Abstract This paper investigates the dynamic relationships between the volatility of Bitcoin and major Indian stock market indices. Employing a dynamic conditional correlationâgeneralized autoregressive conditional heteroskedasticity (DCCâGARCH) model, we explore how volatility shocks and information flow influence the correlations between these asset classes. Our findings reveal a key characteristic: volatility spillovers tend to be shortâlived, indicated by a relatively low DCCâGARCH parameter (dcca1). This suggests that while a surge in volatility in one market might lead to a temporary increase in correlation with the other, this heightened correlation is unlikely to persist for extended periods. However, the model also highlights a high DCCâGARCH parameter (dccb1), signifying that the correlations themselves are responsive to new information. This implies that volatility linkages can adjust rapidly in response to market events or economic data releases. To enhance accessibility for a broad audience, we translate these findings into economic intuitions. We illustrate how the model can be interpreted through realâworld examples, such as the impact of sudden policy changes in India or global market flash crashes. By understanding the shortâlived nature of volatility spillovers and the responsiveness of correlations, investors in the Indian markets can make more informed decisions when considering the potential influence of Bitcoin's volatility while contributing to a deeper understanding of the dynamic interactions between cryptocurrency and traditional financial markets in the Indian context.
Abstract Modeling implied volatility (IV) is important for option pricing, hedging, and risk management. Previous studies of deterministic implied volatility functions (DIVFs) propose two parameters, moneyness and time to maturity, to estimate implied volatility. Recent DIVF models have included factors such as a moving average ratio and relative bid-ask spread but fail to enhance modeling accuracy. The current study offers a generalized DIVF model by including a momentum indicator for the underlying asset using a relative strength index (RSI) covering multiple time resolutions as a factor, as momentum is often used by investors and speculators in their trading decisions, and in contrast to volatility, RSI can distinguish between bull and bear markets. To the best of our knowledge, prior studies have not included RSI as a predictive factor in modeling IV. Instead of using a simple linear regression as in previous studies, we use a machine learning regression algorithm, namely random forest, to model a nonlinear IV. Previous studies apply DVIF modeling to options on traditional financial assets, such as stock and foreign exchange markets. Here, we study options on the largest cryptocurrency, Bitcoin, which poses greater modeling challenges due to its extreme volatility and the fact that it is not as well studied as traditional financial assets. Recent Bitcoin option chain data were collected from a leading cryptocurrency option exchange over a four-month period for model development and validation. Our dataset includes short-maturity options with expiry in less than six days, as well as a full range of moneyness, both of which are often excluded in existing studies as prices for options with these characteristics are often highly volatile and pose challenges to model building. Our in-sample and out-sample results indicate that including our proposed momentum indicator significantly enhances the modelâs accuracy in pricing options. The nonlinear machine learning random forest algorithm also performed better than a simple linear regression. Compared to prevailing option pricing models that employ stochastic variables, our DIVF model does not include stochastic factors but exhibits reasonably good performance. It is also easy to compute due to the availability of real-time RSIs. Our findings indicate our enhanced DIVF model offers significant improvements and may be an excellent alternative to existing option pricing models that are primarily stochastic in nature.
ÎÏÎœÏÏαΜÏÎŻÎœÎżÏ ÎÎșίλλαÏ, Maria Tantoula, Manolis Tzagarakis
Abstract We analyze properties identified in the price volatility of Bitcoin and some of the leading cryptocurrencies namely Litecoin, Ripple, and Ethereum. We employ Heterogeneous Autoregressive models (HAR) in both a univariate and multivariate level of analysis. First, the significance of heterogeneity and jumps is examined, considering the ability of several univariate HAR models, to predict realized volatility of cryptocurrencies. Second, we examine the relevance of realized volatility jumps and covariances in the transmission of volatility spillovers among cryptocurrencies. We perform a comparative spillover analysis of the multivariate HAR models in two versions, considering variances only and covariances as well. Our results indicate that covariances and jumps inclusion lead to an increase in spillovers. The time-varying spillover analysis indicates higher dependency between Bitcoin and the other cryptocurrencies mostly at short frequencies.
