1. Introduction
In the midst of the global financial crisis of 2008, Satoshi Nakamoto published the Bitcoin project. The white paper by Nakamoto [
1] described a digital currency based on a sophisticated peer-to-peer (p2p) protocol that allowed online payments to be sent directly to a recipient without going through a financial institution. At that time, a potential nonsovereign asset fully decentralized and isolated from the uncertainties of a specific country or market was presented as a great value proposition [
2], which took even more value, if possible, during the European sovereign debt crisis of 2010–2013 [
3]. Thus, in 2013, the popularity of cryptocurrencies clearly increased. The market capitalization closed the year exceeding USD 10 billion and the price of Bitcoin reached over a thousand dollars [
4,
5]. Thereafter, the cryptocurrency market size and the Bitcoin price have not stopped growing. In January 2018, capitalization peaked at over USD 800 billion [
6] and, in December 2017, Bitcoin’s price had reached close to USD 20,000, a revaluation to 2700% in 2017 alone [
5]. Although, in September 2018, the cryptocurrencies market had lost 80% of its value and, at the end of the year, Bitcoin closed below USD 6 thousand, charting a market pattern of extreme price instability far removed from those of sovereign currencies [
7,
8]. In any case, since the launch of Bitcoin, cryptocurrencies have become a social and economic trending topic and the blockchain technology, that supports it, in one of the main disruptive innovations [
9,
10].
As of December 2020, there are more than 8265 cryptocurrencies with a market value of around USD 750 billion and a daily trading volume around USD 180 billion, with Bitcoin’s market share being 69.2% [
11].
At this point, the importance of Bitcoin as a new financial asset is obvious, as well as the controversy generated about its nature among market practitioners, academics, and in the economics press [
12,
13]. Particularly, in the financial literature, there is an intense debate about what type of asset Bitcoin is and what its real usefulness is. Thus, references such as [
14,
15,
16,
17,
18,
19] literally ask if it is really a currency, or others analyze its qualities as safe havens [
20]. In this sense, although references such as [
14,
15] recognize some potential for Bitcoin to function as a currency, the common denominator of the literature on Bitcoin is to define it as a speculative investment with extreme volatility and a large average return [
16,
17,
18,
19]. In any case, Bitcoin is an investable asset [
21] whose diversifying factor and high return potential motivate the attention of investment portfolio managers. Consequently, the interest of the Bitcoin analysis goes beyond a normalization of what type of asset it is, but rather a clear definition of its main attributes as an alternative investment, that is: Liquidity, risk, and return.
In the recent literature, some research has tried to understand how Bitcoin’s liquidity is explained [
22,
23] and how efficient its market is [
24,
25,
26,
27,
28,
29]. However, if there is one aspect that has defined the Bitcoin market since its launch, it is the strong volatility it presents.
As Yu [
30] indicates, volatility plays an important role in asset pricing, portfolio allocation, or risk management. Therefore, its forecasting and modelling have received special attention from the scientific community; see the reviews of Zhang and Li [
31] and McAleer and Medeiros [
32]. However, the study of the dynamic Bitcoin volatility is still an emerging line of research with some gaps still to fill. The subject has been treated from different perspectives; among others, Baek and Elbeck [
18] analyze the Bitcoin relative volatility using detrend ratios with economic variables such as the Standard and Poor 500 (SP500) Index to underline its high speculation; Balcilar et al. [
33] find that the volume can predict the Bitcoin returns (except in bear and bull market regimes); Bariviera [
34] tests the presence of long memory in Bitcoin return time series, and on this basis [
35], justifies the application of Generalized Autoregressive Conditional Heteroskedasticity (GARCH)-type models [
36,
37]. Furthermore, the variability in Bitcoin volatility, alternating periods of extreme volatility with others of relative calm, indicates that the bitcoin price is suitable for GARCH modeling [
36]. Thus, Dyhrberg [
38] uses GARCH(1,1)—methodologically tested by Engle and Manganelli [
39]—as a starting point to analyze the volatility of Bitcoin in relation to gold and the dollar. Recent research has used this univariate GARCH model as a benchmark to analyze and compare the volatility estimate of Bitcoin [
40,
41,
42,
43,
44]. Although, as found in references such as [
45,
46,
47,
48], the Multivariate GARCH (MGARCH) approach [
49] allows the model to test the sensitivity of Bitcoin with respect to variables of the economic and financial environment, improving the robustness in general terms.
