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Applying The Local Martingale Theory Of Bubbles To Cryptocurrencies

Author

Listed:
  • SOON HYEOK CHOI

    (Nolan School of Hotel Administration, Cornell University, 537 Statler Hall, Ithaca, NY 14850, USA)

  • ROBERT A. JARROW

    (Samuel Curtis Johnson Graduate School of Management, Cornell University, 451 Sage Hall, Ithaca, NY 14850, USA3Kamakura Corporation, Honolulu, HI 96815, USA)

Abstract

Cryptocurrencies provide a natural setting to test for the existence of price bubbles using the local martingale theory of bubbles because cryptocurrencies have no cash flows. Using a robust statistical algorithm, we test for price bubbles in eight cryptocurrencies, Bitcoin (BTC), Litecoin (LTC), Ethereum (ETH), Ripple (XRP), Bitcoin Cash (BCH), EOS (EOS), Monero (XMR), and Zcash (ZEC), from 1 January 2019 to 17 July 2019. The statistical test first estimates the cryptocurrencies’ volatilities as a function of the price level. Then, these estimates are extrapolated over the positive real line using power functions. Finally, these power functions underly a sequence of hypothesis tests for price bubbles that control for both Type I and Type II errors. Five of the eight currencies (BTC, BCH, EOS, XMR, ZEC) exhibit price bubbles, LTC does not, and the evidence for ETH and XRP is inconclusive. The paper provides strong evidence for the prevalence of bubbles in cryptocurrencies.

Suggested Citation

  • Soon Hyeok Choi & Robert A. Jarrow, 2022. "Applying The Local Martingale Theory Of Bubbles To Cryptocurrencies," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 1-25, May.
    • Handle: RePEc:wsi:ijtafx:v:25:y:2022:i:03:n:s0219024922500133
    DOI: 10.1142/S0219024922500133
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    Cited by:

    1. Lin William Cong & Ke Tang & Yanxin Wang & Xi Zhao, 2023. "Inclusion and Democratization Through Web3 and DeFi? Initial Evidence from the Ethereum Ecosystem," NBER Working Papers 30949, National Bureau of Economic Research, Inc.
    2. Robert A. Jarrow & Simon S. Kwok, 2023. "An explosion time characterization of asset price bubbles," International Review of Finance, International Review of Finance Ltd., vol. 23(2), pages 469-479, June.
    3. Osband, Kent & Filoso, Valerio & Capasso, Salvatore, 2024. "The limits of limitless debt," Journal of Macroeconomics, Elsevier, vol. 79(C).

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