Asymmetric Tail Research Articles

Dynamic asymmetric tail dependence structure among multi-asset classes for portfolio management: Dynamic skew-[formula omitted] copula approach

This study proposes AC dynamic skew-t copula with cDCC model to capture the dynamic asymmetric tail dependence structure among multi-asset classes (government bonds, corporate bonds, equities, and REITs). We provide new evidence that lower tail dependence coefficients increased compared to upper ones for all pairs in the COVID-19 crash and the recent high inflation period, indicating that the diversification effect through multi-asset investment decreased. Our empirical analysis also shows that in terms of AIC and BIC, dynamic AC skew-t copula fits data of multi-asset classes better than other dynamic elliptical copulas because it can consider the above dependence structure characteristics. Furthermore, out-of-sample analysis reveals that considering an asymmetry of tail dependence structure at each point with an AC dynamic skew-t copula enhances expected shortfall (ES) estimation accuracy and the performance of a minimum ES portfolio. These results indicate that capturing dynamic asymmetric tail dependence is crucial for multi-asset portfolio management.

Bitcoin, Fintech, Energy Consumption, and Environmental Pollution Nexus: Chaotic Dynamics with Threshold Effects in Tail Dependence, Contagion, and Causality

The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO2 emissions in addition to examining these series for entropy, long-range dependence, fractionality, complexity, chaos, and nonlinearity with a dataset spanning from 25 June 2012 to 22 June 2024. Empirical results from Shannon, Rényi, and Tsallis entropy measures; Kolmogorov–Sinai complexity; Hurst–Mandelbrot and Lo’s R/S tests; and Phillips’ and Geweke and Porter-Hudak’s fractionality tests confirm the presence of entropy, complexity, fractionality, and long-range dependence. Further, the largest Lyapunov exponents and Hurst exponents confirm chaos across all series. The BDS test confirms nonlinearity, and ARCH-type heteroskedasticity test results support the basis for the use of novel TAR-TR-GARCH–copula causality. The model estimation results indicate moderate to strong levels of positive and asymmetric tail dependence and contagion under distinct regimes. The novel method captures nonlinear causality dynamics from Bitcoin and Fintech to energy consumption and CO2 emissions as well as causality from energy consumption to CO2 emissions and bidirectional feedback between Bitcoin and Fintech. These findings underscore the need to take the chaotic and complex dynamics seriously in policy and decision formulation and the necessity of eco-friendly technologies for Bitcoin and Fintech.

The Asymmetric Tail Risk Spillover from the International Soybean Market to China’s Soybean Industry Chain

China is the largest soybean importer and consumer in the world. Soybean oil is the most-consumed vegetable oil in China, while soybean meal is the most important protein feed raw material in China, which affects the costs of animal husbandry. Volatility in the international soybean market would generate risk spillovers to China’s soybean industrial chain. This paper analyzed the channel of risk spillover from the international soybean market to China’s soybean industry chain and the asymmetry of the risk spillover. The degree of risk spillover from the international soybean market to the Chinese soybean industry chain was measured by the Copula–CoVaR model. The moderating role of inventory and demand in asymmetric risk spillovers was analyzed by quantile regression. We draw the following conclusions: First, the international soybean market impacts China’s soybean industry chain through soybeans rather than soybean meal and oil. The price fluctuation of China soybean market is obviously lower than that of the international soybean market. Second, there are apparent asymmetric risk spillovers from the international soybean market to China’s soybean industry chain, especially the soybean meal market. Third, increasing the Chinese soybean inventory and growing demand could effectively prevent the downside risk spillover from international markets to China’s soybean market. This also explains the asymmetry of risk spillovers. The research enriches the research perspective on food security, and the analysis of risk spillover mechanisms provides a scientific basis for relevant companies to develop risk-management strategies.

Likelihood Inference for Factor Copula Models with Asymmetric Tail Dependence.

