Symmetrized Joe-Clayton Copula Research Articles

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.

Evolution, severity, and spatial extent of compound drought and heat events in north China based on copula model

Compound drought and heat (CDHE) is frequently occurred worldwide and leads to disproportionate impacts on agricultural production than univariate climate extremes, hence continues to receive research attention. However, the driving mechanism and occurrence characteristics of CDHEs remain unclear in some agro-ecological sensitive regions. Here, we adopted standardized precipitation index (SPI) and standardized temperature index (STI) to identify the intensity of drought and heat, respectively, in north China, and then to identify the month and area that most prone to CDHEs. Copulas can simulate the dependence between variables, hence were proposed to construct joint cumulative probability distributions of SPI and STI, so as to simulate the occurrence characteristic of CDHEs. The results demonstrated that in cold season, there were some stations with significant positive correlations between the SPI and STI. However, ∼ 80 % of stations had significant negative correlations between the two variables in July (the month of the year with the most stations). Hence, July is considered as the month most prone to CDHEs among the year in north China. We also found that the Symmetrized Joe-Clayton copula was the best to construct joint probability distributions of SPI and STI in most stations. In July, CDHEs occurred more frequently after 1990s with much higher intensity and wider spatial extent, which was mainly attributed to more severe heats. Spatially, mid-western plain and north mountainous areas were more prone to CDHEs. Our findings provide a better understanding of CDHEs in north China and could offer valuable references for meteorological disaster risk prevention in agriculture production. • Two comparable indexes are used to denote drought and heat in compound events. • Estimate the characteristics of compound events in different periods. • Compound events occurred more frequent and severe due to heats.

The asymmetric contagion effect between stock market and cryptocurrency market

This paper studies asymmetric contagion effects between stock and cryptocurrency markets. We implement the time-varying symmetrized Joe-Clayton copula GARCH model and Bai-Perron breakpoint test to explore dynamic correlations between the daily log-returns of the two markets in each time range. The asymmetric contagion effects between the two markets are studied using the non-linear Granger causality test. We also find that the lower tail dependences are more significant than the upper ones. Our findings can be used as a reference for supervisory authorities, and also provide insights on risk hedging for rational investors to avoid underestimating risk when building their portfolios.

Dependence Structure Analysis and VaR Estimation Based on China’s and International Gold Price: A Copula Approach

Since 2013, China has become the world’s largest gold producer and consumer. To gain the corresponding global pricing power in gold, many actions have been taken by China in recent years, including the International Board at Shanghai Gold Exchange, Shanghai-Hong Kong Gold Connect and Shanghai Gold Fix. Our work studies the dependence structure between China’s and international gold price and examines whether these moves are changing the dependence structure. We use GARCH-copula models to detect the dynamic dependence and tail dependence. The research period is set to contain the Financial Crisis in 2008, the dramatical plunge of gold price in 2013 and a series of black swan events in 2016. The empirical study shows that some event driven dependence structure breaks are statistically insignificant. And the time-varying Symmetrized Joe-Clayton copula is the best copula to model the dependence structure based on AIC value. Finally, an example of applications of this dependence structure is given by estimating the VaR of an equally weighted portfolio with a simulation-based method.

The Dynamic Extreme Co-Movement between Chinese Stock Market and Global Stock Markets

ABSTRACTWe use time-varying Symmetrized Joe-Clayton Copula model to study the extreme co-movement (boom or crash together) between the Chinese stock market and major stock markets in the world from 2007 to 2017, including developed markets and stock markets on “Belt and Road Initiative” (hereafter B.R.I.). We find that the extreme co-movement probability between Chinese market and “Belt and Road Initiative” markets is higher than developed markets at both tails. Then we study important “real” and “non-fundamental” factors affecting the excess co-movement probability, including bilateral trade openness, financial integration, and economic policy uncertainty. The results of panel regression analysis show that: the bilateral financial integration has significant effects over the lower tail dependence between Chinese and developed markets, but does not affect the extreme co-movement between Chinese and B.R.I. markets. And the bilateral trade openness is an important factor for the extreme co-movement at both tail between Chinese and global markets. The economic policy uncertainty index, especially China’s economic policy uncertainty, plays a key role in the extreme co-movement between Chinese and developed markets at both tails. However, it has sizable effects only at the upper tail co-movement between Chinese and B.R.I. markets.

