Critical dynamics related to a recent Bitcoin crash

Highlights

• Method of Critical Fluctuation (MCF) used to detect approach to criticality.

• Critical dynamics detected both in equilibrium and out-of-equilibrium by MCF.

• Specific sequence of indications is identified as evolving towards crash.

• This sequence similar to the evolution towards other extreme events (earthquakes).

• This sequence of indications isn't maintained as sampling frequency is increased.

Abstract

The cryptocurrency market is an emerging market that is characterized by intense volatility and therefore the study of its dynamics presents increased interest. The present work investigates the issue of the critical dynamics of a financial complex system approaching a crash, by using the Method of Critical Fluctuation (MCF) which is known for its ability to uncover critical dynamics. Specifically, we study the recent crash that took place in the cryptocurrency market (starting on 12 May 2021), by analyzing the “Contracts for Difference” (CFDs) prices on Bitcoin/USD (Bitcoin to US-Dollar exchange rate) at five different high frequency trading time intervals (60, 30, 15, 5 and 1 min). The results show that, for the 60-min and 30-min sampling intervals, a specific sequence of indications is identified, in agreement to the evolution towards extreme events in other complex systems, such as earthquakes. This sequence of indications isn't maintained as the sampling frequency is increased. Notably, the existence of critical dynamics during the system's evolution has been detected both in equilibrium and out-of-equilibrium by means of the same analysis method (MCF). The obtained results indicate that the MCF could provide useful information for portfolio analysis and risk management.

Introduction

In today's global financial markets, cryptocurrencies have been gaining the attention of traders, analysts, scientists and regulators (Aslan & Sensoy, 2020; Aysan, Demirtaş, & Saraç, 2021; Kyriazis, 2021). The first cryptocurrency was created in 2008 after publishing a paper titled “Bitcoin: A Peer-to-Peer Electronic Cash System” by an anonymous writer, with the pseudonymous Satoshi Nakamoto (2008). In October 2009, Bitcoin for the first time was listed on an exchange for a price of $0.000764 per Bitcoin (Ammous, 2018). On 22 May 2010, the first real transaction took place in which Bitcoin functioned as a medium of exchange (Ammous, 2018). Since then, >160 million transactions have been held with Bitcoin and the largest companies in the world accepted it for their services (Adhami, Giudici, & Martinazzi, 2018; Ammous, 2018). Bitcoin, as the first decentralized cryptocurrency, pioneers the cryptocurrency markets. Its market cap exceeds 800 billion dollars as of October 2021 (CoinMarketCap, 2021). In addition, financial products, such as “Contracts for Difference” (CFDs) (Le, Do, Nguyen, & Sensoy, 2021) that replicate Bitcoin's price performance, are available on the markets by brokers (Adhami et al., 2018).

The cryptocurrency market, but also the financial markets in general, are a typical example of complex systems characterized by sudden and largely unforeseen phase transition phenomena, at a systemic scale (Battiston et al., 2016; Drożdż, Kwapień, Oświęcimka, Stanisz, & Wątorek, 2020; Kwapień, Wątorek, & Drożdż, 2021; Preis & Stanley, 2010; Wątorek et al., 2020). A phase transition phenomenon is characterized by the transition between two states in which a system could exist (Potirakis, Contoyiannis, Schekotov, Eftaxias, & Hayakawa, 2021). It has been proposed that as a financial system evolves towards an intense crash it can be studied from the phase transitions point of view (Ilinski, 1999; Plerou, Gopikrishnan, & Stanley, 2003; Sornette, 2003; Yalamova & McKelvey, 2011). In many cases, financial crashes are possible to have been triggered by unpredictable stochastic events such as news, central bank decisions or unforeseen economic developments. More often, however, they come from endogenous interactions among the components of the system (Battiston et al., 2016; Petersen, Wang, Havlin, & Stanley, 2010).

It's a widespread belief that financial systems are characterized by heterogeneity as they consist of heterogeneous agents who react differently to incoming information (Bury, 2013; Kristoufek, 2013). For example, an information that is considered negative for an investor and thus it is a selling signal, might be a buying opportunity for another investor, and vice versa. However, in many cases, investors behave homogeneously like a herd (Filip, Pochea, & Pece, 2015; Panjaitan & Simbolon, 2020). According to Bikhchandani and Sharma (2001) and Chiang and Zheng (2010) the herd behavior, i.e., when a large number of single investors buy or liquidate their financial position simultaneously, may lead to volatility, bubbles and crashes. In terms of statistical mechanics, the system is then at a critical point that leads to a phase transition (Johansen, Ledoit, & Sornette, 2000; Crescimanna & Di Persio, 2016).

