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Option Valuation with Observable Volatility and Jump Dynamics

Author

Listed:
  • Peter Christoffersen

    (University of Toronto, Rotman School of Management and CREATES)

  • Bruno Feunou

    (Bank of Canada)

  • Yoontae Jeon

    (University of Toronto, Rotman School of Management)

Abstract
Under very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity dynamics. The volatility and jump intensity dynamics in the model are directly driven by model-free empirical measures of diffusive volatility and jump variation. Because the empirical measures are observed in discrete intervals, our option valuation model is cast in discrete time, allowing for straightforward filtering and estimation of the model. Our model belongs to the affine class enabling us to derive the conditional characteristic function so that option values can be computed rapidly without simulation. When estimated on S&P500 index options and returns the new model performs well compared with standard benchmarks.

Suggested Citation

  • Peter Christoffersen & Bruno Feunou & Yoontae Jeon, 2014. "Option Valuation with Observable Volatility and Jump Dynamics," CREATES Research Papers 2015-07, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2015-07
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    References listed on IDEAS

    as
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    Cited by:

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    2. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    3. Liu, Yi & Liu, Huifang & Zhang, Lei, 2019. "Modeling and forecasting return jumps using realized variation measures," Economic Modelling, Elsevier, vol. 76(C), pages 63-80.
    4. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    5. Pan, Zhiyuan & Shuai, Jiangyu & Liang, Zhilei & Sun, Xianchao, 2022. "Jump dynamics, spillover effect and option valuation," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    6. Chowdhury, Biplob & Jeyasreedharan, Nagaratnam, 2019. "An empirical examination of the jump and diffusion aspects of asset pricing: Japanese evidence," Working Papers 2019-02, University of Tasmania, Tasmanian School of Business and Economics.
    7. Xinglin Yang, 2018. "Good jump, bad jump, and option valuation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(9), pages 1097-1125, September.
    8. 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.
    9. 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.
    10. Fang Liang & Lingshan Du, 2024. "Option pricing with dynamic conditional skewness," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1154-1188, July.
    11. Michael L. McIntyre, 2022. "Capital structure in an option-theoretic setting," SN Business & Economics, Springer, vol. 2(8), pages 1-24, August.
    12. Biao Guo & Hai Lin, 2020. "Volatility and jump risk in option returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(11), pages 1767-1792, November.
    13. Tianyi Wang & Sicong Cheng & Fangsheng Yin & Mei Yu, 2022. "Overnight volatility, realized volatility, and option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1264-1283, July.
    14. Qiao, Gaoxiu & Ma, Xuekun & Jiang, Gongyue & Wang, Lu, 2024. "Crude oil volatility index forecasting: New evidence based on positive and negative jumps from Chinese stock market," International Review of Economics & Finance, Elsevier, vol. 92(C), pages 415-437.
    15. Juho Kanniainen & Martin Magris, 2018. "Option market (in)efficiency and implied volatility dynamics after return jumps," Papers 1810.12200, arXiv.org.
    16. Yipeng Yang & Allanus Tsoi, 2016. "A Level Set Analysis and A Nonparametric Regression on S&P 500 Daily Return," IJFS, MDPI, vol. 4(1), pages 1-24, February.
    17. Qiao, Gaoxiu & Jiang, Gongyue & Yang, Jiyu, 2022. "VIX term structure forecasting: New evidence based on the realized semi-variances," International Review of Financial Analysis, Elsevier, vol. 82(C).
    18. Gongyue Jiang & Gaoxiu Qiao & Feng Ma & Lu Wang, 2022. "Directly pricing VIX futures with observable dynamic jumps based on high‐frequency VIX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1518-1548, August.
    19. Fang Liang & Lingshan Du & Zhuo Huang, 2023. "Option pricing with overnight and intraday volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(11), pages 1576-1614, November.
    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).
    21. Dario Alitab & Giacomo Bormetti & Fulvio Corsi & Adam A. Majewski, 2019. "A realized volatility approach to option pricing with continuous and jump variance components," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 639-664, December.

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    More about this item

    Keywords

    Dynamic volatility; dynamic jumps; realized volatility; realized jumps;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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