Tail dependence networks of global stock markets

AbstractThe Pearson correlation coefficient is used by many researchers to construct complex financial networks. However, it is difficult to capture the structural characteristics of financial markets that have extreme fluctuations. To solve this problem, we resort to tail dependence networks. We first build the edge information of the stock network by adopting Pearson's correlation coefficient and the symmetrized Joe–Clayton copula model, respectively. By using the planar maximally filtered graph method, we filter the edge information, obtain Pearson's correlation coefficient and tail dependence network, and compare their efficiencies. The community structure of the constructed networks is investigated. We find that the global efficiency of tail‐dependent networks is higher than that of the Pearson correlation networks. Further analysis of the nodes in the upper‐ and lower‐tail dependence networks reveals that the European markets are more influential than Asian and African markets during a booming market and a recession market. In addition, different cliques are found in the two tail dependence networks. The finding indicates that financial risks will impact geographically adjacent markets.

The contagion effect in European sovereign debt markets: A regime-switching vine copula approach

Abstract Multidimensional dependence in financial markets has motivated the conception of copulas as a tool to analyze nonlinear connections. However, the dynamics generating the dependence structure is still considered unchanged, whether during turmoil or stable periods, and the curse of dimensionality prevents researchers from detecting the regime shifting that may connect financial markets. In this paper, we develop a tractable Markov regime-switching C-vine and D-vine under the symmetrized Joe-Clayton copula, capable of detecting lower and upper tail dependencies separately. Application is conducted on twelve government bonds, the U.S. and eleven European bonds belonging to the Eurozone. Results show that the regime-switching copula models explain the dynamics of data dependence better than the single-regime copula, which indicates the presence of a contagion effect. Furthermore, for Eurozone bond markets, the contagion remains in its high state since the global financial crisis of 2008 and European sovereign debt crisis of 2009, with a transmission path from core to stressed countries.

Time‐Varying Linkage of Possible Safe Haven Assets: A Cross‐Market and Cross‐asset Analysis

AbstractThis paper contributes to applying the time‐varying symmetrized Joe–Clayton copula to study the dynamic linkage among possible safe haven assets (SHAs) in the major international markets over the past 34 years. We re‐examine four major asset types (long‐term government bonds, equity indices, oil, and gold) and test whether they are qualified individually as a safe haven asset against when paired against each other in a specific market. The empirical analyses indicate that: (1) Government bonds are generally confirmed SHAs. (2) Gold and oil are overwhelming SHAs against government bond across the markets. (3) US and East Asian markets (Japan, Australia and New Zealand) have more SHA options than the other regions against equity index.

Tail dependence structure of the foreign exchange market: A network view

Abstract Tail dependence of financial entities describes when the price of one financial asset has an extreme fluctuation (e.g., price sharply rises or falls), the degree of its effect on the price fluctuation of another asset. Under the background of the global financial crisis, tail dependence structure of financial entities plays an important role in financial risk management, portfolio selection, and asset pricing. In this paper, we propose a concept of tail dependence networks to investigate the tail dependence structure of the foreign exchange (FX) market. Lower- and upper-tail dependence networks for 42 major currencies in the FX market from 2005 to 2012 are constructed by combing the symmetrized Joe-Clayton copula model and two filtered graph algorithms, i.e., the minimum spanning tree (MST) and the planar maximally filtered graph (PMFG). We also construct the tail dependence hierarchical trees (HTs) associated with the MSTs to analyze the currency clusters. We find that (1) the two series of lower- and upper-tail dependence coefficients present different statistical properties; (2) the upper-tail dependence networks are tighter than the lower-tail dependence networks; and (3) different currency clusters, cliques and communities are respectively found in the two tail dependence networks. The key empirical results indicate that market participants should consider the different topological features at different market situations (e.g., a booming market or a recession market) to make decisions on the investing or hedging strategies. Overall, our obtained results based on the tail dependence networks are new insights in financial management and supply a novel analytical tool for market participants.

