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Advanced model calibration on bitcoin options

Author

Listed:
  • Dilip B. Madan

    (University of Maryland)

  • Sofie Reyners

    (University of Leuven)

  • Wim Schoutens

    (University of Leuven)

Abstract

In this paper, we investigate the dynamics of the bitcoin (BTC) price through the vanilla options available on the market. We calibrate a series of Markov models on the option surface. In particular, we consider the Black–Scholes model, Laplace model, five variance gamma-related models and the Heston model. We examine their pricing performance and the optimal risk-neutral model parameters over a period of 2 months. We conclude with a study of the implied liquidity of BTC call options, based on conic finance theory.

Suggested Citation

  • Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2019. "Advanced model calibration on bitcoin options," Digital Finance, Springer, vol. 1(1), pages 117-137, November.
    • Handle: RePEc:spr:digfin:v:1:y:2019:i:1:d:10.1007_s42521-019-00002-1
    DOI: 10.1007/s42521-019-00002-1
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    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. David Garcia & Claudio Juan Tessone & Pavlin Mavrodiev & Nicolas Perony, 2014. "The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy," Papers 1408.1494, arXiv.org.
    3. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    4. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    5. Jose Manuel Corcuera & Florence Guillaume & Peter Leoni & Wim Schoutens, 2009. "Implied Levy volatility," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 383-393.
    6. Madan, Dilip B. & Smith, Robert H. & Wang, King, 2017. "Laplacian risk management," Finance Research Letters, Elsevier, vol. 22(C), pages 202-210.
    7. 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.
    8. Alessandra Cretarola & Gianna Fig`a-Talamanca, 2017. "A confidence-based model for asset and derivative prices in the BitCoin market," Papers 1702.00215, arXiv.org.
    9. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697, October.
    10. 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.
    11. Dwyer, Gerald P., 2015. "The economics of Bitcoin and similar private digital currencies," Journal of Financial Stability, Elsevier, vol. 17(C), pages 81-91.
    12. Baur, Dirk G. & Hong, KiHoon & Lee, Adrian D., 2018. "Bitcoin: Medium of exchange or speculative assets?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 54(C), pages 177-189.
    13. Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Hou, Ai Jun & Wang, Weining, 2018. "Pricing Cryptocurrency options: the case of CRIX and Bitcoin," IRTG 1792 Discussion Papers 2018-004, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    14. Frode Kjærland & Aras Khazal & Erlend A. Krogstad & Frans B. G. Nordstrøm & Are Oust, 2018. "An Analysis of Bitcoin’s Price Dynamics," JRFM, MDPI, vol. 11(4), pages 1-18, October.
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    Citations

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    Cited by:

    1. Yakup Söylemez, 2019. "Cryptocurrency Derivatives: The Case of Bitcoin," Contributions to Economics, in: Umit Hacioglu (ed.), Blockchain Economics and Financial Market Innovation, chapter 0, pages 515-530, Springer.
    2. Matic, Jovanka & Packham, Natalie & Härdle, Wolfgang, 2021. "Hedging cryptocurrency options," IRTG 1792 Discussion Papers 2021-021, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Pierre J. Venter & Eben Maré, 2020. "GARCH Generated Volatility Indices of Bitcoin and CRIX," JRFM, MDPI, vol. 13(6), pages 1-15, June.
    4. Jovanka Lili Matic & Natalie Packham & Wolfgang Karl Härdle, 2023. "Hedging cryptocurrency options," Review of Derivatives Research, Springer, vol. 26(1), pages 91-133, April.
    5. Jörg Osterrieder & Andrea Barletta, 2019. "Editorial on the Special Issue on Cryptocurrencies," Digital Finance, Springer, vol. 1(1), pages 1-4, November.
    6. Kujtim Avdiu, 2023. "Market Liquidity Estimation in a High-Frequency Setup," JRFM, MDPI, vol. 16(9), pages 1-26, September.
    7. Fabian Woebbeking, 2021. "Cryptocurrency volatility markets," Digital Finance, Springer, vol. 3(3), pages 273-298, December.
    8. Jovanka Lili Matic & Natalie Packham & Wolfgang Karl Hardle, 2021. "Hedging Cryptocurrency Options," Papers 2112.06807, arXiv.org, revised Dec 2022.
    9. Boyi Li & Weixuan Xia, 2024. "Crypto Inverse-Power Options and Fractional Stochastic Volatility," Papers 2403.16006, arXiv.org, revised Sep 2024.

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    More about this item

    Keywords

    Cryptocurrency; Modelling; Bitcoin; Calibration;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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