In this paper, we analyze the time-series of minute price returns on the Bitcoin market through the statistical models of generalized autoregressive conditional heteroskedasticity (GARCH) family. Several mathematical models have been proposed in finance, to model the dynamics of price returns, each of them introducing a different perspective on the problem, but none without shortcomings. We combine an approach that uses historical values of returns and their volatilities - GARCH family of models, with a so-called "Mixture of Distribution Hypothesis", which states that the dynamics of price returns are governed by the information flow about the market. Using time-series of Bitcoin-related tweets and volume of transactions as external information, we test for improvement in volatility prediction of several GARCH model variants on a minute level Bitcoin price time series. Statistical tests show that the simplest GARCH(1,1) reacts the best to the addition of external signal to model volatility process on out-of-sample data.
This study investigates the volatility of daily Bitcoin returns and multifractal properties of the Bitcoin market by employing the rolling window method and examines relationships between the volatility asymmetry and market efficiency. Whilst we find an inverted asymmetry in the volatility of Bitcoin, its magnitude changes over time, and recently, it has become small. This asymmetric pattern of volatility also exists in higher frequency returns. Other measurements, such as kurtosis, skewness, average, serial correlation, and multifractal degree, also change over time. Thus, we argue that prope…
In December 2017, two leading derivative exchanges, CBOE and CME, introduced the first regulated Bitcoin futures. Our aim is estimating their causal impact on Bitcoin volatility and trading volume. Employing a new causal approach, C-ARIMA, we find that the CME future triggered an increase in both outcomes. There is also evidence of a positive volume-volatility relationship and that the effect on volatility was partially due to the higher trading volumes induced by the launch of the contract. After controlling for the effect on volumes, we find that the CME instrument caused Bitcoin volatility …
We test various volatility models using the Bitcoin spot price series. Our models include HIST, EMA ARCH, GARCH, and EGARCH, models. Both of our in-sample-fit and out-of-sample-forecast results suggest that GARCH and EGARCH models perform much better than other models. Moreover, the EGARCH model's asymmetric term is positive and insignificant, which suggests that Bitcoin prices lack the asymmetric volatility response to past returns. Finally, we formulate an option trading strategy by exploiting the volatility spread between the GARCH volatility forecast and the option's implied volatility. We…
Recent studies have found that the log-volatility of asset returns exhibit roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using the multifractal detrended fluctuation analysis, we obtain the generalized Hurst exponent of the log-volatility increments and find that the generalized Hurst exponent is less than $1/2$, which indicates log-volatility increments that are rough. Furthermore, we find that the generalized Hurst exponent is not constant. This observation indicates that the log-volatility has multifractal property. Using shuffled time series of…
Using the asymmetric stochastic volatility model, this study investigates the day-of-the-week and holiday effects on the returns and volatility of Bitcoin from January 1, 2013 to August 31, 2019; in this context, we also discuss the characteristics of Bitcoin as a financial asset. The results of the estimation are threefold. First, the finding shows a small day-of-the week effect in volatility on Saturday and Sunday than in the rest of the week. Second, although the holiday effects are examined in active trading countries, namely Japan, China, Germany, and the United States, the positive post-…
This paper investigates the return-volatility asymmetry of Bitcoin. We find that the cross correlations between return and volatility (squared return) are mostly insignificant on a daily level. In the high-frequency region, we find thata power-law appears in negative cross correlation between returns and future volatilities, which suggests that the cross correlation is \revision{long ranged}. We also calculate a cross correlation between returns and the power of absolute returns, and we find that the strength of \revision{the cross correlations} depends on the value of the power.
We show Bitcoin implied volatility on a 5 minute time horizon is modestly predictable from price, volatility momentum and alternative data including sentiment and engagement. Lagged Bitcoin index price and volatility movements contribute to the model alongside Google Trends with markets responding often several hours later. The code and datasets used in this paper can be found at https://github.com/Globe-Research/bitfear.