For multivariate non-Gaussian involving copulas, likelihood inference is dominated by the data in the middle, and fitted models might not be very good for joint tail inference, such as assessing the strength of tail dependence. When preliminary data and likelihood analysis suggest asymmetric tail dependence, a method is proposed to improve extreme value inferences based on the joint lower and upper tails. A prior that uses previous information on tail dependence can be used in combination with the likelihood. With the combination of the prior and the likelihood (which in practice has some degree of misspecification) to obtain a tilted log-likelihood, inferences with suitably transformed parameters can be based on Bayesian computing methods or with numerical optimization of the tilted log-likelihood to obtain the posterior mode and Hessian at this mode.

Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns

Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A stochastic gradient ascent algorithm is used to solve the variational optimization. The methodology is used to estimate skew-t factor copula models with up to 15 factors for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. In a moving window study we show that the asymmetric dependencies also vary over time, and that intraday predictive densities from the skew-t copula are more accurate than those from benchmark copula models. Portfolio selection strategies based on the estimated pairwise asymmetric dependencies improve performance relative to the index.

Measuring Asymmetric Tails Under Copula Distributions

Extensive evidence has been gathered showcasing the prevalence of heavy-tailed distributions and asymmetric tail interdependence within equity and foreign exchange markets, particularly during times of crisis. Tail interdependence in financial markets often manifests as financial contagion, characterized by periods where declining prices and heightened volatility propagate across economic and financial sectors. This phenomenon causes markets that typically exhibit minimal or no correlation to behave similarly, often in opposition to fundamental principles. Instances of unwarranted contagion present a perplexing challenge, suggesting irrationality among market participants and defying conventional risk management strategies and optimal portfolio selections. Our objective is to construct a comprehensive framework for dissecting such occurrences, utilizing a metric of tail-nonexchangeable dependencies employing various copulas with diverse marginal distributions. We offer analytical insights into our measurement of tail order dependence to aid in understanding these events.

A fast-rotating blue straggler star in the tidal tail of the open cluster NGC 752

Context.NGC 752 is a well-known Galactic open cluster of intermediate age. In recent works, a very long and asymmetric tail was revealed. A blue straggler star (BSS) at the periphery of the tidal tail of the cluster was subsequently identified.Aims.We aim to perform a detailed analysis of the newly detected BSS based on the available comprehensive spectroscopic and photometric data. We also explored this BSS’s possible formation pathway and age limitation based on the collected spectroscopic and photometric data.Methods.We reconfirmed the membership of the newly determined BSS of NGC 752, supplemented byGaiaDR3 radial velocity data. Moreover, we also estimated the projected rotational velocity and the mass of the BSS from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope low-resolution spectra and multiband photometric data from various catalogs, respectively.Results.The newly discovered BSS is confirmed as a genuine member of NGC 752. The lack of ultraviolet excess in the spectral energy distribution and no significant variations in the light curve imply that this BSS is likely a single star (mass = 1.86−0.94+3.62 M⊙) formed through stellar mergers. The fast rotation velocity (v sin i = 206.9 ± 4.9 km s−1) of the BSS may provide constraints on its age (less than a hundred million years), but more formation details require further investigation.

Are cleaner energy and financial technologies needed? Contagion and causality evidence between global fintech markets, energy consumption, and environmental pollution

AbstractFinancial technology (FinTech) depends on high amounts of energy with an upward trend, possibly affecting emissions due to energy consumption (EC). The study investigates tail dependence, contagion, and nonlinear between FinTech, EC, and carbon dioxide emissions (CO2e) with MS-GARCH-copula and MS-GARCH-copula-causality with a daily sample covering 02 Jan 2012–28 December 2022. The method is a generalized version of single-regime GARCH-copula and causality tests to Markov-switching. Empirical results indicated that FinTech, EC, and CO2e series follow nonlinear processes in addition to unit roots as determined by BDS nonlinearity tests and a set of linear and nonlinear unit root tests. Further, for all series, heteroskedasticity and nonlinear forms of heteroskedasticity cannot be rejected by ARCH–LM and White heteroskedasticity tests, leading to the estimation of the series and their joint dynamics by MS-GARCH-copula and a new MS-GARCH-copula based nonlinear Granger-causality test, the RSGCC test, under two distinct regimes characterized with the low and high volatility for extreme tails of data. Positivity and significance of copula parameters under both regimes indicate a high degree of positive but asymmetric tail dependence and contagion between FinTech & EC, in addition to contagion between FinTech & CO2e and EC & CO2e. RSGCC results determine unidirectional causalities from EC to CO2e and from FinTech to CO2e, coupled with bidirectional causality between FinTech and EC, which enhance the dynamics due to feedback effects. The findings of this paper are of importance for two central Sustainable Development Goals. Results could also be used to bring the FinTech markets and EC to the attention of policymakers, researchers, and eco-friendliness-focused portfolio managers. Graphical Abstract

