Boost and Burst: Bubbles in the Bitcoin Market

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12137)


This study investigates bubbles and crashes in the cryptocurrency market. In particular, using the log-periodic power law, we estimate the critical time of bubbles in the Bitcoin market. The results indicate that Bitcoin bubbles clearly exist, and our forecast of critical times can be verified with high accuracy. We further claim that bubbles could originate from the mining process, investor sentiment, global economic trend, and even regulation. For policy makers, the findings suggest the necessity of monitoring the signatures of bubbles and their progress in the market place.


Cryptocurrency Bubble Crash Log-periodic power law 

1 Introduction

Cryptocurrency is a digital asset that relies on blockchain technology1 and has attracted much attention from the public, investors, and policy makers. Due to its rapid growth with extreme market volatility, concerns and warnings of bubbles in the cryptocurrency market have continued. As per the dot-com bubble of the 1990s, bubbles might occur during the introduction of new technology [1, 2]. Though it is uncertain whether the post-bubble effect on society is good or not [2], bubbles could create disastrous harm and danger as a consequence. Accordingly, understanding bubbles in the cryptocurrency market and implementing effective policies are vital to prevent such disruptive consequences.

As the market has grown, more than 3,000 cryptocurrencies have emerged. However, Bitcoin still holds leadership: Bitcoin consistently dominates others, the so-called altcoins,2 in terms of market capitalization, number of transactions, network effects, and price discovery role [3, 4, 5]. Therefore, the literature largely discusses the turmoil in the cryptocurrency market through the experiences of Bitcoin [4, 6]. Moreover, there have been several well-known episodes of bubbles and crashes in the Bitcoin market that seem to have similar patterns at first glance, but the origins and consequences are clearly different because of the internal structure of price formation (e.g., over-/undervaluation of price, market efficiency, and investor maturity) and/or environmental changes (e.g., governmental policy, public sentiment, and global economic status) [7]. In this context, we attempt to evaluate two well-known episodes of Bitcoin bubbles and the crashes that followed.

A bubble indicates excessive asset value compared to market equilibrium or that price is driven by stories and not by fundamentals [8, 9]. A market bubble includes its own limit and can “burn” itself out or experience “explosion” associated with several endogenous processes [10]. Much of the relevant studies attempted to test a speculative bubble with unit root tests [11, 12, 13] using the present value model [14, 15]. Besides, the log-periodic power law (LPPL) model has gained much attention with several successful predictions made on well-known episodes about bubbles and crashes [13, 16, 17, 18, 19, 20, 21, 22], so it has recently been applied to the Bitcoin market as well [23, 24]. In this study, we aim to address the following questions: Is there a clear signature for bubbles in the Bitcoin market? Can we precisely predict a critical time at which the bubble in the Bitcoin market will burst? What can be the possible inducers that contribute to the emergence of bubbles?

2 Method and Data

2.1 Log-Periodic Power Law (LPPL)

The LPPL combines both the power law and endogenous feedback mechanisms [10, 25, 26]. The former indicates the existence of a short head that occurs rarely but has enormous effects and a long tail that occurs frequently but with much less impact. The latter, which implies underlying self-organizing dynamics with positive feedback, describes herding behavior in the market place such as purchases in a boom and sales in a slump. Therefore, we can predict the critical time through a signature of faster-than-exponential growth and its decoration by log-periodic oscillations [17, 19]:
$$ Y_{t} = A + B\left( {t_{c} - t} \right)^{\beta } \left\{ {1 + C\cos \left[ {\omega \log \left( {t_{c} - t} \right) + \phi } \right]} \right\} , $$
where \( Y_{t} > 0 \) is the log price at time \( t \); \( A > 0 \) is the log price at critical time \( t_{c} \); \( B < 0 \) is the increase in \( Y_{t} \) over time before the crash when \( C \) is close to 0; \( C \in \left[ { - 1, 1} \right] \) restricts the magnitude of oscillations around exponential trend; \( \beta \in \left[ {0, 1} \right] \) is the exponent of the power law growth; \( \omega > 0 \) is the frequency of fluctuations during a bubble; and \( \phi \in \left[ {0, 2\pi } \right] \) is a phase parameter.

In this study, we estimate the critical time by mainly following Dai et al. [19]: In the first step, we produce the initial value for seven parameters using a price gyration method [27, 28, 29]; and in the second step, we optimize these parameters using a genetic algorithm [30, 31].

