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A confidence-based model for asset and derivative prices in the BitCoin market

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  • Alessandra Cretarola
  • Gianna Fig`a-Talamanca

Abstract

We endorse the idea, suggested in recent literature, that BitCoin prices are influenced by sentiment and confidence about the underlying technology; as a consequence, an excitement about the BitCoin system may propagate to BitCoin prices causing a Bubble effect, the presence of which is documented in several papers about the cryptocurrency. In this paper we develop a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as the behavior of a second factor affecting the price itself, which we name confidence indicator. The two dynamics are possibly correlated and we also take into account a delay between the confidence indicator and its delivered effect on the BitCoin price. Statistical properties of the suggested model are investigated and its arbitrage-free property is shown. Further, based on risk-neutral evaluation, a quasi-closed formula is derived for European style derivatives on the BitCoin. A short numerical application is finally provided.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1702.00215
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    Cited by:

    1. Wolfgang Karl Härdle & Campbell R Harvey & Raphael C G Reule, 2020. "Understanding Cryptocurrencies," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 181-208.
    2. Fabian Woebbeking, 2021. "Cryptocurrency volatility markets," Digital Finance, Springer, vol. 3(3), pages 273-298, December.
    3. 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.
    4. Panagiotidis, Theodore & Stengos, Thanasis & Vravosinos, Orestis, 2019. "The effects of markets, uncertainty and search intensity on bitcoin returns," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 220-242.
    5. Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2019. "Advanced model calibration on bitcoin options," Digital Finance, Springer, vol. 1(1), pages 117-137, November.
    6. Wolfgang Karl Hardle & Campbell R. Harvey & Raphael C. G. Reule, 2020. "Editorial: Understanding Cryptocurrencies," Papers 2007.14702, arXiv.org.

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