Tail Dependence Research Articles

Temporal changes in dependence between compound coastal and inland flooding drivers around the contiguous United States coastline

Flooding in low-lying coastal zones arises from coastal (storm surge, tides, and waves), fluvial (excessive river discharge), and pluvial (excessive surface runoff) drivers. We analyse changes in compound flooding potential around the contiguous United States (CONUS) coastline stemming from select combinations of these flooding drivers using long observational records with at least 55 years of data. We assess temporal changes in the tail (extremal) dependence (χ) using a 30-year sliding time window. Periods of strong tail dependence are found for the windows centered between the 1960s and 1980s/1990s at several locations for surge-discharge (S-Q) and surge-precipitation (S–P) combinations. Changes in dependence are associated with large-scale climate indices such as the Arctic Oscillation (AO) and El Nino Southern Oscillation indices (Niño 1.2 and Niño 3), among others. The significance of potential changes in the dependence structure is subsequently tested using Kullback–Leibler (KL) divergence. We find that changes are mostly not significant. Finally, we perform a complete multivariate statistical analysis exemplarily for one selected pair of variables at one location (S-Q in Washington, DC), allowing for varying dependence strength and structure as well as changes in the marginal distributions. Combined changes with increase in the dependence and marginals exacerbate the predicted compound flood potential. The comprehensive analysis presented here provides new insights into how and where compound flooding potential has changed with time, demonstrates associated links with large-scale climate indices, and highlights the effects of changes in the dependence and marginals in a multivariate statistical framework.

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.

Does COVID-19 impact the dependence between oil and stock markets? Evidence from RCEP countries

This paper studies the dependence between crude oil and RCEP stock markets before and after COVID-19 by using local Gaussian correlations, contagion tests, and time-frequency domain causality tests. Empirical results show that the lower tail dependence considerably enhanced except in China, while the higher tail dependence significantly increased in Australia, New Zealand, Japan, and Thailand. Contagion is detected from the WTI oil to New Zealand and Thailand stocks. The crude oil market has a short-term (0–32 day frequency) effect on RCEP stock markets, whereas the RCEP stock markets have a relatively stronger, long-term (64–128 day frequency) impact on crude oil markets. RCEP public panic disrupted the oil and stock markets during the Delta and Omicron spread. These findings may help the RCEP governments, institutions, and investors boost energy cooperation, capital flow, and cross-border investments under different market states and investment horizons.

Coherent measure of portfolio risk

This study introduces a multivariate entropic Value at Risk (mEVaR) risk measure, broadening the conventional Value at Risk scope to a multi-asset scenario. The mEVaR is coherent and encapsulates the integrated risk of various assets in a portfolio. In addition, a new theoretical result incorporates mutual information into the mEVaR to capture tail dependence during extreme market events. The findings suggest that greater mutual dependence among assets increases risk as the benefit of diversification decreases. Examples, simulations, and empirical studies illustrate the applicability of these risk measures as tools for managing and optimizing investment portfolios.

Nonlinear and asymmetric interconnectedness of crude oil with financial and commodity markets

In light of the COVID-19 outbreak and the recent Russian war in Ukraine, this paper explores the asymmetric and nonlinear interconnectedness between financial and commodity markets using high-frequency intraday data. We employ cross-quantilograms (CQ), paired vine-based copulas, and copula vine-based regression analysis to examine the heterogeneous and asymmetrical connectedness among various assets. Our study presents several key findings: (1) connectedness among assets increases sharply during the COVID-19 pandemic and intensifies with the Russia–Ukraine war; (2) stronger tail dependence is observed in the lower tail, indicating asymmetric connectedness among the assets; (3) the S&P 500 and natural gas have a predictive influence on the crude oil market; and (4) increased uncertainty and volatility in global markets due to these events impact the interconnectedness of the assets in our study, particularly the dependence between crude oil and the other assets in the sample. These results have important implications for governmental agencies, policymakers, investors, and portfolio managers, emphasizing the need for a non-linear framework to capture heterogeneous and asymmetric connectedness dynamics under extreme market conditions.