This study addresses a gap in the literature by exploring the impact of geopolitical risk on cryptocurrency markets, particularly Bitcoin, within different price and volatility regimes. We employed generalized autoregressive conditional heteroskedasticity (GARCH) and Markov-Switching Vector Autoregressive (MS-VAR) models on daily data from January 01, 2015 to January 15, 2024. We found evidence suggesting a strong positive relationship between lagged Bitcoin returns and current returns, indicating persistence or momentum in Bitcoin price movements. Additionally, heightened geopolitical risks were associated with decreased current Bitcoin volatility, particularly in state 1 characterized by lower price levels. Conversely, in state 2, which is characterized by higher price levels, geopolitical risk shocks initially spike, followed by a subsequent decrease in Bitcoin price volatility. Furthermore, shock analysis revealed nuanced reactions of Bitcoin prices and volatility to geopolitical events, with distinct patterns observed for different price regimes. Geopolitical risk can explain the variance in Bitcoin prices and volatility in lower-price-level states. These results suggest that adopting dynamic investment approaches that adjust to changing geopolitical conditions and market regimes can help investors navigate cryptocurrency market fluctuations more effectively.
Dimitar Kitanovski, Igor Mishkovski, Viktor Stojkoski, Miroslav Mirchev
Maintaining a balance between returns and volatility is a common strategy for portfolio diversification, whether investing in traditional equities or digital assets like cryptocurrencies. One approach for diversification is the application of community detection or clustering, using a network representing the relationships between assets. We examine two network representations, one based on a standard distance matrix based on correlation, and another based on mutual information. The Louvain and Affinity propagation algorithms were employed for finding the network communities (clusters) based on annual data. Furthermore, we examine building assets' co-occurrence networks, where communities are detected for each month throughout a whole year and then the links represent how often assets belong to the same community. Portfolios are then constructed by selecting several assets from each community based on local properties (degree centrality), global properties (closeness centrality), or explained variance (Principal component analysis), with three value ranges (max, med, min), calculated on a maximal spanning tree or a fully connected community sub-graph. We explored these various strategies on data from the S\&P 500 and the Top 203 cryptocurrencies with a market cap above 2M USD in the period from Jan 2019 to Sep 2022. Moreover, we study into more details the periods of the beginning of the COVID-19 outbreak and the start of the war in Ukraine. The results confirm some of the previous findings already known for traditional stock markets and provide some further insights, while they reveal an opposing trend in the crypto-assets market.
This paper is concerned with a class of linear-quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by individual noise, and all agents are coupled together via the control average term. Using the mean-field game approach and the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward-backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. By the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related $\varepsilon$-Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.
Quang Phung Duy, Oanh Nguyen Thi, Phuong Hao Le Thi, Hai Duong Pham Hoang · 6 authors
Purpose The goal of the study is to offer important insights into the dynamics of the cryptocurrency market by analyzing pricing data for Bitcoin. Using quantitative analytic methods, the study makes use of a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and an Autoregressive Integrated Moving Average (ARIMA). The study looks at how predictable Bitcoin price swings and market volatility will be between 2021 and 2023. Design/methodology/approach The data used in this study are the daily closing prices of Bitcoin from Jan 17th, 2021 to Dec 17th, 2023, which corresponds to a total of 1065 observations. The estimation process is run using 3 years of data (2021â2023), while the remaining (Jan 1st 2024 to Jan 17th 2024) is used for forecasting. The ARIMA-GARCH method is a robust framework for forecasting time series data with non-seasonal components. The model was selected based on the Akaike Information Criteria corrected (AICc) minimum values and maximum log-likelihood. Model adequacy was checked using plots of residuals and the LjungâBox test. Findings Using the BoxâJenkins method, various AR and MA lags were tested to determine the most optimal lags. ARIMA (12,1,12) is the most appropriate model obtained from the various models using AIC. As financial time series, such as Bitcoin returns, can be volatile, an attempt is made to model this volatility using GARCH (1,1). Originality/value The study used partially processed secondary data to fit for time series analysis using the ARIMA (12,1,12)-GARCH(1,1) model and hence reliable and conclusive results.
Sonal Sahu, Alejandro Fonseca RamĂrez, JongâMin Kim
This study investigates calendar anomalies and their impact on returns and volatility patterns in the cryptocurrency market, focusing on day-of-the-week effects before and during the COVID-19 pandemic. Using advanced statistical models from the GARCH family, we analyze the returns of Binance USD, Bitcoin, Binance Coin, Cardano, Dogecoin, Ethereum, Solana, Tether, USD Coin, and Ripple. Our findings reveal significant shifts in volatility dynamics and day-of-the-week effects on returns, challenging the notion of market efficiency. Notably, Bitcoin and Solana began exhibiting day-of-the-week effects during the pandemic, whereas Cardano and Dogecoin did not. During the pandemic, Binance USD, Ethereum, Tether, USD Coin, and Ripple showed multiple days with significant day-of-the-week effects. Notably, positive returns were generally observed on Sundays, whereas a shift to negative returns on Mondays was evident during the COVID-19 period. These patterns suggest that exploitable anomalies persist despite the marketâs continuous operation and increasing maturity. The presence of a long-term memory in volatility highlights the need for robust trading strategies. Our research provides valuable insights for investors, traders, regulators, and policymakers, aiding in the development of effective trading strategies, risk management practices, and regulatory policies in the evolving cryptocurrency market.