2.2 Data

The Bitcoin market operates for 365 days with a 24-h trading system. Thus, we retrieve daily closing prices, i.e., Bitcoin Price Index, from Coindesk3 at 23:00 GMT. The data span for two periods: from July 2010 to December 2013 and from January 2015 to December 2017. We choose two well-known episodes of bubbles and crashes4: Period 1 is from July 18, 2010, when the Bitcoin market was initiated, to December 4, 2013, when the biggest peak reached at 230 USD in 2013; and Period 2 is from January 14, 2015, when the lowest point was reached after the crash in Period 1, to December 16, 2017, when the historical price run reached nearly 20,000 USD. Then we convert the data into log returns:
$$ x_{t} \equiv \ln \left( {\frac{{p_{t + \Delta t} }}{{p_{t} }}} \right), $$
where \( p_{t} \) represents Bitcoin price at time \( t \).
Table 1 summarizes the descriptive statistics for each period. The data from Period 1 are more volatile, skewed, and leptokurtic5 than those from Period 2. The high volatility is due to decentralization and speculative demands [27]. Bitcoin exhibits positive skewness, implying more frequent drastic rise in price and investor risk-loving attitude. Lastly, excess kurtosis is obvious, indicating that a high proportion of returns are at the extreme ends of distribution.
Table 1.

Summary statistics of the log returns.











8.86 × 10−3

6.48 × 10−1

3.75 × 10−1

6.76 × 10−2



Period 1


1.48 × 10−2

6.48 × 10−1

3.75 × 10−1

8.48 × 10−2



Period 2


6.88 × 10−3

2.54 × 10−1

−2.19 × 10−1

4.36 × 10−2



3 Results and Discussion

Table 2 reports parameter estimates from the LPPL including critical time \( t_{c} \), and clearly shows the proximity of critical time, model implied, to the actual crash. All estimated parameters are well within the boundaries reported in the literature. Two conditions such as (i) \( B < 0 \) and (ii) \( 0.1 \le \beta \le 0.9 \) ensure faster-than-exponential acceleration of log prices [28]. In particular, the exponent of power law \( \beta \) during Period 2 is \( 0.2 \), which corresponds to many crashes on major financial markets \( \beta \approx 0.33 \pm 0.18 \) [29]. Both angular log-frequencies \( \omega \) are higher than the range of \( 6.36 \pm 1.56 \), which is observed in major financial markets [30, 31]. Moreover, the value of \( \omega \) during Period 2 exhibits the presence of second harmonics at around \( \omega \approx 11.5 \) [29], which is associated with strong amplitude and hides the existence of fundamental \( \omega \), which is common in emerging markets [31].
Table 2.

LPPL parameters of the best fit.

Time spana

\( t_{c} \)

\( A \)

\( B \)

\( \beta \)

\( C \)

\( \omega \)

\( \phi \)

Jul 18, 2010–Nov 04, 2013


Dec 16, 2013







Jan 14, 2015–Nov 16, 2017


Dec 27, 2017







aWe also opt for the data period as follows: (i) the time window starts from the end of the previous collapse (the lowest point since the last crash); (ii) the day with the peak value is the point of the actual bubble burst; and (iii) the endpoint is from one month before the critical point [25, 26].

Figure 1 displays the data and prediction results of the LPPL model for the two periods. Each curve represents the best fit among estimates.6 A strong upward trend is observed, indicating fast-exponential growth of Bitcoin price and providing clear evidence of a bubble in the market. Moreover, the prediction of critical times, namely corresponding estimate, exhibits the typical hallmark of the critical time of the bubble in 2013 and 2017 (vertical arrows with red color) with high accuracy around the actual crash. The actual crashes of each term date are Dec 4, 2013 and Dec 16, 2017 (see Appendix A).
Fig. 1.

Logarithm of Bitcoin prices and corresponding alarm.

We hypothesize the plausible origins of the Bitcoin bubbles. First, the decline of a newly mined volume, along with an increase in mining7 difficulty, generated a supply-driven impact on the market (Appendix B: Fig. 3). Moreover, changes in investor sentiment affected the internal structure of price formation on the market and made the price turbulent, namely boosting and bursting the bubbles (Appendix B: Fig. 4). A negative surprise in global markets, such as consecutive devaluations of the Chinese Yuan (CNY) in 2015–2016, also functioned as a catalyst to rebalance the portfolios of Chinese investors (Appendix B: Fig. 5). Furthermore, the Chinese government’s banning of cryptocurrency trading on major exchanges in early 2017 provoked the bubble. The sudden prohibition policy merely accomplished a quick transition of the trading currency from CNY to other key currencies, specifically the US dollar (USD) (Appendix B: Fig. 6).

4 Conclusion

In most countries, the regulatory environment appears largely opposed to Bitcoin in the early stages, and one of the key concerns has been the risk of bubbles and the consequent crashes. There is distinct evidence of multiple bubbles in the Bitcoin market, and we have successfully estimated crashes, showing the typical hallmark of the critical times in 2013 and 2017. We attribute the emergence of bubbles to the mining process, investor sentiment, global economic trend, and the regulatory action. The findings strongly suggest the necessity of ex-ante monitoring, and policy makers should be aware that technology, society, and even regulation could induce bubbles.


