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Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging

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  • Kuo-Shing Chen

    (Department of Accounting, Ming Chuan University, 250 Zhong Shan N. Rd., Sec. 5, Taipei 111, Taiwan)

  • Yu-Chuan Huang

    (Department of Accounting Information, College of Business, Southern Taiwan University of Science and Technology, Tainan 710, Taiwan)

Abstract

In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.

Suggested Citation

  • Kuo-Shing Chen & Yu-Chuan Huang, 2021. "Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging," Mathematics, MDPI, vol. 9(20), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2567-:d:655335
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    References listed on IDEAS

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    2. Leonardo Ieracitano Vieira & Márcio Poletti Laurini, 2023. "Time-varying higher moments in Bitcoin," Digital Finance, Springer, vol. 5(2), pages 231-260, June.
    3. Gholamreza Farahmand & Taher Lotfi & Malik Zaka Ullah & Stanford Shateyi, 2023. "Finding an Efficient Computational Solution for the Bates Partial Integro-Differential Equation Utilizing the RBF-FD Scheme," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    4. Kuo-Shing Chen, 2024. "Investigating the Impact of Financial Reporting for Cryptocurrencies on Company Value," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 14(3), pages 1-6.

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