Blockchain Papers

Seyedeh Fatemeh Mottaghi, Bertram I. Steininger

No abstract is available for this record.

Aubain Nzokem

The paper presents two series representations of a L{\'e}vy process for the Generalized Tempered Stable (GTS) distribution: a series representation generated by the inverse tail integral and a short noise representation. Both series representations are used to simulate the daily returns of Bitcoin and Ethereum. The Q-Q plot analysis shows smooth linear patterns, indicating strong agreement between the empirical and theoretical GTS distributions.

Gabriel Borrego Rold aacute n

No abstract is available for this record.

Ismail Jirou, Ikram Jebabli, Amine Lahiani

No abstract is available for this record.

Tetsuya Takaishi

The finite sample effect on the Hurst exponent (HE) of realized volatility time series is examined using Bitcoin data. This study finds that the HE decreases as the sampling period $Δ$ increases and a simple finite sample ansatz closely fits the HE data. We obtain values of the HE as $Δ\rightarrow 0$, which are smaller than 1/2, indicating rough volatility. The relative error is found to be $1\%$ for the widely used five-minute realized volatility. Performing a multifractal analysis, we find the multifractality in the realized volatility time series, smaller than that of the price-return time series.

Kamphol Panyagometh

During the COVID-19 pandemic and subsequent periods of US monetary policy normalization after quantitative easing during COVID-19, global financial markets have encountered elevated levels of volatility and risk. In response, investors have increasingly sought out unconventional financial assets, such as Bitcoin, to mitigate exposure and enhance portfolio diversification. This study utilizes a Dynamic Conditional Correlation (DCC) Multivariate GARCH model, specifically employing the GARCH (1,1) specification, to analyze the relationship between stock markets index of major countries and cryptocurrency, with a particular focus on Bitcoin. The results indicate statistically significant correlations between Bitcoin and stock market returns in several countries during the COVID-19 period. Volatility appears to be influenced by historical stock market performance during both the pandemic and the subsequent normalization of monetary policy. Furthermore, the DCC-GARCH models reveal low significant coefficients for ASEAN stock market indices before and during the COVID-19 pandemic, indicating that these markets may have displaced Bitcoin as a hedge asset. In contrast, stock market indices in America and Europe consistently show statistical significance across all periods, suggesting that Bitcoin’s role as a hedge in these regions is limited. In contrast, gold clearly demonstrated safe haven properties before the COVID-19 pandemic which a characteristic had not been observed for Bitcoin. However, gold has emerged as a safe haven for only ASEAN stock markets since the U.S. initial 0.25% interest rate hike.

Iulia Cristina Iuga, Raluca Andreea Nerişanu, Larisa-Loredana Dragolea

This study explores the volatility spillover effects between clean and dirty cryptocurrencies and key financial indices, specifically focusing on Green Finance Indices (such as solar, wind, and nuclear) and Economic Indices (like the Baltic Dry Index and CRB Index). Employing the diagonal BEKK model and the DCC GARCH model, the study spans data from February 17, 2020, to September 30, 2024, to analyze how cryptocurrencies, categorized by their environmental impact, influence these indices. The results reveal significant volatility spillovers from both clean and dirty cryptocurrencies, with clean cryptocurrencies such as Cardano showing a stabilizing effect, while dirty cryptocurrencies like Bitcoin exhibit more pronounced and asymmetric volatility impacts on green finance indices. Furthermore, the persistent correlations identified through the DCC GARCH model highlight the dynamic relationships between cryptocurrency markets and green finance, suggesting that shocks in cryptocurrency volatility can significantly affect the financial dynamics of renewable energy investments. These insights are valuable for portfolio diversification and risk management, indicating that certain cryptocurrencies may serve as effective hedging instruments against risks in green finance. This study contributes to a deeper understanding of the interaction between digital financial assets and sustainable investments, offering practical implications for investors, financial managers, and policymakers committed to achieving Sustainable Development Goals (SDGs).