On two new modified tawn copulas

At its core, copula theory focuses on constructing a copula function, which characterizes the structure of dependence between random variables. In particular, the creation of extreme value copulas is crucial because they allow accurate modeling of extreme dependence that traditional copulas can ignore. In this article, we propose theoretical developments on this subject by proposing two new extreme value copulas. They aim to extend the functionalities of the so-called Tawn copula. This is of interest because the Tawn copula is known to be a powerful tool in modeling joint distributions, particularly in capturing asymmetric and upper tail dependences, making it valuable for analyzing extreme events and tail risk. The proposed copulas are designed to go beyond these attractive features. On the mathematical side, they are derived from new Pickands dependence functions; one modifies the Pickands dependence function of the Tawn copula by using a polynomial-exponential function, and the other does the same but by introducing a power function. The proofs are based on diverse differentiation, arrangement, and inequality techniques. Overall, the created copulas are attractive because (i) they possess modulable levels of asymmetry, (ii) they depend on several tuning parameters, making them very flexible in terms of upper tail dependence in particular, and (iii) they benefit from interesting correlation ranges of values. Several figures and value tables support the theoretical findings.

Can green investment funds hedge climate risk?

We analyze tail risk dependence between Green Investment Funds (GIFs) and climate risks, emphasizing diversification benefits, safe-haven, and hedge features from 2009 to 2022. Our methodology, using AGDCC-GARCH, time-varying optimal copula (TVOC), and conditional diversification benefits (CDB), reveal various tail dependence regimes, showcasing the role of GIFs in extreme climate events. Symmetrical co-movement, observed during COVID-19 and Russia-Ukraine war, indicates no asymmetric tail dependence. Notably, GIFs offer substantial diversification benefits against climate risks, providing insights for investors and policymakers to formulate proactive strategies in line with sustainability goals.

Dynamic spillovers in higher moments and jumps across ETFs and economic and financial uncertainty factors in the context of successive shocks

Hedging is a particularly important tool in the Exchange Traded Fund (ETF) markets where market makers seek the best ways to mitigate the uncertainty of their exposures. This study relies on high frequency data to assess the spillover effects among ten US sector ETFs and various economic and financial uncertainty indexes based on realized volatility, realized higher moments as well as jumps under a relatively new spillover framework. Next, a time-varying parameter vector autoregression (TVP-VAR) model is used to examine the dynamic connectedness among ETFs and uncertainty factors volatilities while avoiding the sensitivity of spillover results to the choice of the rolling window. Our results showcase higher total connectedness between the different uncertainty indexes and ETFs, though with varying sensitivities. Notably, skewness and kurtosis can spread from one market to another, especially during times of market turbulence, reflecting the significant spillovers in higher-order moments. Interestingly, the market’s 30-day forward looking expectations of US stock market volatility (VIX) has stronger effect on the US sector equity ETFs than the expected 30-day volatility of returns on oil and gold. This analysis emphasizes the implications and contributions of assessing the spillover in higher-order moments covering volatility, skewness, and kurtosis to portfolio hedging and financial risk management. Overall, the results are of considerable practical interest for economic and market agents who are keen to understand market integration and systemic risk propagation to infer asymmetric or fat tail risk related to extreme or downside/upside risks.

