On the stability of stablecoins

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ On the stability of stablecoins © 2021 The Author(s). Published by Elsevier B.V. Published version Grobys, Klaus; Junttila, Juha; Kolari, James W.; Sapkota, Niranjan Grobys, K., Junttila, J., Kolari, J. W., & Sapkota, N. (2021). On the stability of stablecoins. Journal of Empirical Finance, 64, 207-223. https://doi.org/10.1016/j.jempfin.2021.09.002 2021 Journal of Empirical Finance 64 (2021) 207–223 Contents lists available at ScienceDirect Journal of Empirical Finance journal homepage: www.elsevier.com/locate/jempfin On the stability of stablecoins Klaus Grobys a,b,∗,1, Juha Junttila c,1, James W. Kolari d,1,2, Niranjan Sapkota a,1 aFinance Research Group, School of Accounting and Finance, University of Vaasa, Wolffintie 34, 65200 Vaasa, Finland bInnovation and Entrepreneurship (InnoLab), University of Vaasa, Wolffintie 34, FI-65200 Vaasa, Finland cJyväskylä International Macro & Finance Research Group, School of Business and Economics, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland dDepartment of Finance, Mays Business School, Texas A&M University, College Station, TX 77843-4218, USA ARTICLE INFO JEL classification: C19 C49 C59 G10 G15 G19 Keywords: Bitcoin Financial technology Power laws Spillovers Stablecoins Volatility ABSTRACT This paper investigates the volatility processes of stablecoins and their potential stochastic interdependencies with Bitcoin volatility. We employ a novel approach to choose the optimal combination for the power law exponent and the minimum value for the volatilities bending the power law. Our results indicate that Bitcoin volatility is well-behaved in a statistical sense with a finite theoretical variance. Surprisingly, the volatilities of stablecoins are statistically unstable and contemporaneously respond to Bitcoin volatility. Also, whereas the volatilities of stablecoins are not Granger-causal for Bitcoin volatility, lagged Bitcoin volatility exhibits Granger-causal effects on the volatilities of stablecoins. We conclude that Bitcoin volatility is a fundamental factor that drives the volatilities of stablecoins. 1. Introduction Bitcoin has a number of unique advantages over traditional payment methods, such as user autonomy, discretion, peer-to- peer focus, elimination of banking fees, low transaction fees for international payments, mobile payments, and 24/7 accessibility. However, these advantages come at the cost of volatility that well exceeds the volatility of many other asset classes. Baur et al. (2018) compared the statistical features of Bitcoin and other assets and found that the level of Bitcoin’s historical return and volatility are not comparable to any other asset. The authors observed that Bitcoin has larger negative skewness than high yield corporate bond, gold, and silver returns. This large negative skewness was due to an asymmetric Bitcoin return distribution with fatter left-side than right-side tails. Very high kurtosis implies a large number of tail events in Bitcoin returns. Relevant to the present study, no previous studies investigate Bitcoin volatility and tail events. In a speech at the 2018 World Economic Forum in Davos, Deputy Governor of the Swedish Central Bank Cecilia Skingsley commented that, unlike money, cryptocurrencies do not store value, fluctuate in value, and have unstable exchange rates.3Due ∗Corresponding author at: Finance Research Group, School of Accounting and Finance, University of Vaasa, Wolffintie 34, 65200 Vaasa, Finland. E-mail addresses: [email protected] (K. Grobys), [email protected] (J.P. Junttila), [email protected] (J.W. Kolari), [email protected] (N. Sapkota). 1The authors are thankful for having received useful comments from two anonymous reviewers. 2JP Morgan Chase Professor of Finance. 3See https://www.weforum.org/agenda/2018/01/robert-shiller-bitcoin-is-just-an-interesting-experiment/. https://doi.org/10.1016/j.jempfin.2021.09.002 Received 14 January 2021; Received in revised form 18 August 2021; Accepted 7 September 2021 Available online 17 September 2021 0927-5398/©2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 to Bitcoin’s failure to serve as a substitute for national (fiat)4currencies, stablecoins have been developed as a possible solution. Stablecoins are designed to minimize price volatility by means of: (i) pegging against a national currency or commodity, (ii) collateralization with respect to other cryptocurrencies, or (iii) algorithmic coin supply management. In this regard, the most common type of stablecoin is the U.S. dollar-pegged coin Tether (USDT). On January 4, 2021 the Office of the Comptroller of the Currency (OCC) Chief Counsel issued a letter that legally approved payment-related activities involving new technologies for national banks and federal savings associations, including the use of independent node verification networks (INVNs or networks) and stablecoins.5The natural question that arises is whether this blockchain-based technology can provide stable currency payments. Seminal work by Wei (2018) examined whether the minting of new Tether stablecoins inflated the prices of Bitcoin. The author showed that, contrary to investor expectations, Tether issuances did not impact Bitcoin returns. However, a recent study by Griffin and Shams (2020) employed algorithms to explore blockchain data and found that purchases of Tether were timed following market downturns and resulted in large increases in Bitcoin prices. In another recent paper, Baur and Hoang (2021a) proposed a framework to test for absolute and relative stability of stablecoins. The authors argued that stablecoins are more stable than Bitcoin but less stable than stable benchmarks such as major national currencies. The present paper proposes a new approach to measuring the stability of stablecoins. Given that