Simone Casale-Brunet, Paolo Ribeca, Patrick Charles Doyle, Marco Mattavelli
Non-fungible tokens (NFTs) as a decentralized proof of ownership represent one of the main reasons why Ethereum is a disruptive technology. This paper presents the first systematic study of the interactions occurring in a number of NFT ecosystems. We illustrate how to retrieve transaction data available on the blockchain and structure it as a graph-based model. Thanks to this methodology, we are able to study for the first time the topological structure of NFT networks and show that their properties (degree distribution and others) are similar to those of interaction graphs in social networks. Time-dependent analysis metrics, useful to characterize market influencers and interactions between different wallets, are also introduced. Based on those, we identify across a number of NFT networks the widespread presence of both investors accumulating NFTs and individuals who make large profits.
Barbara Będowska-Sójka, Agata Kliber, Aleksandra Rutkowska
We try to establish the commonalities and leadership in the cryptocurrency markets by examining the mutual information and lead-lag relationships between Bitcoin and other cryptocurrencies from January 2019 to June 2021. We examine the transfer entropy between volatility and liquidity of seven highly capitalized cryptocurrencies in order to determine the potential direction of information flow. We find that cryptocurrencies are strongly interrelated in returns and volatility but less in liquidity. We show that smaller and younger cryptocurrencies (such as Ripple's XRP or Litecoin) have started to affect the returns of Bitcoin since the beginning of the pandemic. Regarding liquidity, the results of the dynamic time warping algorithm also suggest that the position of Monero has increased. Those outcomes suggest the gradual increase in the role of privacy-oriented cryptocurrencies.
Risk management and prediction of market losses of cryptocurrencies are of notable value to risk managers, portfolio managers, financial market researchers and academics. One of the most common measures of an asset’s risk is Value-at-Risk (VaR). This paper evaluates and compares the performance of generalized autoregressive score (GAS) combined with heavy-tailed distributions, in estimating the VaR of two well-known cryptocurrencies’ returns, namely Bitcoin returns and Ethereum returns. In this paper, we proposed a VaR model for Bitcoin and Ethereum returns, namely the GAS model combined with the generalized lambda distribution (GLD), referred to as the GAS-GLD model. The relative performance of the GAS-GLD models was compared to the models proposed by Troster et al. (2018), in other words, GAS models combined with asymmetric Laplace distribution (ALD), the asymmetric Student’s t-distribution (AST) and the skew Student’s t-distribution (SSTD). The Kupiec likelihood ratio test was used to assess the adequacy of the proposed models. The principal findings suggest that the GAS models with heavy-tailed innovation distributions are, in fact, appropriate for modelling cryptocurrency returns, with the GAS-GLD being the most adequate for the Bitcoin returns at various VaR levels, and both GAS-SSTD, GAS-ALD and GAS-GLD models being the most appropriate for the Ethereum returns at the VaR levels used in this study.
Yuzhi Cai, Thanaset Chevapatrakul, Danilo V. Mascia
Abstract We shed light on how the price explosivity characterising Bitcoin and other major cryptocurrencies is triggered, by employing the Quantile Self-Exciting Threshold Autoregressive (QSETAR) model. Our results for Bitcoin, Ripple, and Stellar reveal that the explosive behaviour originates from the extreme upper tails of the return distributions following a price increase in the preceding day. We do not find evidence of explositivity in the price of Litecoin.
In this study, we predicted the log returns of the top 10 cryptocurrencies based on market cap, using univariate and multivariate machine learning methods such as recurrent neural networks, deep learning neural networks, Holt’s exponential smoothing, autoregressive integrated moving average, ForecastX, and long short-term memory networks. The multivariate long short-term memory networks performed better than the univariate machine learning methods in terms of the prediction error measures.
In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.
More and more people are entering the cryptocurrency market after Bitcoin (BTC) soared to nearly USD 20,000 in 2017. To promote the development of information technology and cryptocurrency marketing, various computerized systems integrating information technology with investment and financing are innovated continuously. In this study, the daily cryptocurrency prices were input to Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM); and the developing trend plots were drawn to predict and analyze the future cryptocurrency prices through deep learning. Finally, the business practices of cryptocurrency investment were modularized based on High-Level Fuzzy Petri Nets (HLFPNs) to make a better investment decision so that all investors can use this decision system to quickly understand the future cryptocurrency trend. The experimental results have shown that this decision system can provide effective investment information to achieve investors’ personal financial goals with the expectation of improving financial situations.
