This study interrelates three adjacent topics in data evaluation. The first is the establishment of a relationship between Bregman divergence and probabilistic alpha-divergence. In particular, we demonstrate that square-root-order probability normalization enables the unification of these two divergence families. This yields a new alpha-divergence, which can be used to jointly derive the alpha-EM algorithm (alpha-expectation-maximization algorithm) and the traditional log-EM algorithm. The second topic is the application of the alpha-EM algorithm in the evaluation of graders scoring raw data over a network. We estimate multinomial mixture distributions in this evaluation problem. We note that the convergence speed of the alpha-EM algorithm is significantly higher than that of the log-EM algorithm. Finally, the third topic is the use of this increase in convergence speed to assign the winning evaluator and miner in a blockchain environment. This is achieved by proof-of-review using evaluation scores, which is a class of proof-of-stake. In the second and third topics, we select terminology from wine tasting for brevity in the exposition. However, this formulation can be applied to a broader class of data in a network environment comprising blockchains.
This study investigates how uncertainty surrounding cryptocurrency affects cryptocurrency return (CR) by employing various wavelet techniques. To this end, we concentrate on the recently published cryptocurrency uncertainty index (UCRY) and the top eight cryptocurrencies by virtue of market capitalization for the period from December 30, 2013, until February 21, 2021. Our results show that the UCRY index strongly predicts CR. In particular, the UCRY index has a leading position in all the frequencies for all cryptocurrencies in our sample. Additionally, when the impacts of economic policy uncertainty and the volatility index are eliminated, the significant co-movement of UCRY-CR stays unchanged for short-, medium-, and long-term investment horizons. Thus, we conclude that the UCRY-CR relationships are both persistent and pervasive. Our study contributes to the literature on the relationships between cryptocurrency and market uncertainties as well as to investors who use uncertainty indices to design their investment strategies for their portfolios.
Francis Liu, Natalie Packham, Meng-Jou Lu, Wolfgang Karl HĂ€rdle
The introduction of derivatives on Bitcoin enables investors to hedge risk exposures in cryptocurrencies. Because of volatility swings and jumps in cryptocurrency prices, the traditional variance-based approach to obtain hedge ratios may not be suitable for hedgers. In this work, we consider two extensions of the traditional approach: first, different dependence structures are modelled by different copulae, such as the Gaussian, Student-t, Normal Inverse Gaussian and Archimedean copulae; second, different risk measures, such as value-at-risk, expected shortfall and spectral risk measures are employed to find the optimal hedge ratio. Extensive out-of-sample tests using the data from the time period December 2017 until May 2021 give insights in the practice of hedging various cryptos and crypto indices, including Bitcoin, Ethereum, Cardano, the CRIX index and a number of crypto-portfolios. Evidence shows that BTC futures can effectively hedge BTC and BTC-involved indices. This promising result is consistent across different risk measures and copulae except for the Frank copula. On the other hand, we observe complex and diverse dependence structures between non-BTC-related cryptocurrencies and the BTC futures. As a consequence, the hedge performance of non-BTC-related cryptocurrencies is mixed and even suitable for some assets.
<abstract> <p>The aim of this study was to examine the returns and volatility of Bitcoin. The study uses the daily closing price of Bitcoin from October 1, 2013 to July 31, 2020 as the sample data, which include 2496 observations. About the methodology, the paper describes the utilisation of GARCH models to analyse Bitcoin's returns and volatility. First, the data were tested by using the augmented Dickey-Fuller test to verify the stability and diagram tests sequence. After that, the lag order and determination results of the mean value equation show that the Lag 4 period is the best. Additionally, the paper describes an autocorrelation test of the residual series, which revealed that there is no significant autocorrelation in the residual term for the Bitcoin returns, but that the residual squared has significant autocorrelation. In addition, a linear graph of squared residuals was formulated and the ARCH-LM test was used to find the data that are suitable for modelling with GARCH models since the data have a strong ARCH effect. As result, a GARCH (1, 1) model was used; the findings indicated that the returns and volatility of Bitcoin have clustering characteristics, and that the returns and volatility of Bitcoin constitute a persistent process although the effects gradually reduce over time. Because of the limitations of the GARCH (1, 1) model and researching asymmetry of the returns and volatility of Bitcoin, TARCH and EGARCH models were adopted; the findings indicated that the returns and volatility of Bitcoin are without a "leverage effect". To further explain this special phenomenon, safe-property is quoted in this research. In the end, this paper demonstrates that Bitcoin, as a safe-haven property, can hedge financial risks in times of economic depression. Besides, Bitcoin has a revised asymmetric effect between positive and negative shocks that makes it a viable asset to add to the portfolios of investors.</p> </abstract>