Baur et al. (2018) found that Bitcoin exhibits extremely high kurtosis with relatively more tail events compared to other assets, we employ realized daily volatility to explicitly model the probability density functions of five stablecoins that exhibit the largest market capitalizations. For comparison purposes, we also model Bitcoin volatility using the same methodology. We apply power laws and maximum likelihood estimation (MLE) to estimate the corresponding power law exponents of the realized volatility processes.6A novel aspect of our approach is that it does not rely on the minimum value of the Kolmogorov–Smirnov distance measure used in earlier research. Instead of choosing the minimum value of the realized volatility (𝑥𝑀𝐼𝑁)required in MLE via that approach, we use a goodness-of-fit test in trial-and-error analyses to find the combination of 𝑥𝑀𝐼𝑁 and corresponding power law exponent (𝛼) for which the power law null hypothesis cannot be rejected. We demonstrate that our approach yields combinations of 𝑥𝑀𝐼𝑁 and 𝛼 that are in line with the theoretical data generating process. After evaluating realized volatilities, we explore stochastic interdependencies in volatilities. To do this, we utilize a log–log regression approach for both single and multiple equation models to test whether: (i) Bitcoin volatility and the volatilities of stablecoins are contemporaneously co-moving, (ii) lagged stablecoin volatilities have an impact on Bitcoin volatility, (iii) and lagged Bitcoin volatility has an impact on stablecoin volatility. Our study contributes to previous literature in a number of important ways. First, we extend previous studies on tail risks associated with man-made phenomena. Often-cited work by Clauset et al. (2009) analyzed whether 24 real-world data sets from a range of different disciplines follow power law distributions. The authors’ findings supported Taleb’s (2007) view that power law distributions occur in many situations and help to better understand man-made phenomena. Another well-known study by Gabaix (2009) documented that income and wealth, the size of cities and firms, stock market returns, trading volume, international trade, and executive pay appear to follow different power law processes. Our study contributes to this literature by exploring uncertainty in cryptocurrency markets, which is a man-made phenomenon. It is worthwhile noting that the overall market capitalization of the cryptocurrency market is $1.93 trillion7; hence, this market is not trivial in terms of economic significance. From the perspective of finance research, power law distributions are used to model both financial asset returns and volatilities. A recent paper from Warusawitharana (2018) estimated power law coefficients using 15-minute stock returns for 41 stocks in the period 2003 to 2014. The results confirmed earlier findings by Plerou et al. (1999) by demonstrating that the power law coefficient of the cross-sectional distribution ranges between 2.09 and 3.46. Also, Liu et al. (1999) showed that the asymptotic behavior of the probability density function of the S&P 500 index is described by a power law distribution with an exponent around 4.8Extending these studies, we apply power laws to model the realized volatilities of cryptocurrencies and examine stochastic interdependencies in their volatility processes. As mentioned earlier, the valuation of stablecoins is closely related to the valuation of national currencies (or fiat money) under a fixed exchange rate regime. Models for national currency valuation can be divided into those with macroversus microfoundations.9Macro-factor exchange rate models are based on country differences in money supplies, interest rates, capital flows, financial frictions, commodity prices, and inflation.10 However, these models may not be relevant to the valuation of stablecoins that are not generally accepted as mediums of exchange by central banks in monetary policy. With respect to micro-foundation models, Lyons and Viswanath-Natraj (2019) found that fundamental factors such as order flows are valuation determinants of stablecoins. They also found that parity deviations of Tether (for example) are strongly affected by Bitcoin volatility. Our paper extends their analyses by focusing on the interconnections of volatilities between Bitcoin and stablecoin markets. Additionally, our study contributes to the growing literature on emerging digital ecosystems. Wei (2018) examined the largest stablecoin Tether and its influence on Bitcoin. While he found no price manipulation of Bitcoin, as already mentioned, Griffin 4Similar to Lyons and Viswanath-Natraj (2019), we use the term national currencies instead of fiat currencies (paper-money) when referring to the analysis of stablecoins. Due to their collateral requirements and other characteristics, we treat the pricing of stablecoins in the spirit of valuation models of national currencies under a fixed exchange rate regime. 5See https://www.occ.gov/news-issuances/news-releases/2021/nr-occ-2021-2a.pdf. 6Taleb (2020), p.91) has commented that power laws should be the norm in modeling stochastic processes. 7See coinmarketcap.com (as of August 18, 2021.) 8See Lux and Alfarano (2016) for an excellent overview of power law distribution applications in finance. 9See Lyons (2001) and Evans (2011) for standard text-book presentations covering these models. 10 For example, see studies by Eichengreen et al. (1994), Chen and Rogoff (2003), Engel and West (2005), Gabaix and Maggiori (2015), Itskhoki and Mukhin (2017), among others. 