Asymmetric Dependence in Hydrological Extremes

AbstractExtremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases, there is a natural asymmetry between extreme observations that cannot be captured by such coefficients. An example for such asymmetry is large discharges at an upstream and a downstream stations on a river network: an extreme discharge at the upstream station will directly influence the discharge at the downstream station, but not vice versa. Simple measures for asymmetric dependence in extreme events have not yet been investigated. We propose the asymmetric tail Kendall's τ as a measure for extremal dependence that is sensitive to asymmetric behavior in the largest observations. It essentially computes the classical Kendall's τ but conditioned on the extreme observations of one of the two variables. We show theoretical properties of this new coefficient and derive a formula to compute it for existing copula models. We further study its effectiveness and connections to causality in simulation experiments. We apply our methodology to a case study on river networks in the United Kingdom to illustrate the importance of measuring asymmetric extremal dependence in hydrology. Our results show that there is important structural information in the asymmetry that would have been missed by a symmetric measure. Our methodology is an easy but effective tool that can be applied in exploratory analysis for understanding the connections among variables and to detect possible asymmetric dependencies.

Asymmetric relationships and their effects on coexistence.

Species coexistence attracts wide interest in ecology. Modern coexistence theory (MCT) identifies coexistence mechanisms, one of which, storage effects, hinges on relationships between fluctuations in environmental and competitive pressures. However, such relationships are typically measured using covariance, which does not account for the possibility that environment and competition may be more related to each other when they are strong than when weak, or vice versa. Recent work showed that such 'asymmetric tail associations' (ATAs) are common between ecological variables, and are important for extinction risk, ecosystem stability, and other phenomena. We extend MCT, decomposing storage effects to show the influence of ATAs. Analysis of a simple model and an empirical example using diatoms illustrate that ATA influences can be comparable in magnitude to other mechanisms of coexistence and that ATAs can make the difference between species coexistence and competitive exclusion. ATA influences may be an important new mechanism of coexistence.

Bloodstain tails: Asymmetry aids reconstruction of oblique impact

In the field of forensic science, elongated bloodstains formed from oblique impact of droplets are sometimes used to reconstruct aspects of a bloodletting event. For low impact angles, these stains can include an asymmetric tail that bloodstain analysts can use qualitatively to establish directionality. Quantitative analysis of these bloodstain tails, and any insight that they can provide into the impact dynamics, is lacking due to experimental challenges. Previous studies of bloodstain shapes have predominantly focused on relatively large drip drops that fall vertically on flat and inclined surfaces; yet, for inclinations that produce low impact angles, gravitational effects can reshape and obscure tails, preventing insight into how tails develop on horizontal surfaces. Here, we carry out systematic experiments in which human blood droplets with diameters less than a millimeter impact a horizontal surface at impact angles ranging from 16° to 65°. High-speed imagery confirms that the tail is not part of a prompt splashing event, but rather forms at the last moments of spreading, maintaining its shape as it dries. For each stain, we link the tail length and elliptical geometry to the blood drop size and impact velocity vector that created it. Additionally, we report a power-law correlation of the dimensionless tail length with the angle and Weber and Reynolds numbers, and we describe how this correlation in conjunction with other existing correlations can improve reconstruction of the droplet size and impact velocity.

Aerospace structural reliability analysis method based on regular vine copula model with the asymmetric tail correlation

Considering the asymmetric tail correlations between variables in reliability analysis, an effective aerospace structural reliability analysis method based on regular vine copula models is proposed. Firstly, a product of multiple pair-copula functions and marginal density functions based on regular vine copula models are used to construct the joint probability density function. Secondly, the asymmetric copula functions are introduced into the candidate construction sets of pair-copula functions for capturing asymmetric tail correlations between variables. Meanwhile, the akaike information criterion (AIC) is adopted to select the optimal pair-copula functions. Thirdly, taking the difference of multi-dimensional correlations into account, six different regular vine copula models are used to construct the multivariate joint probability density function. And the corresponding regular vine copula-first order reliability method (RVC-FORM) considering the asymmetric tail correlation is proposed. Finally, three numerical examples and an aerospace turbine blade example are investigated to demonstrate the validity of the proposed method.