More specifically, the application of nonlinear combinations of univariate GARCH models suggests suitable results in determining the conditional covariances of cryptocurrency volatility models. Thus, conditional correlation (CC) models have been applied by Chan et al. [
45] in the Constant variant (CCC) and Kumar and Anandarao [
46], Guesmi et al. [
47], and Kyriazis et al. [
48] in the Dynamic (DCC) [
50] to study the Bitcoin volatility. Meanwhile, according to the literature review, the CC special case, that is, Varying (VCC) MGARCH [
51], has not yet been tested in the cryptocurrencies context.
Therefore, starting from the GARCH(1,1) model as a benchmark, the main objective of this study is to model and assess the relationship between the Bitcoin volatility and key financial environment variables applying the three variants of the Conditional Correlation M-GARCH approach.
The nature of Bitcoin evolves as the cryptocurrency market matures and the critical mass of investors increases. Thus, this research contributes to the existing literature, first in the construction of the models. Thus, CC-MGARCH models have been developed combining traditional financial variables (such as the main commodities, exchange rates, or indices), market benchmarks on blockchain technology, and means of payment such as Visa and Mastercard. On the one hand, this has made it possible to evaluate the Bitcoin connection with variables not yet tested. On the other, the correlation outcomes of the financial environment variables allow us to weigh the diversifying factor of Bitcoin and its usefulness as a safe haven asset. Second, the modeling of the three variants of the CC-MGARCH model makes it possible to measure how the volatility of Bitcoin behaves better, if with a constant or dynamic conditional correlation.
To do this, the daily prices of Bitcoin from the beginning of 2016 to the end of 2018 and the time series of the exogenous financial and economic variables on which the MGARCH models are based have been extracted from the Datastream® database.
The results of this research reveal that a better fit of the time-varying conditional correlation model is found compared to the constant. Like this, the DCC-MGARCH approach presents as best performing. The special case of the VCC model is also presented as a good candidate to explain the price movements and volatility of cryptocurrencies. In the same way, a certain heterogeneity in the fit of the different variables is shown, highlighting an uncorrelation with respect to traditional safe haven assets such as gold and oil. On the other hand, although a better fit is observed in the MGARCH models than in the standard GARCH model, the statistical analysis of precision confirms that GARCH(1,1) continues to be presented as a suitable alternative to model the Bitcoin volatility.
The rest of the paper is structured as follows. In
Section 2, the literature review on the financial nature of Bitcoin and the forecast of its volatility is expanded.
Section 3 presents the data sample used and the models developed. In
Section 4, the main results of our research are described. Finally,
Section 5 summarizes the key conclusions and contributions of this study.
2. Literature Review
The technological development of Bitcoin is supported on two key elements: Blockchain and mining. The blockchain is a smart combination of technologies such as p2p, timestamp, or cryptography, which build a data structure grouped in blocks, whose information can only be updated with the consensus of the system participants and can never be erased [
1,
9]. In practice, it results in an irrefutable and verifiable ledger of all transactions. However, as Crosby et al. [
10] indicate, the blockchain goes beyond Bitcoin. Thus, Ali et al. [
52] present a systematic review of academic research on the benefits and paradigm shift that the integration of blockchain technology in the financial sector is assuming. On the other hand, Bitcoins must be “mined” [
53]. In essence, when a network of advanced computers solves an algorithm, it is rewarded with the Bitcoin units being mined; every 10 min, new coins are put into circulation [
1]. Satoshi Nakamoto defined a limited stock of 21 million coins, so that around the year 2140, the issuance of Bitcoin would be completed. Through this cryptocurrency mining process, the Bitcoin developers establish a controlled currency issuance system inspired by the fixed supply of gold [
17].