208 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 and Shams (2020) demonstrated that purchases of Tether are timed following market downturns and result in notable increases in Bitcoin prices. Also, other studies of stablecoins have analyzed their safe haven properties (Baur and Hoang,2021b) and their pricing mechanisms in view of fixed exchange rate regimes for national currencies (Lyons and Viswanath-Natraj,2019) and associated stability (Baur and Hoang,2021a). While empirically our paper is closest to Baur and Hoang (2021a), unlike their study, we focus on: (i) uncertainty in stablecoin markets using realized volatilities, and (ii) stochastic interdependencies between the volatility processes of stablecoins and Bitcoin from a Granger-causal perspective. Finally, there is a large literature on modeling the volatilities of cryptocurrency data using various Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model specifications.11 In a recent study, Caporale and Zekokh (2019) fitted more than 1000 GARCH-type models to the log-returns of Bitcoin, Ethereum, Ripple and Litecoin. Their results suggested that using standard GARCH models may yield incorrect Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts because cryptocurrency data exhibits a high level of asymmetries and regime switches. The authors argued that using GARCH models results in ineffective risk-management, portfolio optimization, and pricing of derivative securities.12 In this regard, Taleb (2020, pp. 50–51) has stressed that the application of GARCH models is problematic if either the data do not exhibit finite kurtoses or if the kurtoses are not defined. Specifically, given the kurtosis is infinite, estimates of GARCH models may be sample specific. By contrast, Calvet and Fisher (2004) and Lux et al. (2014) showed that power law models usually outperform GARCH models in terms of forecasting financial market volatility. It is interesting to note that Hou et al. (2020) documented that about 80 percent of 452 cross-sectional asset pricing anomalies fails scientific replications. In an earlier contribution, Schwert (2003) pointed out that, once cross-sectional asset pricing phenomena are documented and analyzed in the academic literature, these cross-sectional patterns often seem to disappear, reverse, or attenuate. He explained that asset pricing anomalies could be subject to statistical aberrations, which have attracted the attention of academics and practitioners. Hence, sample specificity could affect the results. Our study contributes to the literature on the volatility of cryptocurrencies by modeling the realized volatilities of cryptocurrencies using power laws. This approach allows (i) modeling of ‘wild volatility’ often observed in cryptocurrency markets, and (ii) determination of whether or not distribution-specific metrics are subject to sample-specificity.13 Our results demonstrate that the volatility processes of both Bitcoin and stablecoins bend power laws. Surprisingly, Bitcoin volatility is rather well-behaved in terms of being a finite and statistically stable process. The power law exponent for Bitcoin volatility conforms to a theoretical variance. However, we do not find such evidence for the volatility processes of stablecoins. While our results suggest that theoretical means of stablecoin volatility processes exist, their corresponding variances are infinite, which indicates statistical instability. Furthermore, using log–log regression analysis to explore potential volatility spillover effects shows that uncertainties in stablecoins and Bitcoin respond contemporaneously. However, the volatilities of stablecoins (including Tether) do not spillover to Bitcoin volatility. Lastly, we find strong volatility spillover effects in a Granger-causal sense from Bitcoin volatility to volatilities of stablecoins. These results support those of Lyons and Viswanath-Natraj (2019) on the role of Bitcoin volatility as a fundamental factor affecting the volatilities of stablecoins. The paper is organized as follows. Section 2provides background discussion. Section 3presents the results of our statistical analyses. Section 4discusses the empirical results. The last section concludes. 2. Background discussion While Bitcoin is the most popular cryptocurrency, it suffers from high volatility imposing high risk on investors. Even intraday price fluctuations are huge. It is no surprise to see Bitcoin’s price moving in excess of 10% in either direction on a daily basis.14 Even long-term price fluctuations are very high — for instance, Bitcoin’s price rose from the level of around $7,500 in November 2017 to about $20,000 in December 2017, and then declined to $4,200 in December 2018. Recently, over-the-counter (OTC) investor interest in Bitcoin caused the price to surge almost 200% reaching $22,800 in December 2020. Due to large volatility and periodic collapses in the Bitcoin market, investors started looking for a less volatile crypto-asset known as stablecoins. Even before the advent of stablecoins, the rapid transformation of payments from a cash to digital ecosystem prompted interest in the issuance of central bank digital currencies. In 2020 the Federal Reserve announced an investigation into its own digital currency with potential stability comparable to the U.S. dollar. There are two main reasons for the price stability of national currencies. First, national currencies are backed by relatively stable underlying or collateral assets, such as gold or forex reserves. And second, when a national currency’s price moves beyond a certain level, central bank authorities can act to maintain price stability. By contrast, cryptocurrencies typically lack both of these supporting features. Consequently, interest in cryptocurrencies resembling the stability of national currencies helped to motivate the development of stablecoins. There are three different types of stablecoins. First, fiat-collateralized (off-chain) stablecoins backed by a national currency (e.g., the U.S. dollar) as collateral for issuing tokens. The token is a 1:1 ratio of cryptocurrency/national money. Other forms of 11 In a recent study, Grobys (2021) provided an intensive review on this literature. 