Danial Saef, Odett Nagy, Sergej Sizov, Wolfgang Karl HĂ€rdle
Abstract Cryptocurrency markets have recently attracted significant attention due to their potential for high returns; however, their underlying dynamics, especially those concerning price jumps, continue to be explored. Building on previous research, this study examines the presence and clustering of jumps in an extensive tick data set covering six major cryptocurrencies traded against Tether on seven leading exchanges worldwide over nearly 2.5 years. Our analysis reveals that jumps occur on up to 58% of trading days, with negative jumps predominating in both frequency and size. Notably, we observe systematic clustering of jumps over time, especially in Bitcoin and Ethereum, indicating interconnected market dynamics and potential predictive power for market movements. By employing high-frequency econometric tools, we identify temporal patterns in jump occurrence, highlighting heightened activity during specific trading hours and days. We also find evidence of jumps influencing intraday returns, underscoring their significance in short-term price dynamics. Our findings enhance understanding of the cryptocurrency market microstructure and offer insights for risk management and predictive modeling strategies. Nevertheless, further research is needed to develop robust methodologies for detecting and analyzing co-jumps across multiple assets.
Cryptocurrency has become a significant subject in the global financial market, attracting investors and traders with its high volatility and profit potential. This study analyzes the daily volatility and GARCH volatility of six major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), USD Coin (USDC), Tether (USDT), and Ripple (XRP). Daily percentage change data and GARCH volatility are analyzed over specific time periods. The analysis reveals that Bitcoin (BTC) has an average daily percentage change of 0.366%, while Ethereum (ETH) has 0.376%. Litecoin (LTC) shows a daily percentage change of 0.166%, whereas USD Coin (USDC) and Tether (USDT) have very low daily percentage changes, nearly approaching zero. In terms of GARCH volatility, Ethereum (ETH) stands out with a volatility of 0.198, followed by Bitcoin (BTC) with a volatility of 0.121. The study's results indicate that cryptocurrencies are vulnerable to extreme price fluctuations, evidenced by their asymmetry distribution and kurtosis. Volatility correlation analysis reveals significant relationships, important for risk management and portfolio diversification. These findings contribute to understanding cryptocurrency volatility characteristics and aid stakeholders in making informed investment decisions.
This study aims to calculate the Value at Risk (VaR) in the cryptocurrency assets portfolio using the Monte Carlo simulation method. Analysts mostly use value at risk to measure the potential loss from many financial assets. This study analyzed four cryptocurrencies, Bitcoin (BTC), Ethereum (ETH), BNB (BNB), and Solana (SOL), from March 1, 2020 to March 31, 2024. The analysis results provide an overview of the expected performance, standard deviation, VaR, and Monte Carlo simulation results. According to the VaR analysis, SOL is the most risky asset, while Bitcoin is the least risky asset Investors should consider VaR before investing in any asset. Investors should also consider this information and their risk profile before making an investment decision.
This study recovers the Bitcoin option-implied risk aversion by jointly estimating a cross-sectional dataset of option prices and time-series data of realized returns on underlying asset prices. The empirical analysis of Bitcoin options on Deribit shows that the risk aversion function exhibits a peak shape, with the level of implied risk aversion of Bitcoin options ranging from â0.2 to 0.05, which is significantly lower than that of the traditional options market; furthermore, maturity affects the level of option-implied risk aversion, with shorter maturity implying higher risk-aversion levels. Moreover, our research indicates that after halving of Bitcoin, investorsâ risk aversion function becomes higher and steeper than before.
Volatility as a measure of financial risk is a crucial input for hedging, portfolio diversification, option pricing and the calculation of the value at risk. In this paper, we estimate the asymmetric and time-varying volatility for Bitcoin as the dominant cryptocurrency in the world market. A novel approach that explicitly separates the falling markets from the rising ones is utilized for this purpose. The empirical results have important implications for investors and financial institutions. Our approach provides a position-dependent measure of risk for Bitcoin. This is essential since the source of risk for an investor with a long position is the falling prices, while the source of risk for an investor with a short position is the rising prices. Thus, providing a separate risk measure in each case is expected to increase the efficiency of the underlying risk management in both cases compared to the existing methods in the literature.