But is Bitcoin a commodity or a currency? As indicated in previous lines, it is still an open debate. As Bouri et al. [
20] point out, cryptocurrencies were presented as a panacea that covered the weaknesses of the financial system at times such as the sovereign debt crisis of 2010–2013 or the Cypriot banking crisis of 2012–2013 [
54]. Although, Bitcoin has not fulfilled its function as a currency, in a strict sense [
17]. Yermack [
17] performs an analysis of the Bitcoin deviations regarding the roles that a currency has to fulfill, that is, medium of exchange, unit of account, and store of value. The author points out a series of form problems in its operative, such as the unorthodox decimal price, delays in verifying transactions, or the acquisition process, among others, that limit Bitcoin to a payment method. In any case, he concludes that, in order for Bitcoin to function as a store of value and unit of account, its price must be more stable, since its volatility is more representative of the behavior of a speculative investment. In this same sense, Baur et al. [
7] define Bitcoin as a speculative and uncorrelated asset and not as an alternative medium of exchange. There are other studies that classify it as a hybrid techno-financial instrument [
19] or suggest that Bitcoin behaves as an asset between currency-fiat and a crypto-commodity used for commercial and investment purposes [
55].
In regulatory terms, under International Financial Reporting Standards (IFRS), the International Financial Reporting Interpretation Committee (IFRIC) transmitted to the International Accounting Standards Board (IASB) that cryptocurrencies are not financial assets or legal tender, but rather intangible assets and not monetary [
56]. Under the Commodity Exchange Act (CEA), Bitcoin is a commodity for the US Commodity Futures Trading Commission (CFTC). Thus, future contracts with Bitcoin as an underlying asset have been traded in the Chicago Board Options Exchange (CBOE) or the Chicago Mercantile Exchange (CME) [
57]. In this regard, Selgin [
58] points out that Bitcoin has characteristics common to commodities and that it could be considered as synthetic commodity money. Like gold, Bitcoin offers an implicit return and presents some of the essence of traditional commodities; it is an exhaustible resource with a fixed supply [
41,
56]. However, Gronwald [
41] finds that Bitcoin’s price dynamics are particularly influenced by extreme price movements due to shocks to its demand. The study supports this differentiation in the immaturity of Bitcoin and, especially, in its certain and programmed supply against an uncertain short-term supply of gold and oil. In this sense, although the design of Bitcoin has been influenced by gold, it has less liquidity, its transactions are more complex and, above all, it is much more volatile [
59].
Focusing on gold and its diversification, hedging, and safe haven properties [
60], numerous academic studies have tried to contrast these same qualities in Bitcoin, and the conclusions have varied depending on the intensity of the stress scenario and the nature of the assets. Moreover, Urquhart and Zhang [
61] define Bitcoin as a reasonable haven against sovereign currencies; Wang et al. [
62] reach the same conclusions regarding the assets of the Chinese financial market; and Dyhrberg [
63] indicates that it has the capacity to hedge positions on the Financial Times Stock Exchange (FTSE) Index and the US dollar. Selmi [
64] places Bitcoin at the same level as gold as a safe haven and diversifier of the oil price. However, despite Bitcoin’s weak correlation with traditional financial assets, some studies analyzed coincide in describing it as poor coverage as a safe-haven value in times of strong stress [
65,
66,
67]. This weakness has been confirmed by Conlon et al. [
68] in the COVID-19 crisis; Bitcoin’s extreme volatility hinders its usefulness as a safe haven and even motivates that, paradoxically, it needs a stable coin as the Tether to cover itself [
68]. In any case, studies such as that of Brieri et al. [
65] show that a small weighting of Bitcoin can improve the risk–return trade-off of well-diversified portfolios; and others such as that of Ghabri et al. [
69] observe that Bitcoin can lower the liquidity risk in the portfolio, under the Mean-Variance-Liquidity framework.
By consequence, inhibiting—for the time being—its usefulness as a currency or safe haven, its diversifying factor and high return potential motivate the interest of investment portfolio managers [
7,
16]. For that purpose, the volatility modeling has focused attention. Volatility is an important measure of market risk and, therefore, a crucial element on investors’ decision-making in portfolio management [
70]. In academic research, the work of Andersen and Bollerslev [
71] signified a point of reference from which significant contributions have been made to model and forecast volatility using high-frequency data [
30]. Thus, the study of volatility is a mature research topic [
31,
32], although the modelling of the cryptocurrency’s volatility is a keyword with many gaps yet to be resolved.