Venator Santiago, Michel Charifzadeh, Tim Alexander Herberger

Purpose This study aims to investigate the impact of the 2022 collapse of the Terra-Luna ecosystem on volatility correlations among digital assets, including U.S. Terra, Luna, Bitcoin, Ether, a Decentralized Finance index and U.S.-sourced conventional assets stocks, bonds, oil, gold and the dollar index. The primary research question addresses whether correlations increased between digital and conventional assets during the collapse. Design/methodology/approach A dynamic conditional correlation generalized autoregressive conditional heteroskedasticity model was used to examine changes in volatility correlations during the market crash. Specifically, a data set of 1,442 close prices from 30-minute interval candles of digital and conventional asset prices are considered to provide a granular view of market dynamics during the sample period from January 3rd, 2022, to May 31st, 2022, including the crash event. Findings While the dynamic conditional correlation plots of the model indicate increased volatility, the results do not offer sufficient evidence to confirm an increase in correlations between digital and conventional assets during the Terra-Luna downfall. Furthermore, the authors confirm Bitcoin’s role as a diversifier with oil and observe the dollar index maintaining a negative correlation with Bitcoin during the crash, supporting Bitcoin’s function as a hedge against the U.S. dollar. However, the findings during the crash diverge from previous studies, reflecting shifts in correlation patterns in broader market downturns. Specifically, the authors identify the need for adaptive capital allocation strategies, as gold’s oscillation during the period suggests it may not serve as an effective hedge during black swan events. Practical implications The findings provide insights for investors, financial institutions and regulators to improve risk management, portfolio diversification, trading strategies and the formulation of consumer protection regulations. In addition, the results underscore the challenges of mitigating risks beyond regulatory measures and emphasize the importance of exercising caution for investors. Originality/value This study addresses the research gap in changes between conventional and digital asset volatility correlations during collapses in the digital asset space.

Limin Wen, Junxue Li, Tong Pu, Yiying Zhang

Abstract Conditional risk measures and their associated risk contribution measures are commonly employed in finance and actuarial science for evaluating systemic risk and quantifying the effects of risk interactions. This paper introduces various types of contribution ratio measures based on the multivariate conditional value-at-risk (MCoVaR), multivariate conditional expected shortfall (MCoES), and multivariate marginal mean excess (MMME) studied in [34] (Ortega-Jiménez, P., Sordo, M., & Suárez-Llorens, A. (2021). Stochastic orders and multivariate measures of risk contagion. Insurance: Mathematics and Economics , vol. 96, 199–207) and [11] (Das, B., & Fasen-Hartmann, V. (2018). Risk contagion under regular variation and asymptotic tail independence. Journal of Multivariate Analysis 165 (1), 194–215) to assess the relative effects of a single risk when other risks in a group are in distress. The properties of these contribution risk measures are examined, and sufficient conditions for comparing these measures between two sets of random vectors are established using univariate and multivariate stochastic orders and statistically dependent notions. Numerical examples are presented to validate these conditions. Finally, a real dataset from the cryptocurrency market is used to analyze the spillover effects through our proposed contribution measures.

Michaël Allouche, Stéphane Girard, Emmanuel Gobet

No abstract is available for this record.

O. D. Agbedeyi, Sadik Olaniyi Maliki, V. E. Asor

In this research work, we developed a predictive model for digital currency prices, involving daily closing price as a function of time. We used the Geometric Brownian motion stochastic differential equation which was solved using inbuild functions in Microsoft Excel. While we used the Bitcoin as our case study, our model was able to predict the daily closing prices of Bitcoin to a reasonable degree of accuracy. We equally observe that the time dependent Geometric Brownian motion stochastic differential equation cannot give digital currency traders and investors a clue on when to trade off their digital assets. Thus, it become very risky using our model to make well informed trading decisions. We therefore, recommend that for minimum risk, trades and investors in digital currencies should consider a combination of other signal tools to take more informed and less risky trading decisions.