12 Caporale and Zekokh’s (2019) finding is supported by Ardia et al. (2019), who tested the presence of regime changes in the GARCH volatility dynamics of Bitcoin log-returns using Markov-switching GARCH (MSGARCH) models. Their findings indicated that MSGARCH models clearly outperform single-regime GARCH for VaR and ES forecasting. 13 Some relevant studies on the applications of power laws for financial market data include Lux and Alfarano (2016), Lux and Ausloos (2002), Calvet and Fisher (2004), Lux et al. (2014), and Liu et al. (1999). Notably, Calvet and Fisher (2004) and Lux et al. (2014) showed that power law models often outperform GARCH models in terms of forecasting financial market volatility. 14 For example, in the sample from March 29th, 2013 to November 22nd, 2020, Bitcoin’s price increased (decreased) more than 10% (-10%) on 61 (53) trading days. 209 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Table 1 Market capitalization. Rank Cryptocurrency Abbreviation Market capitalization Data (MM/DD/YYYY) 1 Bitcoin BTC $340,790,183,317 4/29/2013–11/22/2020 4 Thether USDT $18,495,477,972 2/25/2015–11/22/2020 13 USD Coin USDC $2,871,675,203 10/8/2018–11/22/2020 26 Dai DAI $1,019,324,729 11/22/2019–11/22/2020 37 Binance USD BUSD $653,999,894 9/20/2019–11/22/2020 56 TrueUSD TUSD $314,313,722 3/6/2018–11/22/2020 Daily data were downloaded for Bitcoin (BTC), Thether (USDT), USD Coin (USDC), Dai (DAI), Binance USD (BUSD), and TrueUSD (TUSD) from coinmarketcap.com. Market capitalization, available time period, and rank for each cryptocurrency are as of November 22, 2020. collateral are commodities, including precious metals such as gold and silver. Most fiat-collateralized stablecoins use U.S. dollar reserves. Some popular examples are Circle (USDC), Gemini Dollar (GUSD), and Tether (USDT). However, dollar-based stablecoins can differ in their reserves. Whereas USDC is backed by the USD in the ratio 1:1, USDT is backed by a basket of various U.S. reserves and assets. Off-chain fiat-collateralized stablecoins are created when national currency is held by a centralized issuer and destroyed when the fiat asset is received. Thus, these stablecoins seek to make transactions safe, fast, and secure for daily transactions. Some other advantages of fiat-collateralized stablecoins are convenience, simplicity, and (prima facie) stability. Disadvantages include the use of a centralized blockchain, which is vulnerable to the moral hazards and potential bankruptcy of the central authority. Second, crypto-collateralized (on-chain) stablecoins are tokens backed by other cryptocurrencies. Generally, these stablecoins are backed by a portfolio of different cryptocurrencies for risk management in terms of diversification. They are often over-collateralized to mitigate the risk of price fluctuations of underlying cryptocurrencies. This characteristic implies that a considerable part of the token supply is maintained as a reserve in order to distribute a lower number of stablecoins – a mechanism allowing the issuers to maintain price stability. The most common form of crypto-supported stablecoin requires users to store a fixed deposit or stake a certain amount of digital currencies into a smart contract, known as a Collateralized Debt Position (CDP) or Vault. This requirement results in a fixed ratio of stablecoins. Typically, a decentralized blockchain provides trust, transparency, and security to users. However, there are some disadvantages, particularly the need for excess collateral. For instance, $1,000 worth of Ether may be held as reserves for issuing an equivalent of $500 worth of crypto-collateralized stablecoins. Another example is MakerDAO’s DAI stablecoin generated when the investor opens a CDP, deposits some amount of Ether (ETH) as collateral, and then withdraws DAI from their Vault. Investors must maintain a collateralization ratio of 1.5, which means that investors must collateralize 150% of their DAI holdings. In simple terms, to take a loan of 100 DAI, investors have to deposit $150 worth of ETH into the CDP/Vault. This requirement ensures that the system has enough collateral to account for the whole DAI supply in circulation and maintain solvency. It should be noted that backing by multiple cryptocurrencies makes it difficult to achieve price stability. Since the majority of cryptocurrencies are in the same asset class and follow similar trends over time, a basket of cryptocurrencies is undiversified with little or no reduction in price stability.15 Third, and last, non-collateralized (seigniorage) stablecoins use the Seigniorage Shares System, wherein algorithms seek to maintain price stability without being backed by any national currency, physical asset, or cryptocurrency. This system algorithmically increases or decreases the supply of cryptocurrency in a manner similar to central bank quantitative easing or tightening. The objective of this mechanism is to maintain price stability as close to $1 U.S. dollar as possible by selling tokens if the price falls below the peg or supplying tokens to the market if the value increases. To do this, the cryptocurrency base coin uses a consensus mechanism to determine whether it should increase or decrease the supply of tokens. Non-collateralized cryptocurrencies form the minority group of stablecoins. Some examples are SagaCoin (SAGA), Havven (HAV), and Carbon (CUSD). The main advantage of non-collateralized stablecoins is that there is no reliance on collateral. As such, this type of stablecoin is independent from a central authority. Avoiding collateral also decreases other risks, such as bankruptcy and moral hazard related to centralization. On the other hand, this approach is far more complex than collateralized stablecoins, which makes it difficult to understand for naïve users. 