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4. Shape of the symmetric Lévy distributions with µ = 0.8, 1.2, 1.6 and 2 (this last value actually corresponds to a Gaussian). The smaller µ, the sharper the 'body' of the distribution, and the fatter the tails, as illustrated in the inset.
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Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Addi...
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... The phenomenology of critical phenomena, encompassing phase transitions in diverse contexts, stands as a cornerstone within the framework of Statistical Mechanics theory. Initially conceived within the realm of many-body physics, it has evolved into a concept with far-reaching applications spanning disciplines such as economics, network theory, sociophysics, game theory, and numerous others [1][2][3][4][5]. ...
Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the crossover to tricritical points within the Blume–Capel model. Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a versatile tool for studying critical phenomena. Unlike traditional methods that eschew diagonalization, our method excels in handling short timescales and small system sizes, widening the scope of inquiry into critical behavior.
... and use the leave-one-out rescaling described in [44] to define the rescaled returns, ...
Since the introduction of Bitcoin in 2009, the dramatic and unsteady evolution of the cryptocurrency market has also been driven by large investments by traditional and cryptocurrency-focused hedge funds. Notwithstanding their critical role, our understanding of the relationship between institutional investments and the evolution of the cryptocurrency market has remained limited, also due to the lack of comprehensive data describing investments over time. In this study, we present a quantitative study of cryptocurrency institutional investments based on a dataset collected for 1324 currencies in the period between 2014 and 2022 from Crunchbase, one of the largest platforms gathering business information. We show that the evolution of the cryptocurrency market capitalization is highly correlated with the size of institutional investments, thus confirming their important role. Further, we find that the market is dominated by the presence of a group of prominent investors who tend to specialise by focusing on particular technologies. Finally, studying the co-investment network of currencies that share common investors, we show that assets with shared investors tend to be characterized by similar market behaviour. Our work sheds light on the role played by institutional investors and provides a basis for further research on their influence in the cryptocurrency ecosystem.
... There are a variety of academic communities that have studied financial market dynamics and evolutionary changes in structural dynamics such as those in applied mathematics, complex systems and econometrics [1][2][3]. A wide range of data scientific methodologies has been used to study evolutionary dynamics in financial assets such as linear algebraic-inspired techniques [2,[4][5][6], spectral methods such as random matrix theory [1,[7][8][9][10], a variety of unsupervised learning methodologies [11,12], change point detection [13,14] and a litany of statistical modeling techniques [15]. ...
Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? We have recently explored similar questions with a clear focus on the equity market. There, our research revealed several noteworthy dynamics such as an increase in the market’s collective strength and uniformity during crises, greater diversification benefits across equity sectors (rather than within them), and the existence of a “best value” portfolio of equities. In essence, we can now contrast any potential signatures of maturity we identify in the cryptocurrency market and contrast these with the substantially larger, older and better-established equity market. This paper aims to investigate whether the cryptocurrency market has recently exhibited similar mathematical properties as the equity market. Instead of relying on traditional portfolio theory, which is grounded in the financial dynamics of equity securities, we adjust our experimental focus to capture the presumed behavioral purchasing patterns of retail cryptocurrency investors. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market and to what extent. The results reveal nuanced signatures of maturity related to the equity market, including the fact that correlations collectively spike around exchange collapses, and identify an ideal portfolio size and spread across different groups of cryptocurrencies.
... techniques [2,[4][5][6], spectral methods such as random matrix theory [1,[7][8][9][10], a variety of unsupervised learning methodologies [11,12], change point detection [13,14] and a litany of statistical modeling techniques [15]. ...
... The second least diversified cluster is located at the top of the dendrogram, and includes portfolio combinations such as (1,3), (1,4) and (4,1). Below this, is a significantly larger cluster consists of portfolio combinations such as (8,1), (3,3) and (4,2). Finally the largest, most well diversified fourth cluster consists of portfolio combinations ranging from (4,3) through to (10,4). ...
Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? This paper aims to investigate whether the cryptocurrency market has recently exhibited similarly nuanced mathematical properties as the much more mature equity market. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market, and to what extent.
... and use the leave-one-out rescaling described in [39] to define the rescaled returns, ...
Since the introduction of Bitcoin in 2009, the dramatic and unsteady evolution of the cryptocurrency market has also been driven by large investments by traditional and cryptocurrency-focused hedge funds. Notwithstanding their critical role, our understanding of the relationship between institutional investments and the evolution of the cryptocurrency market has remained limited, also due to the lack of comprehensive data describing investments over time. In this study, we present a quantitative study of cryptocurrency institutional investments based on a dataset collected for 1324 currencies in the period between 2014 and 2022 from Crunchbase, one of the largest platforms gathering business information. We show that the evolution of the cryptocurrency market capitalization is highly correlated with the size of institutional investments, thus confirming their important role. Further, we find that the market is dominated by the presence of a group of prominent investors who tend to specialise by focusing on particular technologies. Finally, studying the co-investment network of currencies that share common investors, we show that assets with shared investors tend to be characterized by similar market behavior. Our work sheds light on the role played by institutional investors and provides a basis for further research on their influence in the cryptocurrency ecosystem.
... The analysis of both the import and the export directions is rather rare, see e.g., [30] where the hubs and authorities of the WTN have been studied, but we think that the Google matrix analysis using the PageRank, the CheiRank and the REGOMAX tools characterizes the economical activities in at a deeper and a more detailed level. The matrix analysis of the financial risks already demonstrated its efficiency for undirected flows [31][32][33]. However, the financial and trade flows are directional, and thus, we hope that the Google matrix tools used here will find further useful applications for the study of financial flows and the understanding of economy complexity. ...
We apply the recently developed reduced Google matrix algorithm for the analysis of the OECD-WTO World Network of Economic Activities. This approach allows to determine interdependencies and interactions of economy sectors of several countries, including China, Russia and the USA, properly taking into account the influence of all the other world countries and their economic activities. Within this analysis, we also obtain the sensitivity of EU countries’ economies to the petroleum activity sector. We show that this approach takes into account the multiplicity of economical interactions between countries and activity sectors, thus providing a richer analysis compared to the usual export-import analysis.
... In this work, we take another step in characterizing the performance of ultra-reliable systems. Our contributions are four-fold: i) we overview and analyze the concepts of asymptotic/non-asymptotic error probability, and their suitability as reliability measures; ii) we highlight that the error probability with FB is a random variable (RV) in fading channels, and provide its probability distribution; iii) we discuss how to use such results for evaluating the Value-at-Risk (VaR) and Conditional VaR (CVaR) measures [17], which are fundamental for answering the motivational questions presented in Section I-A and designing ultra-reliable systems beyond the average performance; and iv) we provide numerical examples and associated discussions, which illustrate the applicability of the proposed approaches. We validate our analytical derivations via simulations. ...
... However, the average error probability is not the only metric, maybe nor the more appropriate, to characterize the reliability performance of a communication system. Next we discuss how the system may be designed considering different risk measures [17] that make use of the error probability for a more detailed analysis. ...
... Thus, VaR 1−α is the maximum error probability in the system the (1 − α)% of the time. • Conditional VaR (CVaR) or Expected Shortfall: Although more directly related to risks than the standard deviation, the concept of VaR still suffers from some inconsistencies [17,Ch. 10]. ...
