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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. 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.
    6. Jose Manuel Corcuera & Florence Guillaume & Peter Leoni & Wim Schoutens, 2009. "Implied Levy volatility," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 383-393.
    7. Madan, Dilip B. & Smith, Robert H. & Wang, King, 2017. "Laplacian risk management," Finance Research Letters, Elsevier, vol. 22(C), pages 202-210.
    8. 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.
    9. 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.
    10. Dwyer, Gerald P., 2015. "The economics of Bitcoin and similar private digital currencies," Journal of Financial Stability, Elsevier, vol. 17(C), pages 81-91.
    11. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697.
    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. Jörg Osterrieder & Andrea Barletta, 2019. "Editorial on the Special Issue on Cryptocurrencies," Digital Finance, Springer, vol. 1(1), pages 1-4, November.
    2. Matic, Jovanka Lili & Packham, Natalie & Härdle, Wolfgang Karl, 2021. "Hedging Cryptocurrency Options," MPRA Paper 110985, University Library of Munich, Germany.
    3. Jovanka Lili Matic & Natalie Packham & Wolfgang Karl Härdle, 2023. "Hedging cryptocurrency options," Review of Derivatives Research, Springer, vol. 26(1), pages 91-133, April.
    4. Fabian Woebbeking, 2021. "Cryptocurrency volatility markets," Digital Finance, Springer, vol. 3(3), pages 273-298, December.
    5. Kujtim Avdiu, 2023. "Market Liquidity Estimation in a High-Frequency Setup," JRFM, MDPI, vol. 16(9), pages 1-26, September.
    6. Jovanka Lili Matic & Natalie Packham & Wolfgang Karl Hardle, 2021. "Hedging Cryptocurrency Options," Papers 2112.06807, arXiv.org, revised Dec 2022.
    7. 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.
    8. Pierre J. Venter & Eben Maré, 2020. "GARCH Generated Volatility Indices of Bitcoin and CRIX," JRFM, MDPI, vol. 13(6), pages 1-15, June.

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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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