3. Data and methodology We download daily data for Bitcoin (BTC) as well as stablecoins Tether (USDT), USD Coin (USDC), Dai (DAI), Binance USD (BUSD), and TrueUSD (TUSD) from coinmarketcap.com. These data include all available opening, high, low, and closing prices over time. Table 1 summarizes the market capitalization, available time period, and rank for each cryptocurrency as of November 22, 2020. The data series for BTC (DAI) covers the longest (shortest) sample period from 4/29/2013–11/22/2020 (11/22/2019–11/22/2020). 15 Stosic et al. (2018) observed the presence of multiple collective behaviors among cryptocurrencies. Also, Bouri et al. (2019) showed that the cryptocurrency market is subject to herding behavior that appears to vary over time. 210 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Table 2 Descriptive statistics. Metric/Cryptocurrency BTC USDT USDC DAI BUSD TUSD Mean 0.5256 0.1670 0.2096 0.2722 0.2256 0.2303 Median 0.3712 0.1158 0.1951 0.2445 0.1982 0.1990 Maximum 7.3973 3.1091 1.8356 2.2510 2.8147 5.7823 Minimum 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Std. Dev. 0.5525 0.2317 0.1849 0.2541 0.2372 0.2777 Skewness 3.9396 3.9485 2.7371 2.5324 4.5522 10.0989 Kurtosis 28.8858 36.4061 18.8971 15.4920 41.7549 175.3898 Observations 2765 2093 777 367 430 993 Descriptive statistics for realized annualized daily volatilities for Bitcoin (BTC), Tether (USDT), USD Coin (USDC), Dai (DAI), Binance USD (BUSD), and TrueUSD (TUSD) from coinmarketcap.com. Following Grobys (2021), realized annualized daily volatilities are computed for each cryptocurrency as proposed in Rogers and Satchell (1991), that is, 𝜎𝑖,𝑡 =√𝑇√(𝑙𝑛 (𝐻𝐼𝐺𝐻𝑖,𝑡 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 )⋅𝑙𝑛 (𝐻𝐼𝐺𝐻𝑖,𝑡 𝑂𝑃 𝐸𝑁𝑖,𝑡 )+𝑙𝑛 (𝐿𝑂𝑊𝑖,𝑡 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 )⋅𝑙𝑛 (𝐿𝑂𝑊𝑖,𝑡 𝑂𝑃 𝐸𝑁𝑖,𝑡 )), where 𝐻𝐼𝐺𝐻𝑖,𝑡,𝐿𝑂𝑊𝑖,𝑡,𝑂𝑃 𝐸𝑁𝑖,𝑡, and 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 denote the highest, lowest, opening, and closing price for cryptocurrency i on day t,𝜎𝑖,𝑡 denotes cryptocurrency i’s corresponding realized annualized volatility, and 𝑇= 365 due to 24/7 cryptocurrency trading. 3.1. Realized volatility We compute realized volatilities for each cryptocurrency. Following Grobys (2021), realized annualized daily volatilities are compounded in line with Rogers and Satchell (1991): 𝜎𝑖,𝑡 =√𝑇√(𝑙𝑛 (𝐻𝐼𝐺𝐻𝑖,𝑡 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 )⋅𝑙𝑛 (𝐻𝐼𝐺𝐻𝑖,𝑡 𝑂𝑃 𝐸𝑁𝑖,𝑡 )+𝑙𝑛 (𝐿𝑂𝑊𝑖,𝑡 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 )⋅𝑙𝑛 (𝐿𝑂𝑊𝑖,𝑡 𝑂𝑃 𝐸𝑁𝑖,𝑡 )),(1) where 𝐻𝐼𝐺𝐻𝑖,𝑡,𝐿𝑂𝑊𝑖,𝑡,𝑂𝑃 𝐸𝑁𝑖,𝑡, and 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 denote the highest, lowest, opening, and closing price for cryptocurrency ion day t, respectively, 𝜎𝑖,𝑡 denotes cryptocurrency i’s corresponding realized annualized volatility, and 𝑇= 365 as cryptocurrencies are traded 24/7. Table 2 reports the descriptive statistics, and Fig. 1 plots the time series evolution of the calculated realized cryptocurrency volatilities. In Table 2 we see that BTC exhibits the highest average volatility equal to 53%, whereas the stablecoins’ average volatilities range between 17% (USDT) and 27% (DAI). Hence, BTC’s average volatility is considerably higher than the average volatilities of stablecoins. An important empirical fact that we can observe from Fig. 1 is that each realized volatility series contains outliers. Statistically, this phenomenon can be measured by the kurtosis value. Table 2 shows that each cryptocurrency’s volatility exhibits very high kurtosis ranging from 18.90 (USDC) to 175.39 (TUSD). For comparison purposes, the thin-tailed normal distribution has a kurtosis of 3. We infer that all cryptocurrency volatilities have extremely heavy fat tails. 3.2. Statistical model To investigate the stability of volatility processes, we model the realized volatilities using the following power laws: 𝑃(𝑋 > 𝑥)=𝑝(𝑥)=𝐶𝑥−𝛼,(2) where 𝐶=(𝛼− 1)𝑥𝛼−1 𝑀𝐼𝑁 with 𝛼∈{R+|𝛼 > 1},𝑥∈{R+||𝑥𝑀𝐼𝑁 ≤𝑥 < ∞},𝑥𝑀𝐼𝑁 is the minimum value of realized volatility that bends the power law, and 𝛼is the magnitude of tail exponent.16 Regarding the latter term, Taleb (2020, p. 34) observed that the tail exponent of a power law function captures via extrapolation the low-probability deviation not seen in the data, which plays a disproportionately large share in determining the mean. It can be shown that the expectation of the volatilities defined as 𝐸[𝑋]is given by 𝐸[𝑋]=∫∞ 𝑥𝑀𝐼𝑁 𝑥𝑝 (𝑥)𝑑𝑥 =(𝛼− 1) (𝛼− 2)𝑥𝑀𝐼𝑁,(3) and that the second moment 𝐸[𝑋2], or the variance of the volatility, is defined as: 𝐸[𝑋2]=∫∞ 𝑥𝑀𝐼𝑁 𝑥2𝑝(𝑥)𝑑𝑥 =(𝛼− 1) (𝛼− 3)𝑥2 𝑀𝐼𝑁.(4) Higher moments of order 𝑘are analogously defined as: 𝐸[𝑋𝑘]=(𝛼− 1) (𝛼−1−𝑘)𝑥𝑘 𝑀𝐼𝑁.(5) 16 We follow notation in Clauset et al. (2009). To keep our notations clear, we drop the index idenoting the respective realized volatility of an individual cryptocurrency. Volatilities are calculated separately for each cryptocurrency 𝑖= 1,…,6. In choosing power laws to model financial data, we follow Liu et al. (1999) among others. 211 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Fig. 1. Time series evolutions of realized volatilities. This figure shows the time series evolutions for the realized annualized daily volatilities for Bitcoin (BTC), Tether (USDT), USD Coin (USDC), Dai (DAI), Binance USD (BUSD), and TrueUSD (TUSD). The realized annualized daily volatility for cryptocurrency iat time tis computed as, 𝜎𝑖,𝑡 =√𝑇√(𝑙𝑛 (𝐻𝐼𝐺𝐻𝑖,𝑡 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 )⋅𝑙𝑛 (𝐻𝐼𝐺𝐻𝑖,𝑡 𝑂𝑃 𝐸𝑁𝑖,𝑡 )+𝑙𝑛 (𝐿𝑂𝑊𝑖,𝑡 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 )⋅𝑙𝑛 (𝐿𝑂𝑊𝑖,𝑡 𝑂𝑃 𝐸𝑁𝑖,𝑡 )), where 𝐻𝐼𝐺𝐻𝑖,𝑡,𝐿𝑂𝑊𝑖,𝑡,𝑂𝑃 𝐸𝑁𝑖,𝑡, and 𝐶𝐿𝑂𝑆𝐸𝑖,𝑡 denote the highest, lowest, opening, and closing price for cryptocurrency ion day t,𝜎𝑖,𝑡 denotes cryptocurrency i’s corresponding realized annualized volatility, and 𝑇= 365 due to 24/7 cryptocurrency trading. From Eq. (3), we know that the mean only exists for 𝛼 > 