This article considers a variety of highly diversified cross-sectional momentum and reversal strategies, with sorting and holding periods from one week up to two years. In a sample of the 2,000 largest cryptocurrencies during the period 2014â2020, we identify positive momentum on short horizons up to two to four weeks and a significant reversal on longer horizons beyond one month. The reversal effect becomes more pronounced once we expand the sorting and/or holding periods. Momentum and, particularly, reversal returns are economically large, statistically significant, and generally not exposed to standard cryptocurrency risk factors. The main drivers of the reversal effect are âpast loserâ cryptocurrencies. The switching of momentum into reversal occurs after approximately one monthâmuch quicker than the equity market, and evidence of the âfaster metabolism of cryptocurrencies.â
This paper uses a search-theoretic model to study conditions under which cryptocurrency is valued and under which it coexists with fiat money. In my model, a cryptocurrency economy is one in which private agentsâ decisions determine the stock of money and in which the marginal cost of producing money is increasing in the existing nominal stock. I show that the inflation rate of cryptocurrency must be zero in a stationary monetary equilibrium. This result is in sharp contrast to models with fiat money in which the stock of money is exogenously given. In fiat money economies, the inflation rate is determined by the rate of growth of the money stock. My result is also in sharp contrast with other types of private money economies, in which the inflation rate must necessarily be different from zero. In such private money economies, the cost of producing additional money does not depend on the existing nominal stock. Moreover, I show that cryptocurrency and fiat money can circulate at the same time and that the rates of return on these two assets may not be the same. Competition with cryptocurrency restricts the governmentâs ability to over-issue fiat money and thereby might improve on pure fiat money equilibria without government commitment.
Abstract About 99% of cryptocurrency trades occur on organized exchanges with many investors subsequently keeping their digital assets in accounts with cryptocurrency markets. This generates exposure to the risk of exchange closures. We construct a database containing eight key characteristics on 238 cryptocurrency exchanges and employ machine learning techniques to predict whether a cryptocurrency market will remain active or whether it will go out of business. Both inâsample and outâofâsample measures of forecasting performance are computed and ranked for four popular machine learning algorithms. Although all four models produce satisfactory classification accuracy, our best model is a random forest classifier. It reaches accuracy of 90.4% on training data and 86.1% on a test dataset. From the list of predictors, we find that exchange lifetime, transacted volume, and cyberâsecurity measures such as security audit, cold storage, and bug bounty programs rank high in terms of feature importance across multiple algorithms. On the other hand, whether an exchange has previously experienced a security breach does not rank highly according to its contribution to classification accuracy.
Abstract We analyze cryptoasset markets (cryptocurrencies and stablecoins) at high frequency. We investigate intraday patterns. We show that Tether plays a crucial role as a safe haven and/or store of value facilitating trading in cryptocurrencies without going through traditional currencies. Markets centered on cryptocurrencies and stablecoins play a primary role aggregating preference/technology shocks and heterogeneous opinions, instead markets centered on the US dollar play a marginal role on price formation.
In this study, the Log-Periodic Power Law Singularity (LPPLS) model is adopted for real-time identification and monitoring of Bitcoin bubbles and crashes using different time scale data, and the modified Lagrange regularization method is proposed to alleviate the impact of potential LPPLS model over-fitting to better estimate bubble start time and market regime change. The goal here is to determine the nature of the bubbles and crashes (i.e., whether they are endogenous due to their own price evolution or exogenous due to external market and/or policy influences). A systematic market event analysis is performed and correlated to the Bitcoin bubbles detected. Based on the daily LPPLS confidence indictor from 1 December 2019 to 24 June 2021, this analysis has disclosed that the Bitcoin boom from November 2020 to mid-January 2021 is an endogenous bubble, stemming from the self-reinforcement of cooperative herding and imitative behaviors of market players, while the price spike from mid-January 2021 to mid-April 2021 is likely an exogenous bubble driven by extrinsic events including a series of large-scale acquisitions and adoptions by well-known institutions such as Visa and Tesla. Finally, the utilities of multi-resolution LPPLS analysis in revealing both short-term changes and long-term states have also been demonstrated in this study.