In recent years, under the long memory assumption [
34,
35], a line of research has emerged focused on the development of GARCH-type models to explain and forecast the volatility of Bitcoin and of the cryptocurrencies, in general. Thus, the GARCH(q,m) model of Bollerslev [
36] has been taken as a benchmark [
44]. In one of the first works, Glaser et al. [
16] successfully apply the standard GARCH(1,1) to determine through the modeling of Bitcoin´s volume and price that the investors’ intention when changing their national currency to digital is not to seek an alternative transaction system, but an alternative investment vehicle. In this line, Ardia et al. [
40] show that the Markov-switching GARCH (MS-GARCH) models improve the results of the single-regime for Bitcoin Value-at-Risk (VaR) forecasting. For his part, Gronwald [
41] compares the GARCH(1,1) with various linear and nonlinear GARCH approaches to model the extreme price movements of Bitcoin. On the other hand, Hung et al. [
42] incorporate jump-robust-realized measures into the simple GARCH model, obtaining a better forecast performance for Bitcoin volatility with the RGARCH(1,1) model built. Furthermore, Trucíos [
43] starting from GARCH(1,1), carried out a profuse comparative of the Bitcoin volatility forecast applying different extensions of the several classical GARCH-type models. The author suggests the use of the generalized autoregressive score (GAS), particularly the t-GAS model [
72], to forecast the volatility in the absence of high-frequency data. Other comparative studies, such as those of Katsiampa [
35] and Conrad et al. [
73], have also taken the simple GARCH models as the initial basis for forecasting Bitcoin movements.
Although the GARCH(1,1) model is presented as a suitable reference point, the development of MGARCH models (see [
37,
49]) can offer a superior capacity by allowing the integration of the relationships between the volatility processes of various time series with Bitcoin [
46]. Chan et al. [
45] analyze the hedging and diversification capacity of Bitcoin against stock indices such as the Euro STOXX, Nikkei, Shanghai A-Share, S&P 500, and the TSX index. To carry out their study, the authors use the GARCH(1,1), Constant Conditional Correlation (CCC) of Bollerslev [
74], and the Dynamic Conditional Correlation (DCC) based in Engle [
50], among others, models. The standard GARCH model and the CCC-MGARCH offer a significant fit and consistent results. Although, the study reveals a nonconvergence of the DCC model, especially for the monthly frequency data, and does not improve its logarithmic probability with respect to the CCC model. By contrast, Kumar and Anandarao [
46] selected the DCC-MGARCH model to study the dynamics of the volatility spill of four cryptocurrencies, due to its ability to capture time-varying conditional-correlations and covariances. Similarly, Guesmi et al. [
47] and Kyriazis et al. [
48] successfully support the DCC process to explain the proprieties of Bitcoin in the financial markets and its relationship with other cryptocurrencies.
In this sense, the DCC-MGARCH models and the VCC-MGARCH model of Tse and Tsui [
51] allow time-varying conditional correlations that can provide a better understanding of the dynamic structure of the conditional correlations [
75]. Although the VCC-MGARCH offers suitable results in the forecast of the volatility of several commodities [
76], no evidence has been found that the variable conditional correlation model has been tested in Bitcoin modeling.
Based on the review literature and on the Bitcoin time-series continuing to build and mature, this research contributes to the existing discussion in several ways. First, the outcomes of the developed models show an additional perspective on the degree of correlation of Bitcoin with the traditional benchmark of the financial market, calibrating its diversification factor. Likewise, in the structure of the models the relationship between the movements of Bitcoin returns and previously untested variables is integrated, but with a possible coherent connection. Second, taking GARCH(1,1) as a starting point, the adequacy and adjustment of the multivariate GARCH models CCC, DCC, and VCC are analyzed to model the volatility of Bitcoin.