2, whereas the variance only exists for 𝛼 > 3. Following White et al. (2008) and Clauset et al. (2009), who found that maximum likelihood estimation (MLE) performs best for estimating power law exponents, we estimate the tail exponent as: 𝛼 = 1 + 𝑁(𝑁 ∑ 𝑖=1 ln (𝑥𝑖 𝑥𝑀𝐼𝑁 ))−1 ,(6) where 𝛼 denotes the MLE estimator, 𝑁is the number of observations exceeding 𝑥𝑀𝐼𝑁 and other notation is as before. Fig. 2 plots the estimated parameters for 𝛼 depending on the value for 𝑥𝑀𝐼𝑁 for all of our cryptocurrency volatilities.17 A crucial question is: How can we determine the corresponding values for 𝛼and 𝑥𝑀𝐼𝑁 to accurately estimate the probability density functions? Clauset et al. pointed out that it is common to choose the value for 𝑥𝑀𝐼𝑁, where 𝑥𝑀𝐼𝑁 denotes the selected value for 𝑥𝑀𝐼𝑁, beyond which 𝛼 is stable. From Figure 3 in Clauset et al. (2009, p. 670), it is evident that this value corresponds to the saddle point in a 𝛼∕𝑥𝑀𝐼𝑁-graph. Clauset et al. proposed the Kolmogorov–Smirnov approach to choose the optimal value for 𝑥𝑀𝐼𝑁. This statistic is simply the maximum distance Dbetween the data and fitted CDFs defined as: 𝐷=𝑀𝐴𝑋𝑥≥𝑥𝑀𝐼𝑁 |𝑆(𝑥)−𝑃(𝑥)|,(7) where 𝑆(𝑥)is the CDF of the data for the observation with value at least 𝑥𝑀𝐼𝑁, and 𝑃(𝑥)is the CDF for the power law model that best fits the data in the region 𝑥≥𝑥𝑀𝐼𝑁. The estimate of the 𝑥𝑀𝐼𝑁 is the value of 𝑥𝑀𝐼𝑁 that minimizes D. This approach may yield accurate estimates in the case of well-behaved 𝛼∕𝑥𝑀𝐼𝑁-functions, such as illustrated in Figure 3 of Clauset et al. (2009, p. 670). However, it could lead to severe errors (as shown in forthcoming results) in the presence of erratic functions.18 For example, we observe from Fig. 2 that the 𝛼∕𝑥𝑀𝐼𝑁-function for BTC looks virtually the same as the 𝛼∕𝑥𝑀𝐼𝑁-function for a simulated power law process in Figure 3 of Clauset et al. By contrast, the 𝛼∕𝑥𝑀𝐼𝑁-functions for our stablecoins do not show this relatively smooth pattern but rather appear to be much more erratic. 17 These graphs are often referred to as Hill plots. 18 Due to finite samples in empirical research, this situation is not unexpected. 212 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Fig. 2. Hill plots. This figure shows the Hill plots for Bitcoin (BTC), Tether (USDT), USD Coin (USDC), Dai (DAI), Binance USD (BUSD), and TrueUSD (TUSD). For each cryptocurrency, the Hill plot shows the estimated 𝛼 as a function of 𝑥𝑀𝐼𝑁 given by the maximum likelihood estimator (MLE), 𝛼 = 1 + 𝑁(∑𝑁 𝑖=1 ln (𝑥𝑖 𝑥𝑀𝐼𝑁 ))−1, where 𝛼 denotes the MLE estimator, 𝑥𝑖is the realized annualized daily volatility of the respective cryptocurrency, provided 𝑥𝑖≥𝑥𝑀𝐼𝑁, and 𝑁denotes the number of observations for which 𝑥𝑖≥𝑥𝑀𝐼𝑁 is satisfied. Therefore, instead of using the Kolmogorov–Smirnov approach as outlined above, we propose a different approach to choose the optimal combination of 𝛼 and 𝑥𝑀𝐼𝑁 – namely, a combination of (𝛼, 𝑥𝑀𝐼𝑁), where the theoretical probability density function conforms to the empirical one. For each realized volatility series, we choose a parameter vector  α= (2.00,2.50,3.00,3.50) in association with the corresponding vector of  𝒙𝑀𝐼𝑁 (as observed in Fig. 2). Note that  αis arbitrarily chosen and covers the space in which we expect to find a combination of (𝛼, 𝑥𝑀𝐼𝑁)wherein the power law null hypothesis is not rejected. Then, for each combination pair (𝛼, 𝑥𝑀𝐼𝑁), as defined by (2.00, 𝑥𝑀𝐼𝑁, 𝛼=2.00),(2.50, 𝑥𝑀𝐼𝑁, 𝛼=2.50),(3.00, 𝑥𝑀𝐼𝑁, 𝛼=3.00), and (3.50, 𝑥𝑀𝐼𝑁, 𝛼=3.50), we determine its specific distance Dper equation (7) and then employ the goodness-of-fit test as detailed in Section 4.1. of Clauset et al. (2009, pp. 675–678). Under the null-hypothesis of this test, it is assumed that the data generating process follows a power law function with the corresponding combination (𝛼, 𝑥𝑀𝐼𝑁). Using a statistical significance level of 5%, we do not reject the power law null hypothesis if the p-value exceeds 5%.19 Using  α= (2.00,2.50,3.00,3.50) in association with the corresponding vector of  𝒙𝑀𝐼𝑁 in our tests allows us to identify whether each volatility series exhibits a mean and/or variance, i.e., the mean (variance) only exists for 𝛼 > 2(𝛼 > 3).20 Considering USDT as an illustrative example, we observe from Table 3 that for the combinations (𝛼 = 2.00, 𝑥𝑀𝐼𝑁 = 0.1011) and (𝛼 = 2.50, 𝑥𝑀𝐼𝑁 = 0.1487)the power law null hypothesis cannot be rejected, whereas the null hypothesis is rejected for (𝛼 = 3.00, 𝑥𝑀𝐼𝑁 = 0.1790)and (𝛼 = 3.50, 𝑥𝑀𝐼𝑁 = 0.3554). This result implies that between 𝛼 = 3.00 and 𝛼 = 2.50 it is possible to find a combination (𝛼, 𝑥𝑀𝐼𝑁)for which the power law null hypothesis cannot be rejected. Here our proposed approach works as follows: On the space 𝛼 ∈{2.5001,2.5002,…,2.9998,2.9999}with corresponding 𝑥𝑀𝐼𝑁, we iteratively determine for each corresponding combination pair (𝛼, 𝑥𝑀𝐼𝑁)its specific distance Das defined in Eq. (7) and then employ Clauset et al.’s goodness-of-fit test. Specifically, moving from the combination (𝛼 = 3.00, 𝑥𝑀𝐼𝑁 = 0.1790)to (𝛼 = 2.50, 𝑥𝑀𝐼𝑁 = 0.1487), we make use of trial-and-error attempts to search for the combination (𝛼, 𝑥𝑀𝐼𝑁)for which we cannot reject the power law null hypothesis the first time. For 19 As pointed out in Clauset et al. (2009), after estimating the KS statistic for each fit, a large number of power-law distributed synthetic data sets with (𝛼, 𝑥𝑀𝐼𝑁)equal to those of the distribution are generated. Each synthetic data set is individually fitted to its own power-law model, and the KS statistic is computed for each one relative to its own model. The fraction of time that the resulting statistic is larger than the value for the empirical data is counted, which is the corresponding p-value. 20 See Eq. (3). 213 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Table 3 Assessing the optimal power law exponent. Exponent/Cryptocurrency BTC USDT USDC DAI BUSD TUSD Panel A. Exponents and p-values. 