Agoestina Mappadang, Bayu Adi Nugroho, Setyani Dwi Lestari, Elizabeth Elizabeth · 5 authors

A significant amount of historical returns is needed for the generalized autoregressive conditional heteroscedasticity (GARCH) models to be calibrated. Newer cryptocurrencies, such as non-fungible tokens (NFTs), have relatively limited data to create robust parameter estimates. This study uses a newly developed method, the exponentially weighted moving average (EWMA) model, that takes into account the fat-tailed distributions of returns and volatility response to forecast Value-at-Risk (VaR) and Expected Shortfall (ES). We employ thorough back tests of daily VaR and ES forecasts, which are widely utilized for regulatory approval and are considered to be industry standards. We also use loss function ratios to select the best model. Our results indicate that simpler models are just as good as the complicated ones, provided the simpler models capture fat-tailed distributions of returns. The primary findings hold up through several tests.

Marcin Wątorek, Marcin Królczyk, Jarosław Kwapień, Tomasz Stanisz · 5 authors

Multifractality is a concept that helps compactly grasping the most essential features of the financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on the centralized exchanges. A new element that adds complexity to cryptocurrency markets is the possibility of decentralized trading. Based on the extracted tick-by-tick transaction data from the Universal Router contract of the Uniswap decentralized exchange, from June 6, 2023, to June 30, 2024, the present study using Multifractal Detrended Fluctuation Analysis (MFDFA) shows that even though liquidity on these new exchanges is still much lower compared to centralized exchanges convincing traces of multifractality are already emerging on this new trading as well. The resulting multifractal spectra are however strongly left-side asymmetric which indicates that this multifractality comes primarily from large fluctuations and small ones are more of the uncorrelated noise type. What is particularly interesting here is the fact that multifractality is more developed for time series representing transaction volumes than rates of return. On the level of these larger events a trace of multifractal cross-correlations between the two characteristics is also observed.

Thabani Ndlovu, Delson Chikobvu

This study uses a hybrid model of the exponential generalised auto-regressive conditional heteroscedasticity (eGARCH)-extreme value theory (EVT)-Gumbel copula model to investigate the dependence structure between Bitcoin and the South African Rand, and quantify the portfolio risk of an equally weighted portfolio. The Gumbel copula, an extreme value copula, is preferred due to its versatile ability to capture various tail dependence structures. To model marginals, firstly, the eGARCH(1, 1) model is fitted to the growth rate data. Secondly, a mixture model featuring the generalised Pareto distribution (GPD) and the Gaussian kernel is fitted to the standardised residuals from an eGARCH(1, 1) model. The GPD is fitted to the tails while the Gaussian kernel is used in the central parts of the data set. The Gumbel copula parameter is estimated to be α=1.007, implying that the two currencies are independent. At 90%, 95%, and 99% levels of confidence, the portfolio’s diversification effects (DE) quantities using value at risk (VaR) and expected shortfall (ES) show that there is evidence of a reduction in losses (diversification benefits) in the portfolio compared to the risk of the simple sum of single assets. These results can be used by fund managers, risk practitioners, and investors to decide on diversification strategies that reduce their risk exposure.

Hanen Ben Ameur, Fouad Jamaani, Mohammed N. Abu-Alfoul

This paper examines gold and cryptocurrencies' hedge and safe-haven capabilities against various downturns, including the COVID-19 pandemic and Geopolitical Risks (GPR), across different market conditions. The study covers a sample period from 2013 to 2021 at a daily frequency, employing the GARCH model and quantile regression with binary variables. The empirical results indicate that neither gold nor cryptocurrencies can act as strong hedges against infectious disease pandemics. However, gold, Bitcoin, and Ethereum exhibit weak safe-haven abilities during geopolitical risks. Using regression quantiles, the study finds that gold demonstrates a strong safe-haven against low and high Infectious Disease Epidemic Market Volatility (IDEMV) during extremely bearish and bullish markets. In contrast, Bitcoin and Ethereum act as strong safe havens only against low IDEMV during extreme bearish markets. Gold also shows a strong hedge propriety against extreme geopolitical events, while cryptocurrencies provide a weak hedge. Overall, gold exhibits strong safe-haven properties against low and high Geopolitical tensions, while cryptocurrencies' hedging and safe-haven abilities vary across markets. These findings convey insights for investors and guidance to supervisors on the evolution of gold, Bitcoin, and Ethereum as safe-haven and hedge instruments during both bearish and bullish markets.