  1. 1.

    “Cryptocurrency” is a medium of exchange designed as a digital currency (and/or asset) which uses cryptography, i.e., blockchain technology, to control the transactions and creation of new units. “Blockchain” is a growing list of blocks that are linked records of data using cryptography.

  2. 2.

    “Altcoins” refers to all cryptocurrencies other than Bitcoin: the other cryptocurrencies launched after Bitcoin.

  3. 3.
  4. 4.

    In technical perspective, the identification of a peak of the bubble is based on the following two conditions: (i) prior to the peak, there is no higher price than the peak from 262 days before; and (ii) after the peak, there is more than 25% decreased ongoing prices by following 60 days [19, 26]. In the economic context, the bursting of a bubble, for example, dramatic collapse of the market, could bring the economy into an even worse situation and dysfunction in the financial system.

  5. 5.

    A leptokurtic distribution exhibits excess positive kurtosis: kurtosis has a value greater than 3. In the financial market, a leptokurtic return distribution means that there are more risks coming from extreme events.

  6. 6.

    To reduce the possibility of false alarms, we conduct two diagnostics to demonstrate the robustness of our prediction. (i) Firstly, using unit root tests (augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests) with 0 to 4 lags for each term, we conclude that the residuals do not have a unit root but are stationary at the 1% significance level. (ii) In addition, the crash lock-in plot (CLIP) further confirms that our results, in particular for the value of the predicted \( t_{c} \), are robust and stable.

  7. 7.

    Mining is a metaphor for the extraction of valuable things or materials from various deposits. In cryptocurrency, when computers solve complex math problems on the Bitcoin network, they produce new Bitcoins or make the Bitcoin payment network trustworthy and secure by verifying its transaction information.



This research was supported by the Future-leading Research Initiative at Yonsei University (Grant Number: 2019-22-0200; K.A.).


