Abstract
This paper presents a new theoretical approach to analyzing the relationship between Bitcoin’s market price and its mining cost, aiming to substantiate the self-sustaining nature of Bitcoin’s security.
Previous empirical studies reveal a long-term correlation between price and cost, while shorter-term analysis often reveals significant divergences, particularly during price bubbles. The correlation between price and cost is a critical feature for the safe confirmation of transactions and suggests that the crypto asset has a fundamental value. On the other hand, divergences, which yield profit for miners, should serve as a factor that encourages organized mining operations, raising the mining cost and thereby enhancing Bitcoin’s security. Thus, Bitcoin’s security seems organically maintained by an interplay of correlation and recurring divergences. Understanding the dynamics of mining costs and the mechanism driving the correlation and divergences between price and cost is essential for comprehending Bitcoin’s security and how it is sustained.
By leveraging recursive methods in economics, this paper introduces a new theoretical model in which the rational decisions of miners determine mining costs. According to this model, the proof-of-work (PoW) mechanism combined with fluctuating Bitcoin price drives the long-term correlation and recurring divergences between price and cost. It demonstrates a rationale for the self-sustainability of Bitcoin’s security.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Brandt, M.W.: CHAPTER 5 - portfolio choice problems. In: A\(\rm \ddot{i}\)t-Sahalia, Y., Hansen, L.P. (eds.) Handbook of Financial Econometrics: Tools and Techniques, pp. 269–336. North-Holland, San Diego (2010)
Fantazzini, D., Kolodin, N.: Does the hashrate affect the bitcoin price? MPRA Paper 103812. University Library of Munich, Germany (2020)
Garcia, D., Tessone, C.J., Mavrodiev, P., Perony, N.: The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy. J. R. Soc. Interface 11(99), 20140623 (2014)
Garratt, R., van Oordt, M.: Why fixed costs matter for proof-of-work based cryptocurrencies. Staff Working Papers 20-27, Bank of Canada (2020)
Gronwald, M.: The economics of bitcoins - market characteristics and price jumps. CESifo Working Paper Series 5121, CESifo (2014)
Hayes, A.S.: Bitcoin price and its marginal cost of production: support for a fundamental value. Appl. Econ. Lett. 26(7), 554–560 (2019)
Hayes, A.S.: Cryptocurrency value formation: an empirical analysis leading to a cost of production model for valuing bitcoin. Telemat. Inform. 34, 1308–1321 (2016)
Katsiampa, P.: Volatility estimation for bitcoin: a comparison of GARCH models. Econ. Lett. 158, 3–6 (2017)
Kjærland, F., Khazal, A., Krogstad, E.A., Nordstrøm, F.B.G., Oust, A.: An analysis of bitcoin’s price dynamics. J. Risk Financ. Manage. 11(4), 63 (2018)
Kristoufek, L.: Bitcoin and its mining on the equilibrium path. Energy Econ. 85(C), 104588 (2020)
Levy, H., Markowitz, H.M.: Approximating expected utility by a function of mean and variance. Am. Econ. Rev. 69(3), 308–317 (1979)
Marthinsen, J.E., Gordon, S.R.: The price and cost of bitcoin. Q. Rev. Econ. Financ. 85, 280–288 (2022)
Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, New York (1995)
Pagnotta, E., Buraschi, A.: An equilibrium valuation of bitcoin and decentralized network assets. SSRN Electron. J. (2018)
Prat, J., Walter, B.: An equilibrium model of the market for bitcoin mining. J. Polit. Econ. 129(8), 2415–2452 (2021)
Pulley, L.B.: A general mean-variance approximation to expected utility for short holding periods. J. Financ. Quant. Anal. 16(3), 361–373 (1981)
Pulley, L.B.: Mean-variance approximations to expected logarithmic utility. Oper. Res. 31(4), 685–696 (1983)
Rosenfeld, M.: Analysis of bitcoin pooled mining reward systems (2011)
Shibuya, Y., Yamamoto, G., Kojima, F., Shi, E., Matsuo, S., Laszka, A.: Selfish mining attacks exacerbated by elastic hash supply. In: Borisov, N., Diaz, C. (eds.) FC 2021. LNCS, vol. 12675, pp. 269–276. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-662-64331-0_14
Thorp, E.O.: The kelly criterion in blackjack sports betting, and the stock market. In: Handbook of Asset and Liability Management, pp. 385–428 (2006)
Acknowledgement
Part of this study was done while I was with NTT Research. I am grateful for many discussions with Tatsuaki Okamoto on using control theory to analyze hash rate dynamics. I greatly appreciate the numerous discussions with Fuhito Kojima and Aron Laszka about the behavior of miners from a microeconomic perspective in the early stages of this research. I am also thankful for many discussions with Katsumi Takahashi from NTT Social Informatics Laboratories. Any possible faults or incomplete discussions that may be present in this paper are solely my responsibility.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 International Financial Cryptography Association
About this paper
Cite this paper
Yamamoto, G. (2024). An Intrinsic Mechanism Deciding Hash Rates from Bitcoin Price. In: Essex, A., et al. Financial Cryptography and Data Security. FC 2023 International Workshops. FC 2023. Lecture Notes in Computer Science, vol 13953. Springer, Cham. https://doi.org/10.1007/978-3-031-48806-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-48806-1_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-48805-4
Online ISBN: 978-3-031-48806-1
eBook Packages: Computer ScienceComputer Science (R0)