(C), pages 104-115.
    8. Cheng, Hung-Wen & Chang, Li-Han & Lo, Chien-Ling & Tsai, Jeffrey Tzuhao, 2023. "Empirical performance of component GARCH models in pricing VIX term structure and VIX futures," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 122-142.
    9. Pacati, Claudio & Pompa, Gabriele & Renò, Roberto, 2018. "Smiling twice: The Heston++ model," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 185-206.
    10. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    11. Yoo, Eun Gyu & Yoon, Sun-Joong, 2020. "CBOE VIX and Jump-GARCH option pricing models," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 839-859.
    12. Xinglin Yang & Peng Wang, 2018. "VIX futures pricing with conditional skewness," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(9), pages 1126-1151, September.
    13. 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.
    14. Peter Reinhard Hansen & Zhuo Huang & Chen Tong & Tianyi Wang, 2021. "Realized GARCH, CBOE VIX, and the Volatility Risk Premium," Papers 2112.05302, arXiv.org.
    15. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    16. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    17. Gaoxiu Qiao & Gongyue Jiang, 2023. "VIX futures pricing based on high‐frequency VIX: A hybrid approach combining SVR with parametric models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(9), pages 1238-1260, September.
    18. Gang Li & Chu Zhang, 2010. "On the Number of State Variables in Options Pricing," Management Science, INFORMS, vol. 56(11), pages 2058-2075, November.
    19. Amengual, Dante & Xiu, Dacheng, 2018. "Resolution of policy uncertainty and sudden declines in volatility," Journal of Econometrics, Elsevier, vol. 203(2), pages 297-315.
    20. 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).

    More about this item

    Keywords

    GARCH; Option valuation; VIX Derivatives; Volatility persistence;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:eee:jbfina:v:146:y:2023:i:c:s0378426622002989. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jbf .

    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.