Aubain Nzokem, Daniel Maposa

The paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes the maximum likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the function characteristic and the fractional Fourier transform (FRFT), we provide a comprehensive approach to circumvent the problem and yield a good parameter estimation of the GTS probability. The methodology was applied to fit two heavily tailed data (Bitcoin and Ethereum returns) and two peaked data (S\&P 500 and SPY ETF returns). For each index, the estimation results show that the six-parameter estimations are statistically significant except for the local parameter, $μ$. The goodness-of-fit was assessed through Kolmogorov-Smirnov, Anderson-Darling, and Pearson's chi-squared statistics. While the two-parameter geometric Brownian motion (GBM) hypothesis is always rejected, the GTS distribution fits significantly with a very high p-value; and outperforms the Kobol, Carr-Geman-Madan-Yor, and Bilateral Gamma distributions.

Kostas Giannopoulos, Ramzi Nekhili, Christos Christodoulou-Volos

Understanding the density of possible prices in one-minute intervals provides traders, investors, and financial institutions with the data necessary for making informed decisions, managing risk, optimizing trading strategies, and enhancing the overall efficiency of the cryptocurrency market. While high accuracy is critical for researchers and investors, market nonlinearity and hidden dependencies pose challenges. In this study, the filtered historical simulation is used to generate pathways for the next hour on the one-minute step for Bitcoin and Ethereum quotes. The innovations in the simulation are standardized historical returns resampled with the method of block bootstrapping, which helps to capture any hidden dependencies in the residuals of a conditional parameterization in the mean and variance. Ordinary bootstrapping requires the feed innovations to be free of any dependencies. To deal with complex data structures and dependencies found in ultra-high-frequency data, this study employs block bootstrap to resample contiguous segments, thereby preserving the sequential dependencies and sectoral clustering within the market. These techniques enhance decision-making and risk measures in investment strategies despite the complexities inherent in financial data. This offers a new dimension in measuring the market risk of cryptocurrency prices and can help market participants price these assets, as well as improve the timing of their entry and exit trades.

Carlos Esparcia, Tarek Fakhfakh, Francisco Jareño, Achraf Ghorbel

Abstract This study examines the link between stocks and decentralized finance (DeFi) in terms of returns and volatility. Major G7 exchange-traded funds (ETFs) and various highly traded DeFi assets are considered to ensure the robustness of the empirical experiment. Specifically, this study applies the vector autoregression generalized autoregressive conditional heteroskedasticity (VAR-GARCH) model to examine the information transmission of these two markets on a two-way basis and the dynamic conditional correlation (DCC)-GARCH model to assess the bivariate correlation structure between each DeFi and ETF pair. The volatility spillover analysis proves a contagion effect occurred between different geographic markets, and even between markets of different natures and typologies, during the most turbulent moments of the COVID-19 crisis and the war in the Ukraine. Our results also reveal a weak positive correlation between most DeFi and ETF pairs and positive hedge ratios that approach unity during turbulent times. In addition, DeFi assets, except for the Bazaar (BZR) Protocol, can offer diversification gains when included in financial investment portfolios. These results are particularly relevant for portfolio managers and policy-makers when designing investment strategies, especially during periods of financial crisis.

Haider Ali, Muhammad Aftab, Faheem Aslam, Paulo Ferreira

Jump dynamics in financial markets exhibit significant complexity, often resulting in increased probabilities of subsequent jumps, akin to earthquake aftershocks. This study aims to understand these complexities within a multifractal framework. To do this, we employed the high-frequency intraday data from six major cryptocurrencies (Bitcoin, Ethereum, Litecoin, Dashcoin, EOS, and Ripple) and six major forex markets (Euro, British pound, Canadian dollar, Australian dollar, Swiss franc, and Japanese yen) between 4 August 2019 and 4 October 2023, at 5 min intervals. We began by extracting daily jumps from realized volatility using a MinRV-based approach and then applying Multifractal Detrended Fluctuation Analysis (MFDFA) to those jumps to explore their multifractal characteristics. The results of the MFDFA—especially the fluctuation function, the varying Hurst exponent, and the Renyi exponent—confirm that all of these jump series exhibit significant multifractal properties. However, the range of the Hurst exponent values indicates that Dashcoin has the highest and Litecoin has the lowest multifractal strength. Moreover, all of the jump series show significant persistent behavior and a positive autocorrelation, indicating a higher probability of a positive/negative jump being followed by another positive/negative jump. Additionally, the findings of rolling-window MFDFA with a window length of 250 days reveal persistent behavior most of the time. These findings are useful for market participants, investors, and policymakers in developing portfolio diversification strategies and making important investment decisions, and they could enhance market efficiency and stability.

