Abstract This paper examines how liquidity risk is priced in the cross‐section of cryptocurrency returns. In doing so, we use the Amihud measure as a liquidity proxy. By employing the univariate portfolio analysis, the bivariate portfolio analysis, and the Fama‐MacBeth regression analysis, we document a negative relationship between liquidity and cryptocurrency returns. Additional tests demonstrate that this finding is robust to alternative liquidity measurement as well as size screens and show no evidence of a significant intertemporal relationship between liquidity and expected returns for three leading cryptocurrencies. Our conclusions add to the understanding of how markets price cryptocurrencies.
В роботі розглянута теорія Ейнштейна про броунівський рух та експеримент Перріна. Описано підхід і теорію Ланжевена в термінах випадкової сили, а також співвідношення Стокса - Ейнштейна. Розглянуто поняття стохастичного диференціального рівняння та його еквівалентний опис у термінах рівнянь Фоккера-Планку. Використано стохастичний метод для побудови моделі геометричного броунівського руху, в результаті якого отримано різні сценарії волатильності цін на криптовалютній біржі.
This article investigates similarities and differences between gold and four cryptocurrencies (Bitcoin, Ethereum, Bitcoin Cash and Litecoin). To do so, we estimate a system-GARCH-in-mean with respect to four determinants for the period starting 7/18/2014 at earliest until 7/12/2021. We find that, first, liquidity premia are less important. Second, volatility premia exist in either gold and cryptocurrencies. Third, the response of cryptocurrencies to ex- change rate changes is more pronounced than for gold at least if developing countries are included. Fourth, gold exhibits a safe haven status, while cryptocurrencies do not. So those cannot be seen as a store of value but rather as speculative assets.
COVID-19 pandemic has caused significant losses and an increase in the level of risk in the financial markets and global economy. Thus in this study, we model the crypto market volatility behavior during the COVID-19 crisis. GARCH (1, 1) and GJR-GARCH (1, 1) were applied to model the volatility clustering and leverage effects in the intraday day (15-minute interval) returns of Bitcoin, Ethereum, and Litcoin ranging from 11th April 2019 to 8th February 2021. The empirical findings from GARCH (1, 1) model indicates the presence of volatility clustering in the crypto market. Moreover, the results of the GJR-GARCH (1, 1) indicate the presence of leverage effects in the financial returns series of all three crypto currencies. Furthermore, the excess kurtosis confirms the existence of fat-tail phenomena in the crypto market. Overall, the findings from this study showed that in times of COVID 19 pandemic the crypto market returns series showed volatility persistence, fat-tail phenomena, and leverage effects. These outcomes provide a better understanding for financial investors to invest rationally and cautiously during pandemic times.
In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price in a specified window surrounding the instant. We price these options whose underlying asset is the CCI30 index of various Cryptocurrencies, as opposed to a single cryptocurrency, with the intention of reducing volatility, and thus, the option price. We employ the Normal Inverse Gaussian (NIG) and Rough Fractional Stochastic Volatility (RFSV) models to the cryptocurrency market and using the Black-Scholes as the benchmark model. In doing so, we intend to capture the extreme characteristics such as jumps and volatility roughness for cryptocurrency price fluctuations. Since there is no availability of a closed-form solution for lookback option prices under these models, we utilize the Monte Carlo simulation for pricing and augment it using the antithetic method for variance reduction. Finally, we present the simulation results for the lookback options and compare the prices resulting from using the NIG model, RFSV model with those from the Black-Scholes model. We found that the option price is indeed lower for our proposed window average lookback option than for a traditional lookback option. We found the Hurst parameter to be H = 0.09 which confirms that the cryptocurrencies market is indeed rough.
This work is a comparative study of different univariate and multivariate time series predictive models as applied to Bitcoin, other cryptocurrencies, and other related financial time series data. ARIMA models, long regarded as the gold standard of univariate financial time series prediction due to both its flexibility and simplicity, are used a baseline for prediction. Given the highly correlative nature amongst different cryptocurrencies, this work aims to show the benefit of forecasting with multivariate time series models—primarily focusing on a novel parameter optimization of VARIMA models outlined in this paper. These models are trained on 3 years of historical data, aggregated from different cryptocurrency exchanges by Coinmarketcap.com, which includes: daily average prices and trading volume. Historical time series data of traditional market data, including the stock Nvidia, the de facto leading manufacture of gaming GPU’s, is also analyzed in conjunction with cryptocurrency prices, as gaming GPU’s have played a significant role in solving the profitable SHA256 hashing problems associated with cryptocurrency mining and have seen equivalently correlated investor attention as a result. Models are trained on this historical data using moving window subsets, with window lengths of 100, 200, and 300 days and forecasting 1 day into the future. Validation of this prediction against the actually price from that day are done with following metrics: Directional Forecasting (DF), Mean Absolute Error (MAE), and Mean Squared Error (MSE).
We consider the hedging problem where a futures position can be automatically liquidated by the exchange without notice. We derive a semi-closed form for an optimal hedging strategy with dual objectives - to minimise both the variance of the hedged portfolio and the probability of liquidations due to insufficient collateral. The optimal solution depends on the statistical characteristics of the spot and futures extreme returns and parameters that characterise the hedger by loss aversion, choice of leverage and collateral management. An empirical analysis of bitcoin shows that the optimal strategy combines superior hedge effectiveness with a reduction in the probability of liquidation. We compare the performance of seven major direct and inverse hedging instruments traded on five different exchanges, based on minute-level data. We also link this performance to novel speculative trading metrics, which differ markedly between venues.