We analyse high-frequency realised volatility dynamics and spillovers in the bitcoin market, focusing on two pairs: bitcoin against the US dollar (the main fiat-crypto pair) and trading bitcoin against tether (the main crypto-crypto pair). We find that the tether-margined perpetual contract on Binance is clearly the main source of volatility, continuously transmitting strong flows to all other instruments and receiving only a little volatility. Moreover, we find that (i) during US trading hours, traders pay more attention and are more reactive to prevailing market conditions when updating thei…
In this paper, an application of three GARCH-type models (sGARCH, iGARCH, and tGARCH) with Student t-distribution, Generalized Error distribution (GED), and Normal Inverse Gaussian (NIG) distribution are examined. The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skewed distributions in the return series of Bitcoin. Comparative to the two distributions, the normal inverse Gaussian distribution captured adequately the fat tails and skewness in all the GARCH type models. The tGARCH model was the best model as it described the asymmetric occurre…
In this paper, we study the possibility of inferring early warning indicators (EWIs) for periods of extreme bitcoin price volatility using features obtained from Bitcoin daily transaction graphs. We infer the low-dimensional representations of transaction graphs in the time period from 2012 to 2017 using Bitcoin blockchain, and demonstrate how these representations can be used to predict extreme price volatility events. Our EWI, which is obtained with a non-negative decomposition, contains more predictive information than those obtained with singular value decomposition or scalar value of the …
While relevant stylized facts are observed for Bitcoin markets, we find a distinct property for the scaling behavior of the cumulative return distribution. For various assets, the tail index $μ$ of the cumulative return distribution exhibits $μ\approx 3$, which is referred to as "the inverse cubic law." On the other hand, that of the Bitcoin return is claimed to be $μ\approx 2$, which is known as "the inverse square law." We investigate the scaling properties using recent Bitcoin data and find that the tail index changes to $μ\approx 3$, which is consistent with the inverse cubic law. This sug…
A reputation of high volatility accompanies the emergence of Bitcoin as a financial asset. This paper intends to nuance this reputation and clarify our understanding of Bitcoin's volatility. Using daily, weekly, and monthly closing prices and log-returns data going from September 2014 to January 2021, we find that Bitcoin is a prime example of an asset for which the two conceptions of volatility diverge. We show that, historically, Bitcoin allies both high volatility (high Standard Deviation) and high predictability (low Approximate Entropy), relative to Gold and S&P 500. Moreover, using tools…
This paper shows that Bitcoin is not correlated to a general uncertainty index as measured by the Google Trends data of Castelnuovo and Tran (2017). Instead, Bitcoin is linked to a Google Trends attention measure specific for the cryptocurrency market. First, we find a bidirectional relationship between Google Trends attention and Bitcoin returns up to six days. Second, information flows from Bitcoin volatility to Google Trends attention seem to be larger than information flows in the other direction. These relations hold across different sub-periods and different compositions of the proposed …
Recently, cryptocurrencies have attracted a growing interest from investors, practitioners and researchers. Nevertheless, few studies have focused on the predictability of them. In this paper we propose a new and comprehensive study about cryptocurrency market, evaluating the forecasting performance for three of the most important cryptocurrencies (Bitcoin, Ethereum and Litecoin) in terms of market capitalization. At this aim, we consider non-Gaussian GARCH volatility models, which form a class of stochastic recursive systems commonly adopted for financial predictions. Results show that the be…
This letter revisits the informational efficiency of the Bitcoin market. In particular we analyze the time-varying behavior of long memory of returns on Bitcoin and volatility 2011 until 2017, using the Hurst exponent. Our results are twofold. First, R/S method is prone to detect long memory, whereas DFA method can discriminate more precisely variations in informational efficiency across time. Second, daily returns exhibit persistent behavior in the first half of the period under study, whereas its behavior is more informational efficient since 2014. Finally, price volatility, measured as the …
Understanding the variations in trading price (volatility), and its response to exogenous information, is a well-researched topic in finance. In this study, we focus on finding stable and accurate volatility predictors for a relatively new asset class of cryptocurrencies, in particular Bitcoin, using deep learning representations of public social media data obtained from Twitter. For our experiments, we extracted semantic information and user statistics from over 30 million Bitcoin-related tweets, in conjunction with 15-minute frequency price data over a horizon of 144 days. Using this data, w…
Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR,…
Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of a wide range of determinants on bitcoins' price direction under the continuous transfer entropy approach as a feature selection criterion. Accordingly, the statistically significant assets in the sense of permutation test on the nearest neighbour estimation of local transfer entropy are used as features or explanatory variables in a deep learning classificat…
The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that the bitcoin price exhibits a very interesting multi-scale correlation structure. This structure can be described by a power-law behavior of the variances of the returns as functions of time increments and it can be characterized by two parameters, the volatility and the Hurst ex…
Asymmetric relationship between price and volatility is a prominent feature of the financial market time series. This paper explores the price-volatility nexus in cryptocurrency markets and investigates the presence of asymmetric volatility effect between uptrend (bull) and downtrend (bear) regimes. The conventional GARCH-class models have shown that in cryptocurrency markets, asymmetric reactions of volatility to returns differ from those of other traditional financial assets. We address this issue from a viewpoint of fractal analysis, which can cover the nonlinear interactions and the self-s…
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a power law, and the exponents $p_\pm$ usually vary with the strength of the large volatilities. The large-volatility dynamics is time-reversal symmetric at the time scale in minutes, while asymmetric at the daily time scale. Careful analysis reveals that the time-reversal asymmetry is mainly induced by exogenous events. It is also the exogenous events which driv…
Cryptocurrencies, especially Bitcoin (BTC), which comprise a new digital asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/BTC include a high level of speculation, extreme volatility and price discontinuity. We propose a pricing mechanism based on a stochastic volatility with a correlated jump (SVCJ) model and compare it to a flexible co-jump model by Bandi and Renò (2016). The estimation results of both models confirm the impact of jumps and co-jumps on options obtained via simulation and an analysis of the implied volatility curve. We show t…
Impact of the COVID-19 pandemic on the financial market efficiency of price returns, absolute returns, and volatility increment: Evidence from stock and cryptocurrency markets
Based on 1-minute price changes recorded since year 2012, the fluctuation properties of the rapidly-emerging Bitcoin (BTC) market are assessed over chosen sub-periods, in terms of return distributions, volatility autocorrelation, Hurst exponents and multiscaling effects. The findings are compared to the stylized facts of mature world markets. While early trading was affected by system-specific irregularities, it is found that over the months preceding Apr 2018 all these statistical indicators approach the features hallmarking maturity. This can be taken as an indication that the Bitcoin market…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility would indicate market inefficiency. Using minute-by-minute data on S&P 500 index options, we provide evidence regarding delayed and gradual movements in implied volatility after the arrival of return jumps. These movements are directed and persistent, especially in the case of negative return jumps. Our results are significant when the implied volatilities …
We analyse a period spanning 35 years of activity in the Sao Paulo Stock Exchange Index (IBOVESPA) and show that the Heston model with stochastic volatility is capable of explaining price fluctuations for time scales ranging from 5 minutes to 100 days with a single set of parameters. We also show that the Heston model is inconsistent with the observed behavior of the volatility autocorrelation function. We deal with the latter inconsistency by introducing a slow time scale to the model. The fact that the price dynamics in a period of 35 years of macroeconomical unrest may be modeled by the sam…
We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger tha…
We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite number of dimensional parameters. Three bounds on the high-volatility limits of the drift and diffusion coefficients of volatility ensure that volatility is mean-reverting, has long memory and is as volatile as the stock price. Dimensional analysis then provides leading-order approximations to the drift and diffusion coefficients of volatility for the high-vola…
We study the impact of volatility on intraday serial correlation, at time scales of less than 20 minutes, exploiting a data set with all transaction on SPX500 futures from 1993 to 2001. We show that, while realized volatility and intraday serial correlation are linked, this relation is driven by unexpected volatility only, that is by the fraction of volatility which cannot be forecasted. The impact of predictable volatility is instead found to be negative (LeBaron effect). Our results are robust to microstructure noise, and they confirm the leading economic theories on price formation.