Future wireless systems are envisioned to support completely new use cases with extremely stringent requirements on both latency and reliability, e.g., Ultra-Reliable Low-Latency Communication. However, guaranteeing truly reliable services is quite challenging, much more under strict latency constraints. Notice that when it comes to reliability, the traditional approaches relying on average performance figures do not provide sufficient reliability guarantees. Instead, analyses/designs based on risk measures are more useful since they offer a more fine-grained probabilistic information of the system reliability. In this paper, we depart from novel information theory results on finite-blocklength (FB) coding, which characterize the error-latency trade-off under strict delay constraints, to highlight that the FB error probability is in fact a random variable in fading scenarios. Then, we provide accurate analytical approximations for the FB error probability distribution. This allows us to evaluate some well-known risk measures and, based on them, quantify the system reliability under strict latency constraints from different standpoints. We validate our results via simulation and provide numerical examples that illustrate, for instance, that two systems performing similar in terms of average reliability, may offer services with different risk perceptions.
... Bridging this gap, many recent studies have started to look at financial markets as complex systems with complex interactions between their various components [4][5][6][7] . One particularly interesting line of research, which was derived from this complex system perspective, is the representation of financial markets as correlation-based networks. ...
The concept of “Structural Diversity” of a network refers to the level of dissimilarity between the various agents acting in the system, and it is typically interpreted as the number of connected components in the network. This key property of networks has been studied in multiple settings, including diffusion of ideas in social networks and functional diversity of regions in brain networks. Here, we propose a new measure, “Structural Entropy”, as a revised interpretation to “Structural Diversity”. The proposed measure relies on the finer-grained network communities (in contrast to the network’s connected components), and takes into consideration both the number of communities and their sizes, generating a single representative value. We then propose an approach for monitoring the structure of correlation-based networks over time, which relies on the newly suggested measure. Finally, we illustrate the usefulness of the new approach, by applying it to the particular case of emergent organization of financial markets. This provides us a way to explore their underlying structural changes, revealing a remarkably high linear correlation between the new measure and the volatility of the assets’ prices over time.
... Among the most relevant statistical properties, volatility seems to be responsible for the observed clustering in price changes. That is, large°uctuations are commonly followed by other large°uctuations and similarly for small changes [7]. Another feature is that in clear contrast with price changes which show negligible autocorrelations, volatility autocorrelation is still signi¯cant for time lags longer than one year [7,14,19,20,26,24]. ...
... That is, large°uctuations are commonly followed by other large°uctuations and similarly for small changes [7]. Another feature is that in clear contrast with price changes which show negligible autocorrelations, volatility autocorrelation is still signi¯cant for time lags longer than one year [7,14,19,20,26,24]. Additionally, there exists the so-called leverage e®ect, i.e., much shorter (few weeks) negative cross-correlation between current price change and future volatility [4][5][6][7]. ...
... Another feature is that in clear contrast with price changes which show negligible autocorrelations, volatility autocorrelation is still signi¯cant for time lags longer than one year [7,14,19,20,26,24]. Additionally, there exists the so-called leverage e®ect, i.e., much shorter (few weeks) negative cross-correlation between current price change and future volatility [4][5][6][7]. ...
Stochastic volatility models describe asset prices [Formula: see text] as driven by an unobserved process capturing the random dynamics of volatility [Formula: see text]. We quantify how much information about [Formula: see text] can be inferred from asset prices [Formula: see text] in terms of Shannon’s mutual information in a twofold way: theoretically, by means of a thorough study of Heston’s model; from a machine learning perspective, by means of investigating a family of exponential Ornstein–Uhlenbeck (OU) processes fitted on S&P 500 data.
... Pfante, O. and Bertschinger, N. (2018), [21] consider the uncertainty of volatility estimates from Heston Greeks. It was stressed in [22] that volatility has been the cause for several Statistical properties of observed stock prices processes. It was further emphasized in [22] that volatility clustering is commonly accompanied by other large fluctuations and similar for small changes. ...
... It was stressed in [22] that volatility has been the cause for several Statistical properties of observed stock prices processes. It was further emphasized in [22] that volatility clustering is commonly accompanied by other large fluctuations and similar for small changes. As volatility is not observed it has to be estimated from market prices, i.e., as the implied volatility from option prices. ...