Bitcoin vs. fiat currencies: Insights from extreme dependence and risk spillover analysis with financial markets

We compare Bitcoin to fiat currencies (EUR, GBP, and JPY) using extreme dependence and temporal dynamic risk spillover analysis with various financial markets covering fixed-income, stock, and commodity indices. Using daily data from October 2010 to December 2022, covering various stress periods including the COVID-19 outbreak and the war in Ukraine, the results are summarized as follows. First, there is a similarity during the bearish market between Bitcoin and fiat currency markets regarding their relationships with fixed-income and gold markets in terms of temporal dynamic upside and downside risk spillover impacts despite the dissimilarity in their tail dependence structures. Thus, Bitcoin and fiat currency markets emerge as very feasible investments due to their insensitivity to the downside risk associated with fixed-income and gold markets. Second, there is a clear difference between Bitcoin and fiat currencies in their relationship with stock and crude oil markets based on the temporal dynamic upside and downside risk spillovers. Investors in stock and crude oil markets should consider fiat currencies for diversification purposes whereas these investors should take a short position on Bitcoin to protect their portfolio against downside extreme events such as the COVID-19 outbreak and Russia–Ukraine conflict. Our findings have implications for investors in terms of how they can protect their portfolios against extreme downward price movements.

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.

Tail Dependence as a Measure of Teleconnected Warm and Cold Extremes of North American Wintertime Temperatures

Abstract Current models for spatial extremes are concerned with the joint upper (or lower) tail of the distribution at two or more locations. Such models cannot account for teleconnection patterns of 2-m surface air temperature (T2m) in North America, where very low temperatures in the contiguous United States may coincide with very high temperatures in Alaska in the wintertime. This dependence between warm and cold extremes motivates the need for a model with opposite-tail dependence in spatial extremes. This work develops a statistical modeling framework that has flexible behavior in all four pairings of high and low extremes at pairs of locations. In particular, we use a mixture of rotations of common Archimedean copulas to capture various combinations of four-corner tail dependence. We study teleconnected T2m extremes using ERA5 of daily average 2-m temperature during the boreal winter. The estimated mixture model quantifies the strength of opposite-tail dependence between warm temperatures in Alaska and cold temperatures in the midlatitudes of North America, as well as the reverse pattern. These dependence patterns are shown to correspond to blocked and zonal patterns of midtropospheric flow. This analysis extends the classical notion of correlation-based teleconnections to considering dependence in higher quantiles.

Imputation of missing values in environmental time series by D-vine copulas

Missing values in environmental time series are common and must be imputed before carrying out an analysis requiring complete data. We propose an imputation method for the time series of a target station using information of neighboring stations measuring the same variable. The method allows these neighboring stations to have missing values themselves. The multivariate dataset comprising the time series of the target station and its neighboring stations is jointly modeled by a vine copula and parametric margins. Multiple imputation takes into account the uncertainty of missing data by generating several plausible values for each missing value in the time series of the target station. This is done in a Bayesian framework by sampling the posterior distribution of a missing value, which is conditional on the observed stations for the date. The method is suitable for extremes because the vine copula can model the eventual tail dependence between stations. The application to a skew surge time series is presented, with cross-validated results and a focus on the performance for the upper extremes.

How does bubble risk propagate among financial assets? A perspective from the BSADF-vine copula model

In this paper, the BSADF method is used to construct the bubble net value sequence of 11 mainstream financial assets, and the vine copula model is used to analyze the characteristics of the bubble-related structure. First, we use the BSADF method to measure the bubbles of various financial assets. The results show that since the outbreak of COVID-19, most types of assets have experienced a sharp bubble rise and their longest bubble period as central banks have implemented quantitative easing policies. Furthermore, this article reveals the path characteristics of bubble risk transmission in different assets using the vine copula model. The R vine copula is found to be best for analyzing the tail dependence structure. The S&P 500 and the international gold price occupy the hub position in the bubble dependence structure of various financial assets. The Shanghai Composite Index and the US Dollar Index can act as relays and accelerators in the transmission of bubble risk across the financial system. Finally, we explore the tail dependence structure between financial assets. The results indicate that gold can be a good hedge against the bubble risk of the Hang Seng Index and WTI crude oil futures. The COVID-19 pandemic and accommodative monetary policies by governments can create conditions for bubble risk to spread between assets such as Bitcoin and China’s 10-year Treasury bonds and between the US Dollar Index and the S&P 500.