4. Results
Table A1 of the
Appendix A shows the bivariate correlations between the price returns of each variable. If the correlation coefficients between Bitcoin and the different assets are observed, it is noted that technology companies such as RIOT (0.689 *), KBR (0.783 **), or NVDA (0.977 **) and electronic payment methods like VISA (0.831 **) are those that seem to be more related to cryptocurrency. This previous analysis helps to select the financial variables to consider for the construction of the multivariate models.
Table 2 shows the conditional correlations between the returns of each of the variables with those of Bitcoin.
As expected in view of the bivariate correlation table, the commodities GOLD and OIL present a nonsignificant conditional correlation. The stock markets indices, SP500 and NIKKEI, with a negative correlation, are not significant in any of the MGARCH models. The USD/EUR exchange rate is also uncorrelated with the Bitcoin returns. On other hand,
Table 3 shows the results obtained in the GARCH(1,1) and
Table 4 describes the outcomes obtained in the three variants of the MGARCH model, using the RIOT Blockchain, VISA, MAST, NVDA, and KBR price returns as independent variables. The MAST correlation (0.578), although not significant, when introduced in the model gives us quality in the results. All
z coefficients are significant in each of the variables considered, both their ARCH and GARCH components, and in the constant term.
In the CCC and VCC variants, they are all significant. In DCC, Bitcoin returns are not significantly correlated with the MASTERCARD variable. As mentioned in the previous paragraph, this variable has been included to improve the quality of the model. In summary, in view of the results and observing the fit of the model (λ), which is significant in DCC and CCC and the AIC and BIC scores although similar, it can be determined that, theoretically, the model that best fits the data is the dynamic model.
In addition,
Table 5 shows the comparison between the quality of the predictions of the MGARCH models and the GARCH(1,1) model. The forecast precision statistics for the developed models do not present notable differences, the smallest difference being the DCC-MGARCH model. The results of the DM test indicate that a greater difference in the precision of the prediction of the GARCH(1,1) model respects each of the variants of the MGARCH approach. Focusing on the MGARCH, the dynamic correlation models—DCC and VCC—improve the test of the constant correlation—CCC—model.
5. Discussion
In the framework of the academic discussion on the nature of Bitcoin, this work has attempted to explain the relationship between the volatility of Bitcoin and those of several key financial variables. For the development of the models, the study has focused on the Conditional Correlation MGARCH approach. However, like authors such as [
40,
41,
42,
43,
44], GARCH(1,1) has been taken as a starting point. In this way, the work coincides with previous studies by defining the GARCH standard model as a suitable alternative for Bitcoin modeling, although it does not reach the efficiency presented by the CCC, DCC, and VCC MGARCH models. Therefore, based on our results, the application of CC-MGARCH models is presented as a suitable alternative to model the volatility of Bitcoin.
The models developed have the ability to predict the volatility of Bitcoin, though the adjustment of each of the financial environment variables tested offers disparate outcomes regarding the significance of its correlation with the cryptocurrency. Thus, in the correlation analysis, it is observed that the Bitcoin volatility is inversely correlated with that of USD/EUR in each of the multivariate models examined. The commodities considered in the study, gold and oil, show a nonsignificant correlation. The volatility of the stocks of companies linked to blockchain technology—RIOT, NVDA, and KBR—and those of payments methods—VISA and MASTERCARD—present a clear and significant conditional correlation with that of the cryptocurrency. Connecting these variables with Bitcoin models can help build more accurate models.
In the comparative study between the three variants of Multivariate GARCH models, that is, CCC, DCC, and VCC, it is observed that the BIC and AIC scores of each of them are very similar, although the DCC suggests the best fit. When the models are evaluated in a practical way through the RMSE, MAE, MAPE, and Diebold–Mariano test, two conclusions are reached. In multivariate models, the forecast accuracy statistics are very similar, although the lowest error between the real and the estimated variance of DCC and VCC models is evidenced.
In the context of Bitcoin, the finding of this research confirms the most realistic hypothesis of time-varying conditional correlation over versus constant-correlation. In any case, the still insufficient maturity of the time-series of this asset means that the study of Bitcoin modeling remains open.