Depending on the chosen perspective, cryptocurrencies either constitute a unique opportunity to end national patronizing built on debt-based fiat money (currency) or a menace to a well-established financial order that ensures economic stability. A central issue in the heated debate surrounding cryptocurrencies is whether they have any intrinsic value at all. In this conceptual position paper, we briefly summarize existing standpoints and suggest three alternative propositions: (1) to avoid using the term âintrinsic valueâ for the valuation of cryptocurrencies, (2) to refer to the sum total of all properties that could potentially qualify them as money, and (3) to consider the amount of capital and energy that is needed to create them. These suggestions bear substantial implications for the economic classification of cryptocurrencies.
Abstract We examine the association of Bitcoin, and other cryptocurrency, returns with changes in inflation expectations, and form a comparison with gold, a traditional inflation hedge. We control for uncertainty in economic policy, cryptocurrency, and financial markets, and show that cryptocurrency returns are positively related to changes in US inflation expectations only for a limited set of circumstances. Unlike with gold, the identified relationship is only significant for shortâterm inflation expectations, and when inflation or marketâimplied inflation expectations are below 2% (the Fed's inflation target). Moreover, cryptocurrency returns tend to be lower on days with monthly consumer price index (CPI) announcements and respond negatively to CPI surprises. Our results suggest that cryptocurrencies do not currently offer investors a viable alternative to gold for hedging inflation.
Lili Matic, Natalie Packham, Wolfgang Karl HĂ€rdle
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Levy processes. First, market data is calibrated to stochastic volatility inspired (SVI)-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an SVCJ model (stochastic volatility with correlated jumps), a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta-Gamma, Delta-Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.
Rabaa Karaa, Skander Slim, John W. Goodell, Abhinav Goyal · 5 authors
We empirically examine whether feedback traders are active in the Bitcoin and the extent to which their presence is affected by a series of noise-related factors (sentiment; volume; liquidity) at three different frequencies (hourly; daily; weekly) for the April 2013âJuly 2019 period based on Bitstamp data. Our findings suggest that positive feedback trading grows stronger for higher (hourly; daily) frequencies, with its presence manifesting itself mainly during periods of high/improving sentiment and high/rising volume/liquidity. Additional tests reveal that the significance of hourly feedback trading is identified during hours corresponding to the trading hours of major European/North American markets. Overall, our results confirm extant literature evidence on the prevalence of noise trading in cryptocurrencies, while further showcasing that the factors motivating feedback trading in other asset classes (equities; ETFs; futures) exhibit similar effects over the presence of feedback traders in the cryptocurrency market.
Maurice OmaneâAdjepong, Paul Alagidede, Anna Gustav Lyimo, George Tweneboah
The letter examines herding in the most liquid cryptocurrency markets relative to traditional financial markets of 10 emerging economies within the G20. Our results reference significant symmetric crowd and imitation trading, which are dependent on time. Additionally, we report asymmetric herd behaviour in the cryptocurrency and stock markets, indicative that traders of these markets react collectively to extreme return movement with implied high risk and consequences for market informational efficiency.
Uniswap is a decentralized exchange (DEX) and was first launched on November 2, 2018 on the Ethereum mainnet [1] and is part of an Ecosystem of products in Decentralized Finance (DeFi). It replaces a traditional order book type of trading common on centralized exchanges (CEX) with a deterministic model that swaps currencies (or tokens/assets) along a fixed price function determined by the amount of currencies supplied by the liquidity providers. Liquidity providers can be regarded as investors in the decentralized exchange and earn fixed commissions per trade. They lock up funds in liquidity pools for distinct pairs of currencies allowing market participants to swap them using the fixed price function. Liquidity providers take on market risk as a liquidity provider in exchange for earning commissions on each trade. Here we analyze the risk profile of a liquidity provider and the so called impermanent (unrealized) loss in particular. We provide an improved version of the commonly denoted impermanent loss function for Uniswap v2 on the semi-infinite domain. The differences between Uniswap v2 and v3 are also discussed.
Massimo Bartoletti, James Hsin-yu Chiang, Alberto Lluch Lafuente
Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. AMMs allow users to trade different types of crypto-tokens, without the need to find a counter-party. There are several implementations and models for AMMs, featuring a variety of sophisticated economic mechanisms. We present a theory of AMMs. The core of our theory is an abstract operational model of the interactions between users and AMMs, which can be concretised by instantiating the economic mechanisms. We exploit our theory to formally prove a set of fundamental properties of AMMs, characterizing both structural and economic aspects. We do this by abstracting from the actual economic mechanisms used in implementations, and identifying sufficient conditions which ensure the relevant properties. Notably, we devise a general solution to the arbitrage problem, the main game-theoretic foundation behind the economic mechanisms of AMMs.