  1. 1.
    Johnson, T.C.: Optimal learning and new technology bubbles. J. Monet. Econ. 54(8), 2486–2511 (2007)CrossRefGoogle Scholar
  2. 2.
    Goldfarb, B., Kirsch, D.A.: Bubbles and Crashes: The Boom and Bust of Technological Innovation, 1st edn. Stanford University Press, Stanford (2019)CrossRefGoogle Scholar
  3. 3.
    Ciaian, P., Rajcaniova, M.: Virtual relationships: short-and long-run evidence from Bitcoin and altcoin markets. J. Int. Financ. Mark. Inst. Money 52, 173–195 (2018)CrossRefGoogle Scholar
  4. 4.
    Gandal, N., Halaburda, H.: Can we predict the winner in a market with network effects? Competition cryptocurrency market. Games 7(3), 16 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Brauneis, A., Mestel, R.: Price discovery of cryptocurrencies: Bitcoin and beyond. Econ. Lett. 165, 58–61 (2018)CrossRefGoogle Scholar
  6. 6.
    Osterrieder, J., Lorenz, J.: A statistical risk assessment of Bitcoin and its extreme tail behavior. Ann. Financ. Econ. 12(1), 1750003 (2017)CrossRefGoogle Scholar
  7. 7.
    Sornette, D., Cauwels, P.: Financial bubbles: mechanisms and diagnostics. Rev. Behav. Econ. 2(3), 279–305 (2015)CrossRefGoogle Scholar
  8. 8.
    Shiller, R.J.: Market volatility and investor behavior. Am. Econ. Rev. 80(2), 58 (1990)Google Scholar
  9. 9.
    Garber, P.M.: Famous First Bubbles: The Fundamentals of Early Manias. MIT Press, Cambridge (2001)Google Scholar
  10. 10.
    Sornette, D.: Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press, Princeton (2017)CrossRefGoogle Scholar
  11. 11.
    Cheung, A., Roca, E., Su, J.J.: Crypto-currency bubbles: an application of the Phillips–Shi–Yu (2013) methodology on Mt. Gox bitcoin prices. Appl. Econ. 47(23), 2348–2358 (2015)CrossRefGoogle Scholar
  12. 12.
    Corbet, S., Lucey, B., Yarovaya, L.: Datestamping the Bitcoin and Ethereum bubbles. Financ. Res. Lett. 26, 81–88 (2018)CrossRefGoogle Scholar
  13. 13.
    Geuder, J., Kinateder, H., Wagner, N.F.: Cryptocurrencies as financial bubbles: the case of Bitcoin. Financ. Res. Lett. 31, 179–184 (2019)CrossRefGoogle Scholar
  14. 14.
    Campbell, J.Y., Shiller, R.J.: Cointegration and tests of present value models. J. Polit. Econ. 95(5), 1062–1088 (1987)CrossRefGoogle Scholar
  15. 15.
    Moosa, I.A.: The bitcoin: a sparkling bubble or price discovery? J. Ind. Bus. Econ. 5, 1–21 (2019)Google Scholar
  16. 16.
    Johansen, A., Ledoit, O., Sornette, D.: Crashes as critical points. Int. J. Theor. Appl. Financ. 3(2), 219–255 (2000)CrossRefGoogle Scholar
  17. 17.
    Zhou, W.X., Sornette, D.: Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000. Phys. A 330(3–4), 543–583 (2003)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Filimonov, V., Bicchetti, D., Maystre, N., Sornette, D.: Quantification of the high level of endogeneity and of structural regime shifts in commodity markets. J. Int. Money Financ. 42, 174–192 (2014)CrossRefGoogle Scholar
  19. 19.
    Dai, B., Zhang, F., Tarzia, D., Ahn, K.: Forecasting financial crashes: revisit to log-periodic power law. Complexity 2018, 4237471 (2018). Scholar
  20. 20.
    Jang, H., Ahn, K., Kim, D., Song, Y.: Detection and prediction of house price bubbles: evidence from a new city. In: Shi, Y., et al. (eds.) ICCS 2018. LNCS, vol. 10862, pp. 782–795. Springer, Cham (2018). Scholar
  21. 21.
    Jang, H., Song, Y., Sohn, S., Ahn, K.: Real estate soars and financial crises: recent stories. Sustainability 10(12), 4559 (2018). Scholar
  22. 22.
    Jang, H., Song, Y., Ahn, K.: Can government stabilize the housing market? The evidence from South Korea. Phys. A 550(15), 124114 (2020). Scholar
  23. 23.
    Wheatley, S., Sornette, D., Huber, T., Reppen, M., Gantner, R.N.: Are Bitcoin bubbles predictable? Combining a generalized Metcalfe’s law and the log-periodic power law singularity model. R. Soc. Open Sci. 6(6), 180538 (2019)CrossRefGoogle Scholar
  24. 24.
    Gerlach, J.C., Demos, G., Sornette, D.: Dissection of Bitcoin’s multiscale bubble history from January 2012 to February 2018. R. Soc. Open Sci. 6(7), 180643 (2019)CrossRefGoogle Scholar
  25. 25.
    Sornette, D., Johansen, A.: Significance of log-periodic precursors to financial crashes. Quant. Financ. 1(4), 452–471 (2001)CrossRefGoogle Scholar
  26. 26.
    Brée, D.S., Joseph, N.L.: Testing for financial crashes using the log periodic power law model. Int. Rev. Financ. Anal. 30, 287–297 (2013)CrossRefGoogle Scholar
  27. 27.
    Sapuric, S., Kokkinaki, A.: Bitcoin is volatile! Isn’t that right? In: Abramowicz, W., Kokkinaki, A. (eds.) BIS 2014. LNBIP, vol. 183, pp. 255–265. Springer, Cham (2014). Scholar
  28. 28.
    Lin, L., Ren, R.E., Sornette, D.: The volatility-confined LPPL model: a consistent model of ‘explosive’ financial bubbles with mean-reverting residuals. Int. Rev. Finan. Anal. 33, 210–225 (2014)CrossRefGoogle Scholar
  29. 29.
    Johansen, A.: Characterization of large price variations in financial markets. Phys. A 324(1–2), 157–166 (2003)CrossRefGoogle Scholar
  30. 30.
    Johansen, A., Sornette, D.: Shocks, crashes and bubbles in financial markets. Brussels Econ. Rev. 53(2), 201–253 (2010)Google Scholar
  31. 31.
    Zhou, W.X., Sornette, D.: A case study of speculative financial bubbles in the South African stock market 2003–2006. Phys. A 388(6), 869–880 (2009)CrossRefGoogle Scholar
  32. 32.
    Fantazzini, D.: Modelling bubbles and anti-bubbles in bear markets: a medium-term trading analysis. In: The Handbook of Trading, 1st edn, pp. 365–388. McGraw-Hill Finance and Investing (2010)Google Scholar
  33. 33.
    Kristoufek, L.: BitCoin meets Google Trends and Wikipedia: quantifying the relationship between phenomena of the Internet era. Sci. Rep. 3, 3415 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.KEPCO E&CGimcheon-siSouth Korea
  2. 2.Korea Advanced Institute of Science and Technology (KAIST)DaejeonSouth Korea
  3. 3.Yonsei UniversitySeoulSouth Korea

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