The Stability of Islamic Cryptocurrencies and Copula-Based Dependence with Alternative Crypto and Fiat Currencies

Purpose — This study aims to examine Islamic cryptocurrencies and their dependency on foreign exchange markets in vine copula architecture (CD-Vine) and provide a framework for detecting complex dependence structures, risk management implications, and hedging effectiveness. Design/Methodology/Approach — This study used gold-backed cryptocurrencies and three fiat currencies. The vine copula approach was preferred because it applies several distributions and estimates complex dependencies. Hedging effectiveness was measured by constructing simulation-based portfolios optimised with DCC-t-Copula. Benford’s law and realized variance were used to determine the stability of Islamic cryptocurrencies. Findings — According to C-Vine and D-Vine copula models, paper money has a weak tail dependence with gold-backed cryptocurrencies. Only OneGram coin, whose volatility matched the risk of Bitcoin, showed zero irregularities in volume trading. The findings were robust to different estimations based on Minimum Spanning Tree and Dendrogram. Originality/Value — This is the first study to examine Islamic cryptocurrencies’ stability and the significance of hedging effectiveness on gold-backed cryptocurrencies under a copula-based approach. Research Limitations — The study did not apply time-varying vine copula. Practical Implications — The risk management perspective shows insignificant hedge effectiveness in the portfolio of fiat and gold-backed cryptocurrencies.

Estimating POT second-order parameter for bias correction

The stable tail dependence function provides a full characterisation of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the Peaks-Over-Threshold (POT) second-order parameter. For this second-order parameter, this paper introduces a penalised estimator that discourages it from being too close to zero. This paper then establishes this estimator's asymptotic consistency, uses it to correct the bias in the estimation of the stable tail dependence function, demonstrates its desirable empirical properties in the estimation of the extremal dependence structures, and illustrates it with an application to liability claim data.

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.

FTX Collapse and systemic risk spillovers from FTX Token to major cryptocurrencies

We examine the dynamic lower tail dependence and downside risk spillover between the FTX Token and seven major cryptocurrencies using Rotated Gumbel copula and GARCH copula quantile regression-based ∆CoVaR models. Daily data is analyzed from May 1, 2020 to December 31, 2022. The results show a strong evidence of risk spillover effects from FTX Token to crypto markets. Solana, followed by Cardano, displays the largest downside risk spillover. Tether and Bitcoin are affected least by the FTX fallout, receiving the lowest downside risk spillovers. Furthermore, the dynamic risk spillover effects are heterogeneous over time and comparatively different for each cryptocurrency.

Construction of bivariate symmetric and asymmetric copulas and its relationship to ratios of conditional hazard rate functions

ABSTRACT A new method for the construction of both symmetric and asymmetric, absolutely continuous bivariate copulas is introduced. This research was inspired by the well-known cross ratio (CR), studied by Clayton (1978), which is a local dependence measure describing the association between the components of a bivariate random vector, as well as by an alternative risk ratio (RR) proposed recently by Abrams et al. (2022), which unravels the local relation between the two components of the vector. The practical meaning of RR is illustrated in two real data sets by the authors. In this article, various properties of the proposed parametric families of copulas are studied, for example quadrant dependence ordering, tail dependence coefficients and several copula-based measures of dependence. Some relationships of the copulas to RR are discussed and illustrative scatterplots are presented.

Subsample analysis of stock market – cryptocurrency returns tail dependence: A copula approach for the tails

This paper describes the extremal and tail dependence between G7 stock market returns (USA, Canada, UK, Japan, Germany, France, Italy) and cryptocurrency returns (Bitcoin, Ethereum, Dash, Monero, Ripple) on the basis of the bivariate extremal dependence model (Padoan and Stupfler, 2022) and the bivariate test for equality of tail copulas (Can et al., 2023). Over a daily data period from January 1, 2016 through January 5, 2023, the findings reveal significant differences in tail risk between the categories of G7 stock market returns and cryptocurrency returns, highlighting the need to find an appropriate asset to hedge individual financial asset tail risks. The results also demonstrate a time-invariant tail dependence between G7 stock market returns and cryptocurrency returns, as the Wald test supports the null of an equal tail dependence structure between stock market and cryptocurrency returns during both calm and crises times. The finding offer important policy implications for portfolio managers and investors.

