Tail Dependence Research Articles

Estimation of Contagion: Bayesian Model Averaging on Tail Dependence of Mixture Copula

This study introduces a novel approach to estimate tail dependence in financial contagion using mixture copulas. Addressing the challenges of weight parameter estimation in conventional models, we propose a Bayesian model averaging method to determine optimal copula weights. Through both simulations and empirical studies, the proposed method demonstrates improved robustness and accuracy, particularly when handling extreme weight scenarios. These advancements offer more reliable measurements of financial contagion, contributing to enhanced risk management and policy-making in interconnected financial markets.

Tail index estimation for tail adversarial stable time series with an application to high‐dimensional tail clustering

For stationary time series with regularly varying marginal distributions, an important problem is to estimate the associated tail index which characterizes the power‐law behavior of the tail distribution. For this, various results have been developed for independent data and certain types of dependent data. In this article, we consider the problem of tail index estimation under a recently proposed notion of serial tail dependence called the tail adversarial stability. Using the technique of adversarial innovation coupling and a martingale approximation scheme, we establish the consistency and central limit theorem of the tail index estimator for a general class of tail dependent time series. Based on the asymptotic normal distribution from the obtained central limit theorem, we further consider an application to cluster a large number of regularly varying time series based on their tail indices by using a robust mixture algorithm. The results are illustrated using numerical examples including Monte Carlo simulations and a real data analysis.

Multivariate copula-based conditional quantiles: analytic higher-order moments and ratio estimation approaches

ABSTRACT In this paper, we aim to modify multivariate copula-based conditional quantiles for a targeted random variable, given multiple random variables attaining their respective quantiles. Specifically, we propose two modifications through the Cornish–Fisher expansion, one of which involves its analytic higher-order unconditional moments. The second one accounts for its higher-order conditional moments estimated using a ratio estimation method. By considering multivariate elliptical and Archimedean copulas with Johnson's SU margins, our simulation study shows that this method provides more accurate conditional moment estimators compared to the naive method. They result in expanded conditional quantile estimators, whose efficiency is relatively better than their unexpanded versions, particularly at lower and higher quantile levels under a stronger (tail) dependence assumption. A much higher efficiency is gained when the first modification is performed. These findings are validated using an empirical study based on cryptocurrency return data and a comparative analysis against the existing estimation approaches.

Inflation hedging: a comparative wavelet quantile correlation analysis of real estate and alternative assets

PurposeConducting an analysis spanning from 2000 to 2023, this research evaluates the effectiveness of real estate assets in hedging against global and energy inflation, benchmarked against other compelling investment options such as oil, gold, silver and stocks.Design/methodology/approachThis study employs the wavelet quantile correlation (WQC) methodology. The latter sheds light on dynamic market interactions by scrutinising dependency structures across multiple time scales and also by capturing tail dependence. The adaptability of the wavelet transform, across a spectrum of frequencies, emerges as an indispensable tool for studying time series while also unravelling relationships among variables across diverse quantiles.FindingsThe findings reveal that the response to inflationary pressures is contingent upon the asset class, investment horizon and type of inflation under consideration. While precious metals demonstrate effectiveness over short-term horizons, French-listed real estate exhibits compelling inflation-hedging characteristics as the investment horizon extends. Oil emerges as an unequivocal hedge against both global and energy inflation.Practical implicationsTo counteract the effects of inflation, investors and households may feel compelled to refine their investment strategies, opting to bolster their portfolios with instruments proven to serve as reliable safeguards against inflation, as indicated by this study.Originality/valueIn conjunction with a surge in inflationary pressures, this study delves into the hedging capabilities of assets, exploring their efficacy not only across short- and long-term investment horizons but also within diverse scenarios characterized by fluctuating levels of global and energy-related inflation. To the best of our knowledge, no previous article employed the WQC technique to evaluate the inflation-hedging nexus.