2.00 1.0000 1.0000 0.9978 1.0000 1.0000 1.0000 2.50 1.0000 1.0000 0.0004 0.5029 0.9934 1.0000 3.00 0.9977 0.0000 0.0000 0.0090 0.0004 0.0170 3.50 0.7494 0.0000 0.0000 0.0469 0.0044 0.0000 Panel B. Exponents and xMIN values. 2.00 0.1824 0.1011 0.0895 0.1073 0.0954 0.0924 2.50 0.3591 0.1487 0.1318 0.1667 0.1414 0.1347 3.00 0.6947 0.1790 0.1579 0.2433 0.1699 0.1639 3.50 1.2846 0.3554 0.1864 0.3881 0.1882 0.1816 Panel C. Optimal estimates based on trial-and-error. 𝛼 3.4643 2.9024 2.3607 2.8699 2.8273 2.9123 𝑥𝑀𝐼𝑁 1.0950 0.1752 0.1224 0.2268 0.1595 0.1587 p-value 0.5027 0.3125 0.2325 0.0534 0.6000 0.6297 To find the optimal combination of 𝛼 and 𝑥𝑀𝐼𝑁 (i.e., the combination that is most likely to have generated the underlying stochastic process of the data), for each volatility series a parameter vector  𝜶= (2.00,2.50,3.00,3.50) is chosen in association with the corresponding vector of  𝒙𝑀𝐼𝑁 (see Fig. 2). Next, for each combination pair (𝛼, 𝑥𝑀𝐼𝑁),the specific distance Das defined in Eq. (7) is determined and then the goodness-of-fit test is employed as discussed in Section 4.1. of Clauset et al. (2009, pp. 675–678). Under the null-hypothesis of this test, it is assumed that the data generating process follows a power law with the corresponding combination (𝛼, 𝑥𝑀𝐼𝑁). Using a statistical significance level of 5%, the power law null hypothesis is not rejected if the p-value exceeds 5%. instance, in the case of USDT, we cannot reject the power law null hypothesis for the combination (𝛼 = 2.9024, 𝑥𝑀𝐼𝑁 = 0.1752), which results a p-value of 0.3125 for the goodness-of-fit test.21 In the same manner we evaluated the (𝛼, 𝑥𝑀𝐼𝑁)for USDC, DAI, BUSD, and TUSD. Next, analyzing the volatility process of BTC, we also observe from Table 3 that for any combination of (𝛼, 𝑥𝑀𝐼𝑁)the power law null hypothesis holds. Consequently, we can simply rely on the saddle point in the 𝛼∕𝑥𝑀𝐼𝑁-graph for BTC (see Fig. 1), which reaches the optimum for the combination (𝛼 = 3.4643, 𝑥𝑀𝐼𝑁 = 1.0950). Our findings have a number of important implications. First, since 𝛼 > 3, the volatility of BTC has both a theoretical mean and theoretical variance. In this regard, Taleb (2020, p. 50) noted: ‘‘If we don’t know anything about the fourth moment, we know nothing about the stability of the second moment. It means we are not in a class of distribution that allows us to work with the variance, even if it exists’’. The same holds for the variance of the variance or the variance of the volatility. If the second moment of a distribution does not exist, we know nothing about the stability of the first moment, such that we cannot make inference based on the mean even if it exists. Since Bitcoin volatility’s theoretical variance exists, the mean of Bitcoin’s volatility is stable. This finding has some important implications. For example, if the sample size is large enough, the mean of realized Bitcoin volatility converges towards its true value; hence, the mean is both computable and informative. This statistical stability is manifested in Bitcoin volatility’s power law exponent > 3. However, this outcome is obviously not the case for stablecoins. From Table 3 we observe that the second moments for none of the realized stablecoins’ volatilities exist. Infinite variances imply that the true mean of realized volatilities is unobservable in finite samples. This statistical instability is manifested in stablecoins volatilities’ power law exponents < 3. From a practical point of view, this statistical instability is manifested in huge spikes in the volatility processes for stablecoins (see Fig. 1), which become increasingly larger across time, even though their occurrence may be less frequent. Given the large literature on GARCH-type modeling of cryptocurrencies’ volatilities, it is reasonable to investigate the difference between GARCH models, realized volatilities, and power laws. Using a standard GARCH(1,1) model, which is often used as a benchmark model in empirical finance research, we employ the log-returns of cryptocurrency idenoted here as 𝑐𝑟𝑦𝑝𝑡𝑜𝑖and estimate the following model: 𝑐𝑟𝑦𝑝𝑡𝑜𝑖,𝑡 =𝑎𝑖+𝑒𝑖,𝑡, 𝜎2 𝑖,𝑡 =𝑏𝑖,0+𝑏𝑖,1𝑒2 𝑖,𝑡−1 +𝑏𝑖,2𝜎2 𝑖,𝑡−1, 𝑒𝑖,𝑡 =√𝜎2 𝑖,𝑡𝜖𝑖,𝑡, where 𝑎𝑖denotes the intercept for the mean equation, 𝑏𝑖,0,𝑏𝑖,1,𝑏𝑖,2denote the parameters for the variance equation, 𝑒𝑖,𝑡 denotes the residual term at time tfor the mean equation for 𝑐𝑟𝑦𝑝𝑡𝑜𝑖,𝑡, and 𝜎2 𝑖,𝑡 denotes the conditional variance at time t. This model can be estimated via MLE in which it is typically assumed that the innovation process 𝜖𝑖,𝑡 is distributed as normal, or 𝜖𝑖,𝑡 ∼𝑁(0,1). 21 For the goodness-of-fit tests, we make use of the Matlab code plpva written by Aaron Clauset. The code is available at http://www.santafe. edu/∼aaronc/powerlaws/. We thank Professor Clauset for making this code available. The Matlab script used to estimate the maximum likelihood functions is written by the present authors and available upon request. 214 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Fig. A.1. Kolmogorov–Smirnov distances depending on 𝒙𝑴𝑰𝑵 for Bitcoin volatility. We used maximum likelihood estimation (MLE) for the realized annualized daily volatility of Bitcoin and estimated 𝛼 as a function of 𝑥𝑀𝐼𝑁 as, 𝛼 = 1 + 𝑁(∑𝑁 𝑖=1 ln (𝑥𝑖 𝑥𝑀𝐼𝑁 ))−1, where 𝛼 denotes the MLE estimator, 𝑥𝑖is the realized annualized daily volatility of the respective cryptocurrency, provided 𝑥𝑖≥𝑥𝑀𝐼𝑁, and 𝑁denotes the number of observations for which 𝑥𝑖≥𝑥𝑀𝐼𝑁 is satisfied. Next, we employ the Kolmogorov–Smirnov approach to choose the optimal value for 𝑥𝑀𝐼𝑁. This statistic is simply the maximum distance Dbetween the data and fitted CDFs defined as, 𝐷=𝑀𝐴𝑋𝑥≥𝑥𝑀𝐼𝑁 |𝑆(𝑥)−𝑃(𝑥)|, where 𝑆(𝑥)is the CDF of the data for the observation with value at least 𝑥𝑀𝐼𝑁, and 𝑃(𝑥)is the CDF for the power law model that best fits the data in the region 𝑥≥𝑥𝑀𝐼𝑁. The estimate of the 𝑥𝑀𝐼𝑁 is the value of 𝑥𝑀𝐼𝑁 that minimizes D. In this figure we plot the empirical distribution of the