It has been suggested that market crashes can be studied using the theory of critical phenomena (Ilinski, 1999; Sornette, 2003). This view has been reinforced by the study of Kiyono, Struzik, and Yamamoto (2006), who found an abrupt transition of the non-Gaussian probability density function (PDF) to scale invariant behavior during the black Monday crash in October 1987, a fact that supports that the black Monday crash was triggered by a critical phenomenon. Also, Bury (2013), studying the Dow Jones and indices sets, found that they are not rigorously critical. However, financial systems are closer to criticality in the crash neighborhood. He also expressed the view that the criticality in finance is a competition between global effects inducing homogeneity and local effects inducing heterogeneity in trades. Schmidhuber (2021), analyzed the interplay between trends and reversion in detail, of daily futures prices for interest rates, equity indices, commodities and currencies. His empirical results pointed towards a potential deep analogy between financial markets and critical phenomena. The results support the conjecture that financial markets can be modeled as statistical mechanical systems near criticality, whose microscopic constituents are Buy/Sell orders. Kaizoji (2000), proposed an interacting-agent model of speculative activity explaining crashes in stock markets. The author, using the idea of matching the trades on the stock market (Buy/Sell), with the numbers +1, −1, respectively, expresses the dynamics of the system with Ising models that lead to an order parameter expressed by means of a hyperbolic tangent. Also, the author argues that when the interactions among investors become stronger and reach some critical values, a second-order phase transition and critical behavior can be observed. The results of his study demonstrate that the Japan financial crisis (1987–1992) can be explained by the model that crashes have their origin in the collective crowd behavior of many interacting agents. This study is compatible with the mean field approximation of the theory of critical phenomena, revealing the existence of first and second order phase transition. Moreover, using all the values and not with the coarse-graining description of +1, −1, then the order parameter is expressed by the representation of type I intermittency, as we describe it in the present article. Mariani and Liu (2007), studied the Asian crisis of 1997 using a phase transition model. In their analysis, they used data before the true crash date in order to obtain the predicted critical date. The results showed that the estimation of the critical date was excellent for all indices that they studied except for the MERVAL index. Through the study of critical phenomena, Gonçalves, Borda, Vieira, and Matos (2022), explored the possibility of predicting financial bubbles and crashes. More specifically, they used the theory of self-similar oscillatory time singularities to analyze the Portuguese stock market in 1998, 2007, and 2015 crises. Their results showed that the Log Periodic Power-Law/Model (LPPM) methodology, would provide very important indications for portfolio managers. da Silva, Zembrzuski, Correa, and Lamb (2010) studied the Brazilian Stock Market by monitoring global persistence. Their results showed a deviation of power-law behavior during the crisis in a strong analogy with spin systems. They also compared their results with universal exponents obtained from the international stock markets. This suggests how a thorough analysis of suitable exponents can bring a possible way of forecasting market crises characterized by non-criticality. Chudzyński and Struzik (2021), examined Bitcoin to investigate the link between criticality and market crash. Their results showed scale invariance across a large range of scales in the years 2012–2019, which indicates that the Bitcoin market might be in a critical state not only during the crash.

As it is evident, the identification of criticality in a financial system is a research subject that continues to be investigated in the literature. The application of methods of statistical physics and the theory of complex systems has made a decisive contribution to the study of this issue. Nevertheless, the majority of the relevant articles investigate the phenomenon of criticality out-of-equilibrium. Detecting criticality in a financial system in equilibrium is, to the best of our knowledge, a relatively unexplored topic in the existing literature. In the present article, the Method of Critical Fluctuation (MCF) is used to investigate the critical dynamics of CFD prices on Bitcoin/USD as a crash approach. The MCF is a method known for its ability to uncover critical dynamics in equilibrium. In addition, it has the advantage that the MCF power-law exponent is directly connected to the isothermal critical exponent δ. Therefore, it is possible to accurately determine the state of the system (critical state / tricritical state) through the estimation of the MCF exponents. Another important property of MCF that has recently been studied (Contoyiannis et al., 2022), is its ability to detect criticality both in equilibrium and out-of-equilibrium (see Section 5). Numerous crashes in the cryptocurrency market have occurred, we focus on the recent Bitcoin crisis that began on 12 May 2021 (Anastasiou, Ballis, & Drakos, 2021; Fruehwirt, Hochfilzer, Weydemann, & Roberts, 2021; Merkaš & Roška, 2021). Moreover, since earlier studies have shown that the Bitcoin market system behavior varies at different observation time intervals (Aslan & Sensoy, 2020; Lahmiri & Bekiros, 2020; Vidal-Tomás, 2020; Zargar & Kumar, 2019), we also examine the critical dynamic of the system at different observation time intervals.

Although the MCF has been successfully applied to many systems approaching an extreme event, this is the first time that it has been applied to the analysis of a financial crash. It is also the first time that the critical dynamics of a financial system in a state of equilibrium and out-of-equilibrium are explored by the same method. The results show significant similarities with the behavior of other complex systems before extreme events, such as earthquakes. Also, as far as we know, the analysis of critical dynamics of a financial complex system at different time intervals is relatively unexplored. The results show that the analysis of financial time series at very high frequencies is an issue that needs further investigation.

The rest of the paper is organized as follows: Section 2 provides an overview of the theory of critical phenomena (Section 2.1), as well as key information about the MCF (Section 2.2). Section 3 provides information about the employed data. Section 4 presents the analysis results, Section 5 presents the criticality out-of-equilibrium, and Section 6 summarizes the conclusions.