Forecasting nonlinear dependency between cryptocurrencies and foreign exchange markets using dynamic copula: evidence from GAS models

PurposeThis paper examines and forecasts correlations between cryptocurrencies and major fiat currencies using Generalized Autoregressive Score (GAS) time-varying copulas. The authors examine to which extent the multivariate GAS method captures the volatility persistence and the nonlinear interaction effects between cryptocurrencies and major fiat currencies.Design/methodology/approachThe authors model tail dependence between conventional currencies and Bitcoin utilizing a Glosten-Jagannathan-Runkle Generalized Autoregressive Conditional Heteroscedastic model (GJR-GARCH)-GAS copula specification, which allows detecting the leptokurtic feature and clustering effects of currency returns distribution.FindingsThe authors' results show evidence of multiple tail dependence regimes, implying the unsuitability of applying static models to entirely describe the extreme dependence between Bitcoin and fiat currencies. Compared to the most common constant copulas, the authors find that the multivariate GAS copulas better forecast the volatility and dependency between cryptocurrencies and foreign exchange markets. Furthermore, based on the value-at-risk (VaR) and expected shortfall (ES) analyses, the authors show that the multivariate GAS models produce accurate risk measures by adding cryptocurrencies to a portfolio of fiat currencies.Originality/valueThis paper has two main contributions to the existing literature on cryptocurrencies. First, the authors empirically examine the tail dependence structure between common conventional currencies and bitcoin using GJR-GARCH GAS copulas which consider the leptokurtic feature and clustering effects of currency returns distribution. Second, by modeling VaR and ES, the authors test the implication of using time-varying models on the performance of currency portfolios, including cryptocurrencies.

Extreme spillovers between insurance tokens and insurance stocks: Evidence from the quantile connectedness approach

This study examines potential tail spillovers between insurance tokens and conventional stocks using the quantile connectedness approach by Ando et al. (2022). In particular, this study explores static and dynamic spillovers at lower and upper tails of the return distribution. In line with previous studies, tokens and conventional stocks within the insurance market may show positive but low connectedness levels. Furthermore, our findings confirm a higher sensitivity of the insurance system at both tails of the distribution in comparison with the median (Q=0.50). As expected, dynamic connectedness measures change over time, intensifying at the extremes of the distribution. This finding is confirmed by the robustness test that consists of analyzing the RTD (Relative Tail Dependence) measure, as we reject the symmetric response, since its values are clearly different from zero in most of the sample period. These results are of interest to portfolio managers, as the findings will allow them to suggest adjustments to investment portfolios according to the evolution of the dynamic spillovers found.

The oil price-macroeconomy dependence.

This paper investigates the relationship between the price of oil and real output in the United States in the context of a Markov regime switching, identified, structural GARCH-in-Mean VAR model with copulas. We use the copula method to investigate the nonlinear dependence structure, as well as (upper and lower) tail dependence, between the price of oil and real output growth, and Markov regime switching to account for changing oil price dynamics over the sample period. We find an asymmetric negative dependence structure between oil price and output growth shocks and that oil price uncertainty has a negative and statistically significant effect on real output growth.

Impact of SST Anomalies on Coral Reefs Damage Based on Copula Analysis

The condition of coral reefs in Indonesia is alarming. One of the influenting factors of coral reefs damage is extreme climate change. The aim of this study is to determine the relationship of climate change, that is Sea Surface Temperature (SST) anomaly index, and coral reefs damage in West, Central and East Region of Indonesia. The method used in this study is Copula analysis. Copula is one of the statistical methods used to determine the relationship of two or more variables, in which case the distribution can be normal or not. First, data is transformed into Uniform [0,1] domain. Then, Copula parameter is estimated to get significance parameter. Lastly, the best Copula that has the highest log likelihood value is selected to represent the relationship of data. The result indicates that percentage of coral reefs damage in West and Central Region has relationship with SST Nino 4, while coral reefs damage in East Region does not have relationship with any of SST Nino anomalies. In West Region, the best Copula represents the relationship is Gaussian Copula (parameter = -0.32); it concludes that the higher the value of SST Nino 4, the lower the percentage of coral reefs damage and otherwise. While in Central Indonesia, Frank Copula (parameter = -4.89) is selected; it does not have tail dependency so that the SST Nino 4 and the percentage of coral reefs in damage condition in Central Region has low correlation.