TAIL DEPENDENCE OF COMMODITY FUTURES RETURNS IN THE AGRICULTURAL AND ENERGY SECTORS

The goal of this research was to examine tail dependence structures between selected commodity futures returns. Tail dependence, called also extremal dependence, was evaluated for the pairs of commodities coming from the same sector (energy or agricultural). The study covers the years 2018-2023, embracing the COVID-19 pandemic and the outbreak of the Russia-Ukraine war. To achieve the goal, bivariate dynamic models were applied to percentage log returns of commodity futures. Marginal distributions were described using the ARMA-GARCH models. Joint distributions were constructed using the symmetrized Joe-Clayton copula, which allowed to model asymmetric dependence in the tails of a distribution. Time variation of the copula parameters, here equal to tail dependence coefficients, was described using the evolution equations [Patton 2006]. In the energy sector, the dependence in both tails of analyzed distributions was relatively strong, dynamic and higher in the lower tail than in the upper tail. On the contrary, the agricultural sector lacks common patterns of tail dependency. This feature of the agricultural sector creates an opportunity for investors or risk managers to build well-diversified portfolios.

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.

Risk spillovers and diversification benefits between crude oil and agricultural commodity futures markets

This study examines the dependence structure and risk spillovers between crude oil and eight major agricultural futures (wheat, corn, soybean coffee, cotton, lumber, cocoa, and live cattle) markets. It also analyzes the potential conditional diversification benefits using a variety of copula functions and Conditional Value at Risk (CoVaR) measure. The results show significant crisis-sensitive and temporal dependence between oil and agricultural markets. Moreover, crude oil shows a symmetric tail dependence with both wheat, corn, soybeans, and cotton futures, whereas oil exhibits an average dependence with coffee. A strong dependence is observed between oil and cocoa (lumber) during bearish (bullish) market conditions. Oil and Live cattle have a symmetric dependence during bearish and bullish market conditions. On the other hand, we find asymmetric and bidirectional risk spillovers from oil to agricultural markets. Furthermore, the wheat futures contract appears to be the most dominating and vulnerable asset to oil price shocks, followed by lumber and corn futures, respectively, while the live cattle contracts are the least. Finally, an equally weighted portfolio offers the highest diversification benefits at a 5 % expected shortfall.

Modelling Risk Dependencies in Insurance Using Survival Clayton Copula

Our aim in this paper is to show the use of survival Clayton copula as a suitable tool for modelling risk dependencies in insurance. A purpose-built simulation of an adequate upper tail dependence can be an important part of the aggregation of risks in an insurer’s internal models. The occurrence of extreme values of the aggregate random variable might have a very negative impact on the insurer when securing coverage of unexpected losses. The upper conditional quantile exceedance probability of the copula is a suitable indicator. In addition an analysis of its effect on the level of modelling of the risk scenario is available. This effect is measured using the Tail Value at Risk of the aggregate random variable. To simplify our description of the given principle for aggregating risks we will in this paper only consider the two-dimensional case. The programming language R was used to simulate the values of the joint distribution of the marginal random variables.

ETFs and tail dependence: Evidence from Chinese stock market

Using Chinese A-share market data, we empirically examine the impact of exchange-traded funds (ETFs) on tail dependence of the underlying securities. Our results show that ETFs can increase the tail dependence of stocks in their basket, showing that the average tail dependence of a stock is higher when it has stronger ETF holding similarity with other stocks. We investigate the role of arbitrage activity and find that ETF holding similarity increases stocks’ ETF arbitrage activity. This effect is primarily on discount arbitrage rather than premium arbitrage, which leads to higher tail dependence among stocks. Alongside propagating demand shocks from the ETF market to underlying securities, ETFs also propagate tail event shock from one stock to other stocks in their baskets. Additionally, arbitrage activities through ETFs add a new layer of non-fundamental tail dependence to the underlying securities. Unlike mutual funds, ETFs lead to more frequent and idiosyncratic tail risk contagion among underlying securities. Our study sheds light on how ETFs provide new channels for risk contagion among underlying securities in emerging markets.

Joint meta-analysis of two diagnostic tests accounting for within and between studies dependence.