The clustering of cryptocurrencies - as an emerging field in investment management - is the main topic of this research. Applying the information-based distance matrices, we clustered the 30 most valuable cryptocurrencies. Then, we identified the most influential clustering by the concept of Minimum Spanning Tree (MST) and the centrality measures of graph theory. A second-order clustering, which is defined as the clustering of hierarchical clusterings, is applied to cluster 56 dendrograms. Using the most influential clustering, we identified the main clusters of cryptocurrencies and sub-clusters. The results show that the clustering composition of cryptocurrencies changed at the period I (before COVID-19) and II (pandemic time).
Sep 30, 2021·Vestnik Voronezhskogo gosudarstvennogo universiteta Ser Ekonomika i upravlenie = Proceedings of Voronezh State University Series Economics and Management
Dmitry А. Endovitsky, Вячеслав Владимирович Коротких
Introduction. Digital financial assets are a relatively new phenomenon. More and more, they include virtual currencies, and in particular cryptocurrencies. Both regulators and financial market players are becoming increasingly interested in such assets. Cryptocurrencies have no intrinsic value, and this encourages scientific studies on the problem of price formation and risk management associated with cryptocurrency operations. Most papers on the problem lack a systematic ap-proach and do not provide solutions to a large number of fundamental issues. Purpose. The purpose of our study was to develop a method for the risk analysis of operations with digital financial assets, namely cryptocurrencies. Methodology. In our study, we used parametric methods of data analysis and ma-chine learning methods, description, analysis, synthesis, induction, deduction, comparison, and grouping method. The sample was accumulated between April 2013 and April 2021 and included cryptocurrencies with the market capitalization of over 1 million USD. Results. The study determined the common risk factors for the cryptocurrency market. The risk factors are presented as linear combinations of returns of subsets of cryptocurrencies with dynamically changing weight coefficients. The risk factors were formed based on the market information, which included the price of the cryptocurrency, the trading volume, and its market capitalization. Conclusions. The study demonstrated that the cryptocurrency market is suscepti-ble to market anomalies common to traditional financial asset markets. In addition to the risk factors based on the market capitalization of cryptocurrencies (the size) and their aggregate profitability (the momentum), the article presents statistically relevant risk factors which reflect the growth rate of the market capitalization and the level of illiquidity of cryptocurrencies. In order to explain the market anomalies and the arbitrary strategies based on them, the article presents several factor models of cryptocurrency price formation. These models can be used to develop an in-tegrated approach to the risks associated with operations with digital financial assets.
The paper is devoted to studying the bitcoin blockchain as a new global phenomenon in monetary economics, which requires comprehending from the economic theory view - a self-regulating system of decentralized emission without participation of a central monetary authority. Mathematical modelling is the instrument of this studying. The author has analyzed the Bitcoin system parameters that determine dynamics of a self-regulating emission mechanism. This mechanism operates in a peer-to-peer computer network and provides a smooth increasing of the "money supply" with a gradually decreasing rate of growth. The limit of this growth is determined by maximal volume 21 million BTC. Self-regulation is implemented through negative feedback between changes of control parameters (the target interval for the hash function values and the Bitcoin Difficulty level) and the speed of mining process. Control parameters depend on the real speed deviations from the target value. This mechanism provides a stable mining speed and determines annual rate of emission. The author suggests a spline-function for describing the annual rate of the cryptocurrency emission in accordance with the Proof-of-Work protocol in the Bitcoin blockchain algorithm. This spline-function gives possibility to find a monetary rule for annual rate of emission. The author in the paper proposes to call this monetary rule by the name of the Bitcoin system inventor - Nakamoto Monetary Rule. The Nakamoto Monetary Rule could be seen as the first example of a programmable monetary rule of the decentralized emission algorithm on the basis of blockchain technology. Central banks could use a similar approach, with the necessary modifications, to develop their programmable monetary rules for Central Bank Digital Currencies (CBDCs) emission based on DLT or blockchain technology
The blockchain technology introduced by bitcoin, with its decentralised peer-to-peer network and cryptographic protocols, provides a public and accessible database of bitcoin transactions that have attracted interest from both economics and network science as an example of a complex evolving monetary network. Despite the known cryptographic guarantees present in the blockchain, there exists significant evidence of inconsistencies and suspicious behavior in the chain. In this paper, we examine the prevalence and evolution of two types of anomalies occurring in coinbase transactions in blockchain mining, which we reported on in earlier research. We further develop our techniques for investigating the impact of these anomalies on the blockchain transaction network, by building networks induced by anomalous coinbase transactions at regular intervals and calculating a range of network measures, including degree correlation and assortativity, as well as inequality in terms of wealth and anomaly ratio using the Gini coefficient. We obtain time series of network measures calculated over the full transaction network and three sub-networks. Inspecting trends in these time series allows us to identify a period in time with particularly strange transaction behavior. We then perform a frequency analysis of this time period to reveal several blocks of highly anomalous transactions. Our technique represents a novel way of using network science to detect and investigate cryptographic anomalies.