Kolmogorov–Smirnov distance (y-axis) depending on the 𝑥𝑀𝐼𝑁 (x-axis). Fig. A.2. Empirical and theoretical density function at the optimum for Bitcoin volatility. Plot of the empirical density function for Bitcoin volatility on the y-axis and the theoretical density function for the power law model with (𝛼, 𝑥𝑀𝐼𝑁)= (3.4643,1.0950) on the x-axis. If the data fit was perfect, all observations would lie on the 45 degree line. the spillover index is 0.79. Since the spillover index is strictly above 0.50, we interpret this as evidence supporting our previous finding that the volatilities of our set of cryptocurrencies share a common factor. Notably, using one or two lags in the VAR model as additional robustness checks strongly supports our finding, that is, irrespective of which lag-order we use for the underlying VAR model specifications, there is strong evidence for a common factor that drives the volatilities. In view of earlier findings, we infer that the Bitcoin volatility is the common factor. 5. Conclusion This paper sought to investigate the volatility processes of stablecoins and their potential stochastic interdependencies with Bitcoin volatility. We employed an established measure of daily volatility using high, low, open, and closing prices for a number of cryptocurrencies. Our findings indicated that Bitcoin volatility is stable in the statistical sense that a theoretical variance exists. While Bitcoin volatility is relatively well-behaved, the volatilities of stablecoins are more erratic. For this reason, we cannot utilize Clauset et al.’s (2009) approach for estimating the power law exponent 𝛼 by using the value of 𝑥𝑀𝐼𝑁 that minimizes the (global) Kolmogorov–Smirnov distance. Instead, we proposed an alternative (local) approach that is based on trial-and-error to search for the parameter combination (𝛼,𝑥𝑀𝐼𝑁) for which the power law null hypothesis cannot be rejected. Our empirical results indicated the volatilities of stablecoins are statistically unstable due to infinite theoretical variances. Why are stablecoins unstable? Whereas Bitcoin is not pegged to any underlying, the stablecoins under study here are pegged to the U.S. dollar; hence the volatility of these cryptocurrencies is constrained. According to Taleb (2012, p. 106), if volatility is artificially suppressed, the system can become not only fragile but visibly reveal little or no risks even though such risks are latently growing. 221 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Fig. A.3. Kolmogorov–Smirnov distances depending on 𝒙𝑴𝑰𝑵 for DAI volatility. We used maximum likelihood estimation (MLE) for the realized annualized daily volatility of Dai and estimated 𝛼 as a function of 𝑥𝑀𝐼𝑁 as, 𝛼 = 1 + 𝑁(∑𝑁 𝑖=1 ln (𝑥𝑖 𝑥𝑀𝐼𝑁 ))−1, where 𝛼 denotes the MLE estimator, 𝑥𝑖is the realized annualized daily volatility of the respective cryptocurrency, provided 𝑥𝑖≥𝑥𝑀𝐼𝑁, and 𝑁denotes the number of observations for which 𝑥𝑖≥𝑥𝑀𝐼𝑁 is satisfied. Next, we employ the Kolmogorov–Smirnov approach to choose the optimal value for 𝑥𝑀𝐼𝑁. This statistic is simply the maximum distance Dbetween the data and fitted CDFs defined as, 𝐷=𝑀𝐴𝑋𝑥≥𝑥𝑀𝐼𝑁 |𝑆(𝑥)−𝑃(𝑥)|, where 𝑆(𝑥)is the CDF of the data for the observation with value at least 𝑥𝑀𝐼𝑁, and 𝑃(𝑥)is the CDF for the power law model that best fits the data in the region 𝑥≥𝑥𝑀𝐼𝑁. The estimate of the 𝑥𝑀𝐼𝑁 is the value of 𝑥𝑀𝐼𝑁 that minimizes D. In this figure we plot the empirical distribution of the Kolmogorov–Smirnov distance (y-axis) depending on the 𝑥𝑀𝐼𝑁 (x-axis). Fig. A.4. Empirical and theoretical density function at the KS optimum for DAI volatility. Plot of the empirical density function for DAI volatility on the y-axis and the theoretical density function for the power law model with (𝛼, 𝑥𝑀𝐼𝑁)= (4.0077,0.0708) on the x-axis. If the data fit was perfect, all observations would lie on the 45 degree line. Fig. A.5. Empirical and theoretical density function at the trial-and-error optimum for DAI volatility. Plot of the empirical density function for DAI volatility on the y-axis and the theoretical density function for the power law model with (𝛼, 𝑥𝑀𝐼𝑁)= (2.8699,0.2268) on the x-axis. If the data fit was perfect, all observations would lie on the 45 degree line. 222 K. Grobys, J.P. Junttila, J.W. Kolari et al. Journal of Empirical Finance 64 (2021) 207–223 Next, we found that Bitcoin volatility exhibits volatility spillover effects on stablecoins in a Granger-sense. Previous work by Lyons and Viswanath-Natraj (2019) found that on average an increase in the volatility of Bitcoin trading had a positive effect on the Tether price that was particularly pronounced in turbulent periods. Extending their analyses, our study examined interdependencies in the second moment and found a negative relation in the volatility processes — that is, as lagged Bitcoin volatility decreases, the volatilities of stablecoins (including Tether) tends to increase. This effect was statistically significant across different stablecoins. Based on our empirical results, we conclude that Bitcoin volatility is a fundamental factor that drives the volatilities of stablecoins. Since our research showed that our models explain, on average, about half of the variation of the realized stablecoin volatilities, what remaining forces drive stablecoin volatility? Further research is recommended on the identification of sources of cryptocurrency uncertainty that drive this process. Also, future research is encouraged to elaborate more on the negative relationship between lagged Bitcoin volatility and stablecoin volatility. CRediT authorship contribution statement Klaus Grobys: Conceptualization, Data, Methodology, Software, Writing - original draft, Validation. Juha Junttila: Supervision, Writing - review & editing, Methodology, Validation. James W. Kolari: Supervision, Writing - review & editing. 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