Extreme return-volume relationship in cryptocurrencies: Tail dependence analysis

This article defines coefficient of upper-lower tail dependence and coefficient of lower-upper tail dependence based on coefficient of upper tail dependence and coefficient of lower tail dependence and does an empirical research on tail dependence in China stock market. A mixed Copula that can well describe dependence structure between Shanghai Exchange Composite Index(SHECI) and Shenzhen Exchange Component Index(SZECI) is found by empirical analysis firstly, and is used to calculate coefficients of tail dependence. The results show that there are strong upper tail dependence and lower tail dependence, but no upper-lower tail dependence and lower-upper tail dependence between daily returns of SHECI and SZECI.

In this paper, we clarify dependence properties of elliptical distributions by deriving general but explicit formulae for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the tail dependence coefficients are fully determined by the tail index of the random vector (or equivalently of its components) and the linear correlation coefficient. Whereas Kendall's tau is invariant in the class of elliptical distributions with continuous marginals and a fixed dispersion matrix, we show that this is not true for Spearman's rho. We also show that sums of elliptically distributed random vectors with the same dispersion matrix (up to a positive constant factor) remain elliptical if they are dependent only through their radial parts.

We use a semiparametric GARCH-in-Mean copula model to examine the price evolution and volatility dynamics of crude oil, natural gas, and hydrocarbon gas liquids markets using data from January 2002 to December 2021. We find that uncertainty has a positive and statistically significant effect on the returns of crude oil and natural gas, but has a negative and statistically significant effect on ethane returns. We also find that the Frank copula is the best copula to describe the (bivariate) dependence structures between the crude oil, natural gas, and hydrocarbon gas liquids markets, except for the relationship between ethane and butane where the Clayton copula is the most fitted copula. It suggests that weak lower and upper tail dependence exists between the energy returns, and there is statistically significant lower tail dependence between ethane and butane. In other words, extremely low crude oil prices are associated with low prices of natural gas and hydrocarbon gas liquids, and vice versa. When ethane returns go down, there is excess comovement in the returns of butane. Moreover, the tail dependence is strongest between crude oil and natural gas.

This thesis presents the concept of tail dependence in a financial context as one tool to measure dependence in the extremes of a bivariate distribution. Copulae can separate the problem of estimating a multidimensional distribution into the estimation of the marginal distributions and the dependence between the onedimensional random variables. Therefore, copulae are used in order to carry out the estimation of the tail dependence coefficient (TDC). Four estimators of the TDC are presented and compared in a simulation study for various distributions and copulae. Furthermore, an introduction into bivariate Extreme Value Theory (EVT) is given, which tries precisely to analyze the behavior at the tail of a bivariate distribution. EVT allows to construct estimators of the TDC and to derive a test for tail independence, which is recognized to be indispensable but rarely utilized in a financial context. As an application to nine different financial data sets shows, the phenomenon of tail dependence is less common than often argued in the literature: the periods where indeed tail independence can be rejected are few.

Hierarchical Risk Parity: Accounting for Tail Dependencies in Multi-Asset Multi-Factor Allocations

Empirical evidence shows that asset returns appear to be more highly correlated on the downside than on the upside, particularly for equities. This is in addition to the well-established property that return variances vary over time. GARCH-type models allow for the latter, but disturbances are typically assumed to be multivariate Gaussian or Student- t , which forces the correlations to be symmetric. This is especially problematical in estimating extreme risk exposures using standard measures like value at risk (VaR) and expected shortfall (ES), for which lower tail dependence causes symmetric models to underestimate downside exposure. Tsafack proves this proposition using a new concept of lowerstochastic ordering. He then explores how much difference it makes to estimate VaR and ES for portfolios of U.S. and Canadian stocks and bonds allowing dependence in the extreme left tail with a Gumbel copula. The data show significant asymmetric tail dependence especially for stocks, and the models that impose symmetry underestimate the risk of extreme tail events. VaR at the 5% level is fairly accurately estimated by standard symmetric models but they do not capture the behavior of the more remote tails, so that VaR at 1% and 0.5% and ES at 5% and beyond are underpredicted.