Adam Zaremba, Mehmet Hüseyin Bilgin, Huaigang Long, Aleksander Mercik · 5 authors
We demonstrate a new powerful predictive signal for cryptocurrency returns: the last day's return. Based on daily prices of more than 3600 coins, we document that the cryptocurrencies with low last day's return significantly outperform their counterparts with high last day's return. The effect is confirmed by a battery of cross-sectional tests and portfolio sorts, and is not subsumed by a broad range of other return predictors. We argue that the daily reversals result from the illiquidity of the vast majority of traded cryptocurrencies. In consequence, the pattern is cross-sectionally dependent on liquidity, and the handful of largest and most tradeable coins exhibit daily momentum rather than a reversal. Our findings help to reconcile earlier conflicting evidence on return persistence in cryptocurrency markets.
Abootaleb Shirvani, Stefan Mittnik, W. Brent Lindquist, Svetlozar T. Rachev
We propose a doubly subordinated Levy process, NDIG, to model the time series properties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed properties of bitcoin prices and gives rise to an arbitrage free, option pricing model. In this framework we derive two bitcoin volatility measures. The first combines NDIG option pricing with the Cboe VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both are compared to a volatility based upon historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures observed, in-sample, volatility.
In this paper we extend the analysis of an agent-based model for adaptive trading, called asynchronous stochastic price pump (ASPP) introduced by Perepelitsa and Timofeyev (2019), to the model with heterogeneous distribution of psychological parameters of speculative optimism and pessimism across the population of traders. We show that the new model has a range of qualitatively different dynamics when the correlation between those factors ranges from low negative to large positive values. A statistical parameter estimation suggests a heterogeneous ASPP with negative correlation as a model of price variations of Bitcoin.
We study recurrent patterns in volatility and volume for major cryptocurrencies, Bitcoin and Ether, using data from two centralized exchanges (Coinbase Pro and Binance) and a decentralized exchange (Uniswap V2). We find systematic patterns in both volatility and volume across day-of-the-week, hour-of-the-day, and within the hour. These patterns have grown stronger over the years and can be related to algorithmic trading and funding times in futures markets. We also document that price formation mainly takes place on the centralized exchanges while price adjustments on the decentralized exchanges can be sluggish.
Non-linear interactions between cryptocurrency price movements can elicit cross-frequency coupling (CFC) wherein one set of frequencies in the 1st timeseries is coupled to another set of frequencies in the 2nd timeseries. To investigate this, we use a generalized coherence approach to detect and quantify both linear (i.e., iso-frequency coupling, IFC) and non-linear coherence (CFC) and the associated phase relationships between the intra-day price changes of various pairs of cryptocurrencies for the year 2020. Using this information, we further assess the risk reduction associated with diversification of portfolios between each pair of a small market capital and a large market capital cryptocurrency, for both synchronous and asynchronous trading conditions. While mean pairwise IFC values were lower for smaller cryptocurrencies, pairwise CFC values were more heterogeneous and had no correlation with the market capital size. Diversification of portfolios resulted in reduced risk for synchronously-traded pairs of those cryptocurrencies which had low IFC. For asynchronous trading conditions, if the larger market capital cryptocurrency was traded at a higher frequency, diversification almost always reduced risk. Thus, the novel approach used in this study reveals important insights into the complex dynamics that govern the price trends of cryptocurrencies.
We review different classes of cryptocurrencies with emphasis on their economic properties. Pure-asset coins such as Bitcoin, Ethereum and Ripple are characterized by not being a liability of any economic agent and most resemble commodities such as gold. Central bank digital currencies, at the other end of the economic spectrum, are liabilities of a Central Bank and most resemble cash. In between, there exist a range of so-called stable coins, with varying degrees of economic complexity. We use balance sheet operations to highlight the properties of each class of cryptocurrency and their potential uses. In addition, we propose the basic structure for a macroeconomic model incorporating all the different types of cryptocurrencies under consideration.
