Applying the Local Martingale Theory of Bubbles to Cryptocurrencies

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.

An explosion time characterization of asset price bubbles

“…For a review of the local martingale theory of bubble mathematics, see Protter (2013). Recent empirical evidence provides strong support for the usefulness of this theory in practice, see Jarrow et al (2011), Obayashi et al (2017), Jarrow and Kwok (2021), and Choi and Jarrow (2022).…”

“…see Jarrow et al (2011), Obayashi et al (2017, Jarrow and Kwok (2021), and Choi and Jarrow (2022). However, it provides limited economic intuition for understanding when price bubbles exist in markets.…”

“…This theorem forms the basis for numerous empirical methods created to test for the existence of price bubbles; see Jarrow et al (2011), Obayashi et al (2017), Jarrow and Kwok (2021), and Choi and Jarrow (2022). However, it provides limited economic intuition for understanding when price bubbles exist in markets.…”

Effect of Monetary Policy Decisions and Announcements on the Price of Cryptocurrencies: An Elastic-Net With Arima Residuals Approach

“…The initial focus pertains to the multifaceted dimensions intrinsic to cryptocurrencies. This encompasses an examination of the efficacy of the cryptocurrency market (Bariviera, 2017;Nadarajah & Chu, 2017;Tiwari et al, 2018;Urquhart, 2016;Vidal-Tomás & Ibañez, 2018;Wei, 2018), the segregation of cryptocurrencies from other financial and speculative instruments (Bhanja et al, 2023;Bhuiyan et al, 2021;Corbet et al, 2018;Harb et al, 2022), patterns of price and volatility clustering (Baig et al, 2019;Hu et al, 2019;Li et al, 2020;Ma & Tanizaki, 2022;Urquhart, 2017;Zhang et al, 2018), the emergence and consequences of price bubbles (Cheah & Fry, 2015;Choi & Jarrow, 2022;Hayes, 2018;Moosa, 2020;Su et al, 2018), regulatory frameworks surrounding cryptocurrencies (Corbet et al, 2019;Monrat et al, 2019;Pieters & Vivanco, 2017;Schaupp et al, 2022), and the prevalence of fraudulent activities (Bartoletti et al, 2020;Nghiem et al, 2021;Shayegan et al, 2022).…”