Mar Grande, F. Borondo, Juan Carlos Losada, J. Borondo

Pairs trading is a short-term speculation trading strategy based on matching a long position with a short position in two assets in the hope that their prices will return to their historical equilibrium. In this paper, we focus on identifying opportunities where mean reversion will happen quickly, as the commission costs associated with keeping the positions open for an extended period of time can eliminate excess returns. To this end, we propose the use of the local Hurst exponent as a signal to open trades in the cryptocurrencies market. We conduct a natural experiment to show that the spread of pairs with anti-persistent values of Hurst revert to their mean significantly faster. Next, we verify that this effect is universal across pairs with different levels of co-movement. Finally, we back-test several pairs trading strategies that include H<0.5 as an indicator and check that all of them result in profits. Hence, we conclude that the Hurst exponent represents a meaningful indicator to detect pairs trading opportunities in the cryptocurrencies market.

Iqra Hussain, Nazakat Ali, Hafiz Bilal Ahmad, Suhail Ashraf

This paper explores the volatility spillover effects between the cryptocurrency market and the Pakistan Stock Exchange (PSX). Utilising data from January 1, 2019, to April 5, 2024, sourced from Investing and Yahoo Finance, the study employs the Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MGARCH) BEKK model to assess the dynamic interactions between these markets. Stationarity tests confirmed the non-stationarity of time series data at their levels, which became stationary after first differencing, ensuring robust econometric analysis. The results indicate significant volatility spillovers from major cryptocurrencies, such as Bitcoin and Ethereum, to the PSX, highlighting a solid interconnectedness between these markets. This suggests that digital asset volatility significantly influences traditional financial systems. The study concludes that integrating cryptocurrencies into global financial markets introduces risks and opportunities for investors and policymakers. The findings underscore the need for market participants to account for these volatility interactions in their risk management strategies. Additionally, policymakers must consider these interlinkages to maintain financial stability. This research contributes to the literature on financial market volatility by emphasising the importance of understanding the impact of emerging digital currencies on traditional stock markets.

Piotr Fiszeder, Marta Małecka, Péter Molnár

Traditional volatility models do not work well when volatility changes rapidly and in the presence of outliers. Therefore, two lines of improvements have been developed separately in the existing literature. Range-based models benefit from efficient volatility estimates based on low and high prices, while robust methods deal with outliers. We propose a range-based GARCH model with a bounded M-estimator, which combines these two improvements with a third new improvement: a modified robust method, which adds elasticity in treating the outliers. We apply this model to Bitcoin , Ethereum Classic, Ethereum, and Litecoin and find that it forecasts variances, value at risk, and expected shortfall more accurately than the standard GARCH model, the standard range-based GARCH model, and the GARCH model with the robust estimation. Utilization of high and low prices joined with a novel treatment of outliers makes our model perform well during extreme periods when traditional volatility models fail.

Robin Thomas

Abstract This paper investigates the dynamic relationships between the volatility of Bitcoin and major Indian stock market indices. Employing a dynamic conditional correlation–generalized autoregressive conditional heteroskedasticity (DCC‐GARCH) 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 short‐lived, indicated by a relatively low DCC‐GARCH 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 DCC‐GARCH 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 real‐world examples, such as the impact of sudden policy changes in India or global market flash crashes. By understanding the short‐lived 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.

F.H.F. Leung, Martin Law, Shih-Kien Djeng

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 model’s 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.