We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold $q$ are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 sto…
Bitcoin is considered the most valuable currency in the world. Besides being highly valuable, its value has also experienced a steep increase, from around 1 dollar in 2010 to around 18000 in 2017. Then, in recent years, it has attracted considerable attention in a diverse set of fields, including economics and computer science. The former mainly focuses on studying how it affects the market, determining reasons behinds its price fluctuations, and predicting its future prices. The latter mainly focuses on its vulnerabilities, scalability, and other techno-crypto-economic issues. Here, we aim at…
We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-minute and 5-minute price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate true inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative f…
With the daily and minutely data of the German DAX and Chinese indices, we investigate how the return-volatility correlation originates in financial dynamics. Based on a retarded volatility model, we may eliminate or generate the return-volatility correlation of the time series, while other characteristics, such as the probability distribution of returns and long-range time-correlation of volatilities etc., remain essentially unchanged. This suggests that the leverage effect or anti-leverage effect in financial markets arises from a kind of feedback return-volatility interactions, rather than …
Low-frequency historical data, high-frequency historical data and option data are three major sources, which can be used to forecast the underlying security's volatility. In this paper, we propose two econometric models, which integrate three information sources. In GARCH-Itô-OI model, we assume that the option-implied volatility can influence the security's future volatility, and the option-implied volatility is treated as an observable exogenous variable. In GARCH-Itô-IV model, we assume that the option-implied volatility can not influence the security's volatility directly, and the relation…
In the past decade, Bitcoin as an emerging asset class has gained widespread public attention because of their extraordinary returns in phases of extreme price growth and their unpredictable massive crashes. We apply the log-periodic power law singularity (LPPLS) confidence indicator as a diagnostic tool for identifying bubbles using the daily data on Bitcoin price in the past two years. We find that the LPPLS confidence indicator based on the daily Bitcoin price data fails to provide effective warnings for detecting the bubbles when the Bitcoin price suffers from a large fluctuation in a shor…
Based on the minute-by-minute data of the Hang Seng Index in Hong Kong and the analysis of probability distribution and autocorrelations, we find that the index fluctuations for the first few minutes of daily opening show behaviors very different from those of the other times. In particular, the properties of tail distribution, which will show the power law scaling with exponent about -4 or an exponential-type decay, the volatility, and its correlations depend on the opening effect of each trading day.
The cryptocurrency ecosystem has been the centre of discussion on many social media platforms, following its noted volatility and varied opinions. Twitter is rapidly being utilised as a news source and a medium for bitcoin discussion. Our algorithm seeks to use historical prices and sentiment of tweets to forecast the price of Bitcoin. In this study, we develop an end-to-end model that can forecast the sentiment of a set of tweets (using a Bidirectional Encoder Representations from Transformers - based Neural Network Model) and forecast the price of Bitcoin (using Gated Recurrent Unit) using t…
Probabilistic Forecasting Cryptocurrencies Volatility: From Point to Quantile Forecasts
Faculty of Electrical Engineering Częstochowa University of Technology（电气工程学院切斯托楚瓦技术大学）；Faculty of Economic Sciences（经济科学学院）；Nicolaus Copernicus University in Toruń（托伦尼科拉乌斯·哥白尼大学）；Prague University of Economics（布拉格经济大学）
In this study we examine the evolution of price, volume, and the bid-ask spread after extreme 15 minute intraday price changes on the NYSE and the NASDAQ. We find that due to strong behavioral trading there is an overreaction. Furthermore we find that volatility which increases sharply at the event decays according to a power law with an exponent of approximately 0.4, i.e., much faster than the autocorrelation function of volatility.
We study the continuous time random walk theory from financial tick data of the yen-dollar exchange rate transacted at the Japanese financial market. The dynamical behavior of returns and volatilities in this case is particularly treated at the long-time limit. We find that the volatility for prices shows a power-law with anomalous scaling exponent k = 0.96 (one minute) and 0.86 (ten minutes), and that our behavior occurs in the subdiffusive process. Our result presented will be compared with that of recent numerical calculations.
A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked according to their size to form a probability distribution function and finally fed in the expression of the Shannon entropy. In this work, such entropy measure is implemented on the time series of prices and volatilities of six financial markets. The analysis has been performed, on tick-by-tick data sampled every minute for six years of data from 1999 to 2004, fo…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price fluctuations as a non-Markovian stochastic process using the first-passage statistical concepts of persistence and survival. We report the results of empirical measurements of the normalized $q$-order correlation functions $f_q(t)$, survival probability $S(t)$, and persistence probability $P(t)$ for several stock market dynamical sets. We analyze both minut…