The objective of this thesis is to formally examine whether mutual fund returns are asymmetric and to test whether they display lower tail dependence with the Australian stock market. A model free test of asymmetry proposed by Hong, Tu and Zhou (2006) is applied to a set of Australian mutual fund returns. A Clayton copula is also fitted to the data to obtain a measure for lower tail dependence. The analysis shows that there is clear evidence of lower tail dependence for the majority of mutual funds in the sample and for the mutual fund market as a whole. The degree of lower tail dependence is significantly greater than that present in the market. A subsequent regression of several possible determinants of fund dependence suggests that managers have some ability to reduce the fund asymmetry and increase their management fees accordingly. However, there is strong evidence that their ability to reduce the lower tail dependence is dwarfed by an amplification effect, where the mutual fund magnifies the dependence structures present in the assets in their portfolio.

PurposeThis paper examines the extreme dependence and asymmetric risk spillovers between crude oil futures and ten US stock sector indices (consumer discretionary, consumer staples, energy, financials, health care, industrials, information technology, materials, telecommunication and utilities) before and during COVID-19 outbreak. This study is based on the rationale that stock sectors exhibit heterogeneity in their response to oil prices depending on whether they are classified as oil-intensive or non-oil-intensive sectors and the possible time variation in the dependence and risk spillover effects.Design/methodology/approachThe authors employ static and dynamic symmetric and asymmetric copula models as well as Conditional Value at Risk (VaR) (CoVaR). Finally, they use robustness tests to validate their results.FindingsBefore the COVID-19 pandemic, crude oil returns showed an asymmetric tail dependence with all stock sector returns, except health care and industrials (materials), where an average (symmetric tail) dependence is identified. During the COVID-19 pandemic, crude oil returns exhibit a lower tail dependency with the returns of all stock sectors, except financials and consumer discretionary. Furthermore, there is evidence of downside and upside risk asymmetric spillovers from crude oil to stock sectors and vice versa. Finally, the risk spillovers from stock sectors to crude oil are higher than those from crude oil to stock sectors, and they significantly increase during the pandemic.Originality/valueThere is heterogeneity in the linkages and the asymmetric bidirectional systemic risk between crude oil and US economic sectors during bearish and bullish market conditions; this study is the first to investigate the average and extreme tail dependence and asymmetric spillovers between crude oil and US stock sectors.

Dynamic Asymmetric Dependencies between Equities and Exchange Rate Markets

This paper is concerned with a procedure for financial time series clustering, aimed at creating groups of time series characterized by similar behavior with regard to extreme events. The core of our proposal is a double clustering procedure: the former is based on the lower tail dependence of all the possible pairs of time series, the latter on the upper tail dependence. Tail dependence coefficients are estimated with copula functions. The final goal is to exploit the two clustering solutions in an algorithm designed to create a portfolio that maximizes the probability of joint positive extreme returns while minimizing the risk of joint negative extreme returns. In financial crisis scenarios, such a portfolio is expected to outperform portfolios generated by the traditional methods. We describe the results of a simulation study and, finally, we apply the procedure to a dataset composed of the 50 assets included in the EUROSTOXX index.

Interval estimation for a measure of tail dependence

Wind speed scenario generation based on dependency structure analysis

Tail dependence is understood as the dependence between the variables assuming that these variables take the values from the tails of univariate distributions. In the paper two approaches of tail dependence determination are discussed: conditional correlation coefficient and tail dependence coefficients. It can be argued that both approaches are the generalizations of the well-known univariate approach, based on conditional excess distribution. In the paper the proposal is also given to extend tail dependence coefficients to the general multivariate case and to represent these coefficients through copula function.

Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls

Among bivariate tail dependence measures, the tail dependence coefficient has emerged as the popular choice. Akin to the correlation matrix, a multivariate dependence measure is constructed using these bivariate measures, and this is referred to in the literature as the tail dependence matrix (TDM). While the problem of determining whether a given d × d matrix is a correlation matrix is of the order O(d3) in complexity, determining if a matrix is a TDM (the realization problem) is believed to be non-polynomial in complexity. Using a linear programming (LP) formulation, we show that the combinatorial structure of the constraints is related to the intractable max-cut problem in a weighted graph. This connection provides an avenue for constructing parametric classes admitting a polynomial in d algorithm for determining membership in its constraint polytope. The complexity of the general realization problem is justifiably of much theoretical interest. Since in practice one resorts to lower dimensional parametrization of the TDMs, we posit that it is rather the complexity of the realization problem restricted to parametric classes of TDMs, and algorithms for it, that are more practically relevant. In this paper, we show how the inherent symmetry and sparsity in a parametrization can be exploited to achieve a significant reduction in the LP formulation, which can lead to polynomial complexity of such realization problems - some parametrizations even resulting in the constraint polytope being independent of d. We also explore the use of a probabilistic viewpoint on TDMs to derive the constraint polytopes.