Ndeye Fatou Sene, Mamadou Abdoulaye Konté, Jane Aduda
The objective of this study is, to show the importance of incorporating jumps in both returns and volatility dynamics for Bitcoin. For that purpose, we introduce the Double Exponential Jump-Diffusion model with Stochastic Volatility (DEJDSVJ) that contains asymmetric jumps. The use of the Markov Chain Monte Carlo methods for estimation has proved the meaningful presence of jumps in Bitcoin price and volatility. Moreover, based on the Bitcoin options market, a comparison between the underlying model, the Double Exponential Jump Diffusion model (DEJD) with Stochastic Volatility (no Jumps) and the Stochastic Volatility (SV) shows the goodness of the DEJDSVJ model’s calibration over others for pricing Bitcoin options.
Since the advent of Bitcoin, the cryptocurrency market has become an important financial market. However, due to the existence of the cryptocurrency bubble, investors face more difficulties in risk portfolios. We adopt wavelet packet decomposition, nonlinear Granger causality test, risk spillover network, and STVAR model; retain the mature research of multiscale systemic risk based on time and frequency; and thus extend systemic risk to different regimes. We found that when frequency is combined with regimes, the risk spillover center will undergo subversive changes in the long run. We also proposed that BTC will be more robust at extreme values (like longest and shortest periods), while cryptocurrencies with smaller market capitalization will be stronger in the medium term. At the same time, the recession period will also spur on it.
The cryptocurrency market recently gained a lot of attention from investors. But, its volatility has been acting as a disincentive to investment. Volatility plays an important role in shaping market riskiness and investment behavior. We study the volatility of the Ethereum (ETH) cryptocurrency from the following perspectives. The first goal of this study is to identify risk-seeking behavior in the ETH cryptocurrency market. We examine this propensity by measuring the effect of the volatility of Ethereum on the total ETH assets. This investigation also takes the form of a case-study of an unexpected ETH fund-stolen event, DAO Hack, and the hard fork treatment. We also forecast a downward volatility trend in the near future based on Autoregressive models. This is the first study to analyze DAO Hack with empirical methods and marks the starting point for more rigorous models to predict the volatility of Ethereum.
This paper implements the analysis of volatility behaviour of the eight major cryptocurrencies (Bitcoin, Ethereum, Ripple, Litecoin, Monero, Stellar, Dash and Tether) for the period starting from October 13th 2015 to November 18th 2019. The GARCH-type models with heavy-tailed distributions are fitted to filter the conditional volatility exhibited by cryptocurrencies. Extreme value analysis based on the peak over threshold approach is then used to model the extreme tail behaviour of the cryptocurrencies. The predictive performance of the GARCH-EVT model in forecasting Value-at-Risk is evaluated at both 5% and 1% levels of significance. The backtesting results demonstrate the superiority of the GARCH-EVT model in both out-of-sample forecasts and goodness-of-fit properties to cryptocurrency returns and forecasting Value-at-Risk. Overall, the empirical results of this study recommend the heavy-tailed GARCH-EVT based model for modelling and forecasting the volatility of cryptocurrencies.
We investigate the dynamics of daily realised returns and risk premiums for a large cross-section of cryptocurrency pairs through the lens of an Instrumented Principal Component Analysis (IPCA) (see Kelly et al., 2019). We show that a model with three latent factors and time-varying factor loadings significantly outperforms a benchmark model with observable risk factors: the total (predictive) R2 from the IPCA is 17.2% (2.9%) for individual returns, against a benchmark 9.6% (-0.02%) obtained from a model with six observable risk factors explored in previous literature. By looking at the characteristics that significantly matter for the dynamics of risk premiums, we provide robust evidence that liquidity, size, reversal, and both market and downside risks represent the main driving factors behind expected returns. These results hold for both individual assets and characteristic-based portfolios, pre and post the Covid-19 outbreak, and for weekly individual and portfolio returns.
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 Härdle
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.
Emmanuel Asafo‐Adjei, Peterson Owusu, Anokye M. Adam
The world has witnessed the adverse impact of the COVID‐19 pandemic. Accordingly, it is expected that information transmission between equities and digital assets has been altered due to the hostile impact of the pandemic outbreak on financial markets. As a result, the ensuing perverse risk among markets is presumed to rise during severe uncertainties occasioned by the COVID‐19 pandemic. The impetus of this study is to examine the degree of asymmetry and nonlinear directional causality between global equities and cryptocurrencies in the frequency domain. Hence, we employ both the variational mode decomposition (VMD) and the Rényi effective transfer entropy techniques. Analyses of the study are presented for three sample periods; these are the full sample period, the pre‐COVID‐19 period, and the COVID‐19 pandemic period. We gauge a mixture of asymmetric and nonlinear bidirectional and unidirectional causality between global equities and cryptocurrencies for the sample periods. However, the COVID‐19 pandemic period appears to be driving the estimates for the full sample period, which indicates a negative flow. Thus, the direction and significance of the information flow between the markets for the full sample correspond to the one observed during the COVID‐19 pandemic period. We, consequently, establish a significant directional, dynamical, and scale‐dependent information flow between global equities and cryptocurrencies. Notwithstanding, throughout the study samples, we mainly find a negative significant information flow from global equities to cryptocurrencies. We detect that most cryptocurrencies exhibit similar behaviour of information flow to global equities for each of the sample periods. The outcome provides pertinent signals to investors with diverse investment horizons who would want to diversify, hedge, or employ cryptocurrencies as a safe haven for global equities during uncertainties, specifically the COVID‐19 pandemic.
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.