There is an extensive literature on methods for meta-analysis of diagnostic test accuracy, but it mainly focuses on a single test. A multinomial generalised linear mixed model was recently proposed for the joint meta-analysis of studies comparing two tests on the same participants in a paired tests design with a gold standard. In this setting, we propose a novel model for joint meta-analysis of studies comparing two diagnostic tests which assumes independent multinomial distributions for the counts of each combination of test results in diseased and non-diseased patients, conditional on the latent vector of probabilities of each combination of test results in diseased and non-diseased patients. For the random effects distribution of the latent proportions, we employ a one-truncated D-vine copula that can provide tail dependence or asymmetry. The proposed model includes the multinomial generalised linear mixed model as a special case, accounts for the within-study dependence induced because the tests are applied to the same participants, allows for between-studies dependence, and can also operate on the original scale of the latent proportions. The latter enables the derivation of summary receiver operating characteristic curves. Our methodology is demonstrated with simulation studies and a meta-analysis of screening for Down's syndrome with two tests: shortened humerus and shortened femur.

Tail dependence, risk contagion and industry systemic risk: Based on method of Lasso-Expectile

Tail dependence, risk contagion and industry systemic risk: Based on method of Lasso-Expectile

A study of one-factor copula models from a tail dependence perspective

AbstractModeling multivariate dependence in high dimensions is challenging, with popular solutions constructing multivariate copula as a composition of lower dimensional copulas. Pair-copula constructions do so by using bivariate linking copulas, but their parametrization, in size, being quadratic in the dimension, is not quite parsimonious. Besides, the number of regular vines grows super-exponentially with the dimension. One parsimonious solution is factor copulas, and in particular, the one-factor copula is touted for its simplicity – with the number of parameters linear in the dimension – while being able to cater to asymmetric non-linear dependence in the tails. In this paper, we add nuance to this claim from the point of view of a popular measure of multivariate tail dependence, the tail dependence matrix (TDM). We focus on the one-factor copula model with the linking copula belonging to the BB1 family, pointing out later the applicability of our results to a wider class of linking copulas. For this model, we derive tail dependence coefficients and study their basic properties as functions of the parameters of the linking copulas. Based on this, we study the representativeness of the class of TDMs supported by this model with respect to the class of all possible TDMs. We establish that since the parametrization is linear in the dimension, it is no surprise that the relative volume is zero for dimensions greater than three, and hence, by necessity, we present a novel manner of evaluating the representativeness that has a combinatorial flavor. We formulate the problem of finding the best representative one-factor BB1 model given a target TDM and suggest an implementation along with a simulation study of its performance across dimensions. Finally, we illustrate the results of the paper by modeling rainfall data, which is relevant in the context of weather-related insurance.

A generalization of the Topological Tail Dependence theory: From indices to individual stocks

This study investigates the Topological Tail Dependence (TTD) theory’s applicability to individual stock volatility and high dimensions. Utilizing a comprehensive dataset from the S&P 100, the research employs various methodologies to test the predictions and implications of the TTD theory. The theory’s main prediction of Wasserstein Distance’s predictive utility, particularly in nonlinear models during volatile periods, is confirmed. The research suggests extending the TTD theory’s application to various financial instruments and incorporating dynamic topological features to enhance understanding market dynamics. This study validates the TTD theory for individual stocks and highlights the necessity of topological considerations in financial modeling, promising advancements in financial econometrics and risk management strategies.

Exploring the Spillover effects of tail risk fluctuations in the RMB exchange rate—The time-frequency and quantile connectivity perspective

This study constructs spillover indices from a volatility spillover network perspective using the Quantile Vector Autoregression (QVAR) model, capturing the RMB exchange rate's tail risk and time-frequency effects across varying shock sizes. Empirical results show that the QVAR-based spillover index more effectively captures the tail risk spillover effects across different quantiles. In the time domain, spillovers between RMB exchange rates are dynamic and particularly sensitive to extreme contingencies. In the frequency domain, RMB exchange rates demonstrate significant spillovers, primarily at low frequencies. During extreme upward events, dynamic observations show high-frequency spillovers surpassing low-frequency ones as dominant drivers in the tail spillovers of the RMB exchange rate. Additionally, the analysis of tail dependence indicators indicates a strong asymmetry in RMB exchange rate correlations, emphasizing market participants' heightened sensitivity to unfavorable shocks. These findings can serve as a reference for policymakers to strengthen risk management of the RMB exchange rate.