The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics from the past bull market in 2017 to the present the COVID-19 pandemic. To confirm the evolutionary complexity of the cryptocurrency market, three general complexity analyses based on nonlinear measures were used: approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ). We analyzed the market complexity/unpredictability for 43 cryptocurrency prices that have been trading until recently. In addition, three non-parametric tests suitable for non-normal distribution comparison were used to cross-check quantitatively. Finally, using the sliding time window analysis, we observed the change in the complexity of the cryptocurrency market according to events such as the COVID-19 pandemic and vaccination. This study is the first to confirm the complexity/unpredictability of the cryptocurrency market from the bull market to the COVID-19 pandemic outbreak. We find that ApEn, SampEn, and LZ complexity metrics of all markets could not generalize the COVID-19 effect of the complexity due to different patterns. However, market unpredictability is increasing by the ongoing health crisis.
Klaus Grobys, Juha-Pekka Junttila, James W. Kolari, Niranjan Sapkota
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.
Lykke Øverland Bergsli, Andrea Falk Lind, Péter Molnár, Michał Polasik
Since Bitcoin price is highly volatile, forecasting its volatility is crucial for many applications, such as risk management or hedging. We study which model is the most suitable for forecasting Bitcoin volatility. We consider several GARCH and two heterogeneous autoregressive (HAR) models and compare them. Since we utilize realized variance estimated from high frequency data as a proxy for true volatility, we can draw sharper conclusions than studies which use only daily data. We find that EGARCH and APARCH perform best among the GARCH models. HAR models based on realized variance perform better than GARCH models based on daily data. Superiority of HAR models over GARCH models is strongest for short-term volatility forecasts.
This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be indefinite in cost functional. This setup is innovative and has great theoretical and realistic significance as its applications in mathematical finance (e.g., portfolio selection in mean-variation model). Using some fully-coupled variational analysis under the person-by-person optimality principle, and the mean-field approximation method, the decentralized social control is derived by a class of new type consistency condition (CC) system for typical representative agent. Such CC system is some mean-field forward-backward stochastic differential equation (MF-FBSDE) combined with embedding representation. The well-posedness of such forward-backward stochastic differential equation (FBSDE) system is carefully examined. The related social asymptotic optimality is related to the convergence of the average of a series of weakly-coupled backward stochastic differential equation (BSDE). They are verified through some Lyapunov equations.
We investigate any similarity and dependence based on the full distributions of cryptocurrency assets, stock indices and industry groups. We characterize full distributions with entropies to account for higher moments and non-Gaussianity of returns. Divergence and distance between distributions are measured by metric entropies, and are rigorously tested for statistical significance. We assess the stationarity and normality of assets, as well as the basic statistics of cryptocurrencies and traditional asset indices, before and after the COVID-19 pandemic outbreak. These assessments are not subjected to possible misspecifications of conditional time series models which are also examined for their own interests. We find that the NASDAQ daily return has the most similar density and co-dependence with Bitcoin daily return, generally, but after the COVID-19 outbreak in early 2020, even S&P500 daily return distribution is statistically closely dependent on, and indifferent from Bitcoin daily return. All asset distances have declined by 75% or more after the COVID-19 outbreak. We also find that the highest similarity before the COVID-19 outbreak is between Bitcoin and Coal, Steel and Mining industries, and after the COVID-19 outbreak is between Bitcoin and Business Supplies, Utilities, Tobacco Products and Restaurants, Hotels, Motels industries, compared to several others. This study shed light on examining distribution similarity and co-dependence between cryptocurrencies and other asset classes.
Walid Mensi, Mobeen Ur Rehman, Muhammad Shafiullah, Khamis Hamed Al‐Yahyaee · 5 authors
This paper examines the high frequency multiscale relationships and nonlinear multiscale causality between Bitcoin, Ethereum, Monero, Dash, Ripple, and Litecoin. We apply nonlinear Granger causality and rolling window wavelet correlation (RWCC) to 15 min-data. Empirical RWCC results indicate mostly positive co-movements and long-term memory between the cryptocurrencies, especially between Bitcoin, Ethereum, and Monero. The nonlinear Granger causality tests reveal dual causation between most of the cryptocurrency pairs. We advance evidence to improve portfolio risk assessment, and hedging strategies.