The Financial Risk Meter (FRM) employs Quantile-LASSO regression to identify systemic financial risk and dependencies among tail events across financial assets. This paper establishes, both theoretically and empirically, a meaningful economic relationship between the FRM index, derived from the penalization parameter in quantile LASSO regression, and the volatility of assets' pricing kernels, the attainable maximal Sharpe ratio, and market volatility. Despite the rapid growth of the crypto market and its increasing integration with traditional financial markets, there remains a dearth of risk measures in this space. FRM@Crypto exhibits robust predictive capabilities in anticipating future market risk, potentially filling a critical void in this market.
This research analyzes the dynamic relationships between the economic and political uncertainty index and the fear index in global markets and cryptocurrencies using the wavelet-based DCC-GARCH method, considering different time scales. Monthly data sets for the periods 2012âApril 2024 for GEPU,VIX, and Bitcoin and April 2016âApril 2024 for Ethereum are used in the study. Findings are obtained in terms of the volatility interaction between cryptocurrencies (Bitcoin and Ethereum) and GEPU and VIX, as well as four different time scales representing the short, medium, and long term. As a result of the analysis based on raw data, it was found that there is no volatility interaction between cryptocurrencies and GEPU and VIX returns. However, there is a volatility interaction between past volatility shocks and current period volatility shocks in the 4-8 and 16-32 month investment cycle periods of VIX, Bitcoin, GEPU, and Ethereum and time scales. These results, which show that volatility shocks persist in both 4-month and 16-month investment cycles, have significant implications for investors and policymakers. They highlight the need for comprehensive information about changes in the global economy and politics, and they are expected to provide insights for both investors and policymakers.
Cryptoassets are extremely volatile with possible volatility jumps and infrastructure noise, making the estimation of true volatility process challenging. When the high-frequency data are not available, the true volatility needs to be estimated to be further studied or forecasted. The GARCH-family models have become a norm in the field. Here, we examine the performance of 6 GARCH-type specifications with 4 distributional assumptions and compare them with 4 non-parametric range-based models built on the daily âcandlesâ. Our study focuses on five popular cryptocurrencies (Bitcoin, Ethereum, BNB, XRP, and Dogecoin) between 1 July 2019 and 30 September 2022, utilizing Binance 5-minute data for realized measures as the high-frequency estimators of the true volatility process. The results reveal that the Garman-Klass estimator clearly outperforms the GARCH-family models in all studied settings, and the other range-based estimators remain competitive with the GARCH-family models. These results are crucial for studies on volatility in cryptoassets where using the GARCH-type models is a standard. When the high-frequency data are not available, the range-based estimators, and the Garman-Klass estimator in particular, should be preferred as proxies for the true volatility process over the GARCH-type models, be it in the in-sample, more qualitative studies, or the forecasting, out-of-sample exercises.
Soccer is the most popular sport in the world, and bitcoin is a global asset. Penalty shootouts represent an important stage in a soccer match and generate an enormous amount of public interest and attention. Bitcoin trading experiences a significant drop in volume and volatility during penalty shootouts at major international soccer tournaments. After the conclusion of penalty shootouts, the intensity of bitcoin trading exhibits a swift and a strong rebound. Significant fluctuations in trading volume and volatility of bitcoin around penalty shootouts are primarily driven by the variation in number of trades rather than in trade size.
We present tail risk analysis of cryptocurrencies (Bitcoin, Ethereum and Litecoin), non-fungible tokens, stocks (FTSE 100 and S&P 500) and Gold from November 12, 2017 to March 31, 2022 using conditional model-based Value-at-Risk (VaR). We explored which model specification and distributional innovation could best capture the tail risk in these assets. Using the VaR and other risk metrics, we showed that there is no superior model/metric for capturing tail risk. We found that, for all the assets, non-Gaussian distributional assumptions best modelled the asymmetry and fat-tails in the distributions of the returns; though there was more homogeneity in the distributional assumptions for Gold unlike the other assets. Our research is crucial for internal risk modelling and may increase global investor confidence for those who blend conventional and unconventional assets. Also, this study can help investors make informed decisions about asset allocation and risk tolerance in the events of extreme market conditions. Understanding the tail risks in financial assets can help investors hedge and diversify against risk in their portfolios. The theoretical implications also show a trade-off between the different assets as the presence of tail risk reflect the potential of returns, yet possible losses in the presence of extreme events. Last, the findings reinforce the need for risk managers to re-focus their attention to a set of superior models rather than a single best model for risk assessment.
Abstract We aim to identify the determinants of nonâfungible tokens (NFTs) returns. The 10 most popular NFTs based on their price, trading volume, and market capitalisation are examined. Twentyâthree potential drivers of the returns of each NFT are considered. We employ a Bayesian LASSO model which takes into account stochastic volatility and leverage effect. The results indicate that NFTs returns are primarily driven by volatility and ethereum returns. We find a weak connection between NFTs returns and conventional assets, such as stock, oil, and gold markets.