Monte Carlo Estimation of CoVaR

CoVaR is an important measure of financial systemic risk due to its ability to capture tail dependence between the losses of different portfolios and its capacity to predict financial crises. Estimating CoVaR is challenging because its definition involves a zero-probability event, which is unobservable in the data. The existing model-based methods address this issue by assuming simplified structural models, which introduce biases that are difficult to eliminate. In “Monte Carlo Estimation of CoVaR,” Huang, Lin, and Hong propose using Monte Carlo methods to estimate CoVaR, leveraging the modeling flexibility of Monte Carlo simulation. Specifically, they introduce a batching estimator applicable to a wide range of financial models and prove that its best rate of convergence is [Formula: see text], where n is the sample size. Under the widely used delta-gamma approximation model, they further introduce an importance sampling–inspired estimator and prove that its best rate of convergence can be improved to [Formula: see text].

A new family of copulas based on probability generating functions

Abstract We propose a method to obtain a new class of copulas using a probability generating function (PGF) of positive-integer valued random variable. Some existing copulas in the literature are sub-families of the proposed copulas. Various dependence measures and invariant property of the tail dependence coefficient under PGF transformation are also discussed. We propose an algorithm for generating random numbers from the PGF copula. The bivariate concavity properties, such as Schur concavity and quasi-concavity, associated with the PGF copula are studied. Two new generalized FGM copulas are introduced using PGFs of geometric and discrete Mittag-Leffler distributions. The proposed two copulas improved the Spearman’s rho of FGM copula by (−0.3333, 0.4751) and (−0.3333, 0.9573). Finally, we analyse a real dataset to illustrate the practical application of the proposed copulas.

Modelling the VaR Using Integral Probability and Tail Dependence

In this paper, a method is proposed to estimate value at risk (VaR) in a multivariate context by employing the probability integral transformation (PIT) and tail dependence function to model extreme dependence structure. The proposed method involves two vectorial measures of VaR, which use either the distribution function or the survival function. Moreover, properties of these risk measures are analysed, and a connection between them and tail dependence functions is established.

A non‐stationary factor copula model for non‐Gaussian spatial data

AbstractWe introduce a new copula model for non‐stationary replicated spatial data. It is based on the assumption that a common factor exists that controls the joint dependence of all the observations from the spatial process. As a result, our proposal can model tail dependence and tail asymmetry, unlike the Gaussian copula model. Moreover, we show that the new model can cover a full range of dependence between tail quadrant independence and tail dependence. Although the log‐likelihood of the model can be obtained in a simple form, we discuss its numerical computational issues and ways to approximate it for drawing inference. Using the estimated copula model, the spatial process can be interpolated at locations where it is not observed. We apply the proposed model to temperature data over the western part of Switzerland, and we compare its performance with that of its stationary version and with the Gaussian copula model.

Extreme Risk Spillovers From US Soybean Futures Market to China's Soybean‐Linked Futures Markets

ABSTRACTThis study investigates the cross‐border risk spillovers between the US soybean futures market and Chinese soybean‐related futures markets. We first confirm the existence of strong tail dependence between US soybean futures and four Chinese soybean‐related futures by conducting a novel quantile‐Granger causality test. Second, tests under MVMQ‐CAViaR further provide evidence of risk spillovers from CBOT soybean futures to the DCE No.1 soybean, No.2 soybean, soybean meal, and soybean oil futures in value‐at‐risk at different quantiles. Lastly, results from the quantile impulse‐response function reveal the time‐varying and asymmetric property of risk spillover effects. In addition, we compare the results from two subsample periods and identify different risk spillover effects across markets at different quantiles that may contribute to the investors' decision‐making under extreme market conditions.

Dynamic Dependence between Oil and Stock Markets: International Evidence with Stochastic Copula Approach

Modeling the dependency structure between variables has recently received increasing attention in many disciplines, especially finance and economics. In this study, the dependence between oil prices and stock markets is investigated through the stochastic copula approach, which is a class of time-varying copulas. This model enables to capture whole dependency between variables dynamically. Unlike time-varying copulas, it takes into account the latent process as well as observations in modeling dependency and thus evaluates the dependency structure in a more comprehensive framework. Empirical findings suggest that dependency between oil and stock markets evolve over time. There is a symmetric dependence between oil and the UK stock market, but the relationship between oil and the US stock market is measured by upper tail dependence. This indicates that oil and the US stock market are more likely to move together during periods of market uptrend.