Can China's national carbon trading market hedge the risks of light and medium crude oil? A comparative analysis with the European carbon market

The study explores whether China's national carbon market can hedge the risks of light and medium crude oil compared with the European carbon market, through the diversified and hedging portfolios estimated by the NAGARCHSK-Mixed Copula. The current work confirms the existence of conditional higher moments and asymmetric tail dependence structures in the crude and carbon markets. Furthermore, for all crude oil, although the China's carbon market is slightly inferior to the European carbon market in terms of hedging costs and stability, the hedging effectiveness of the former is better than that of the latter. And Oman crude oil gets better hedging protection from the carbon markets than Brent crude oil. Finally, the diversified portfolios obviously outperform the hedging portfolios in terms of hedging effectiveness.

Commodity market financialization, herding and signals: An asymmetric GARCH R-vine copula approach

Institutional investors have significantly increased their exposure to commodity futures after 2004 in the process of commodity market financialization, raising questions about the risk-sharing and price-discovery functions of the market. We identify some symptoms of financialization through examining S&P500, JPM bond index, and 18 S&P GSCI excess return indices, employing ARMA-GARCH R-vine copula approach that can flexibly model high-dimensional multivariate asymmetric tail dependence. We discover three trends: an increased resemblance between the news impact curve of stocks and those of commodities; an increased bi-variate stock-commodity tail dependence; and an increased multivariate tail-dependence across all commodities. We also explore the market structural change underlying these symptoms using an augmented news impact curve. We suggest and provide evidence that herding, in addiction to leverage effect, explains the observed symptoms. The findings have profound implications for commercial hedgers and financial traders, and for regulators who are concerned about the functionalities of commodity futures market.

Vine copula-based Bayesian classification for multivariate time series of electroencephalography eye states

Abstract Sometimes classification tasks have to be based on multivariate time series data collected for each class. In these situations the data for each class might exhibit non-stationary behaviour together with complex dependence structures. We propose a vine copula-based approach to capture these features in each class before applying a Bayesian classifier. Vine copulas have been very successful in modelling asymmetric tail dependence among variables and are coupled with non-stationary univariate time series to model the multivariate time series data for each class. We illustrate this classification approach using data from a neural activity experiment using electroencephalography, where we want to classify the eye state. The level of neural activity was collected over time for multiple locations on the scalp. Our approach is able to identify relevant locations and allows for a model-based interpretation of the data generating process. A cross-validation study with comparison to competitor classifiers for this data set shows good performance of the proposed classifier.

Asymmetric tail risk contagion across China’s automotive industrial chain: a study based on input–output network

The input-output network of an industrial chain provides a channel for risk transmission. Using Smooth-Transition Vector Autoregression model (STVAR) and Diebold-Yilmaz directional connectedness measures, we explore tail risk (extreme risk) contagion across China’s automotive industrial chain. We find significant spillover effects that are asymmetric in different phases of China’s business cycle, monetary cycle, and policy uncertainty. When China’s economy is in a recession, under a monetary expansion, or at a high level of policy uncertainty, the total risk spillover across the chain is higher. We also find apparent risk spillover from the financial services industries to the automotive industrial chain as China’s economy is in a recession or a monetary expansion period. Still, a reverse spillover is found as policy uncertainty is at a high level. Meanwhile, the direction of risk propagation across the automotive industrial chain may change with the transition in the economic state or policy uncertainty state.

Financial and Macroeconomic Data Through the Lens of a Nonlinear Dynamic Factor Model

Through the lens of a nonlinear dynamic factor model, we study the role of exogenous shocks and internal propagation forces in driving the fluctuations of macroeconomic and financial data. The proposed model 1) allows for nonlinear dynamics in the state and measurement equations; 2) can generate asymmetric, state-dependent, and size-dependent responses of observables to shocks; and 3) can produce time-varying volatility and asymmetric tail risks in predictive distributions. We find evidence in favor of nonlinear dynamics in two important U.S. applications. The first uses interest rate data to extract a factor allowing for an effective lower bound and nonlinear dynamics. Our estimated factor coheres well with the historical narrative of monetary policy. We find that allowing for an effective lower bound constraint is crucial. The second recovers a credit cycle. The nonlinear component of the factor boosts credit growth in boom times while hinders its recovery post-crisis. Shocks in a credit crunch period are more amplified and persist for longer compared with shocks during a credit boom.