Can analysts predict rallies better than crashes?

Abstract We use the copula approach to study the structure of dependence between sell-side analysts’ consensus recommendations and subsequent security returns, with a focus on asymmetric tail dependence. We match monthly vintages of I/B/E/S recommendations for the period January–December 2011 with excess security returns during six months following recommendation issue. Using a mixed Gaussian–symmetrized Joe–Clayton copula model we find evidence to suggest that analysts can identify stocks that will substantially outperform, but not underperform relative to the market, and that their predictive ability is conditional on recommendation changes.

Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm

Abstract This paper presents a novel four-stage algorithm for the measurement of the rank correlation coefficients between pairwise financial time series. In first stage returns of financial time series are fitted as skewed- t distributions by the generalized autoregressive conditional heteroscedasticity model. In the second stage, the joint probability density function (PDF) of the fitted skewed- t distributions is computed using the symmetrized Joe–Clayton copula. The joint PDF is then utilized as the scoring scheme for pairwise sequence alignment in the third stage. After solving the optimal sequence alignment problem using the dynamic programming method, we obtain the aligned pairs of the series. Finally, we compute the rank correlation coefficients of the aligned pairs in the fourth stage. To the best of our knowledge, the proposed algorithm is the first to use a sequence alignment technique to pair numerical financial time series directly, without initially transforming numerical values into symbols. Using practical financial data, the experiments illustrate the method and demonstrate the advantages of the proposed algorithm.

Large asymmetry and directional dependence by using copula modeling to currency exchange rates

To examine the asymmetry of financial data in detail, we have considered both the tail dependence with diverse copulas and Jung et al.'s (8) directional dependence by copula. From the empirical study in this paper, we have found that the tail dependence by Patton's (11) modified symmetrized Joe-Clayton copula function did not show the asymmetry property sufficiently because there is no tail dependence for the currency exchange rates of Republic of Korea and Japan against the US dollar after the 2008 financial crisis. However, by using the copula approach for directional dependence, we showed that there exists the asymmetry of the currency exchange rates of Republic of Korea and Japan against the US dollar before and after the 2008 financial crisis because the directional dependence only when existing an asymmetry of data can be found. We conclude that the copula approach for directional dependence can be supplemented to explain the asymmetry property in addition to the tail dependence approach.

Analysis of co-movements between the capital markets in Brazil and the United States

In this article copula theory is used to analyze the co-movements between the Brazilian and American capital markets. To formulate an effective asset allocation strategy, it is important to understand extreme events – both positive (booms) and negative (crashes) – and their effects on markets. The market indexes used are the Ibovespa and the S&P 500, covering the period from March 2001 to April 2007. We tested the adherence to the log-returns of the main copulas found in the financial literature, using the following criteria: log-likelihood, Akaike information criterion and Bayesian information criterion. The results show that the symmetrized Joe-Clayton copula is most suitable to model the dependence structure between the log-returns of the Ibovespa and the S&P500. This work differs from some previous ones (e.g., Mendes & Moretti, 2005 and Canela & Collazo, 2005) because we take into account the modeling of dynamic copulas, as introduced by Patton (2006). Finally, from the tail-dependence indexes over time, it can be concluded that the occurrence of crashes in the American market tends to affect the Brazilian market more than does the occurrence of booms.

The dependence structure between the Canadian stock market and the USD/CAD exchange rate: a copula approach

Abstract This paper investigates the dependence structure between the real Canadian stock returns and the real USD/CAD exchange rate returns, using the Symmetrized Joe‐Clayton (SJC) copula function. We estimate the SJC copula with monthly data over the period 1995:1 to 2006:12. Our results show significant asymmetric static and dynamic tail dependence between the real stock returns and the real exchange rate returns, such that the two returns are more dependent in the left than in the right tail of their joint distribution. We explain this asymmetric dependence in terms of an asymmetric interest rate policy by Canadian monetary authorities in response to changes in the real exchange rate during sub‐periods of falling and rising commodity prices.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein–Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe–Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12)

Tail Dependence in International Real Estate Securities Markets

“Tail dependence” characterizes the cross market linkages during stressful times. Analyzing tail dependence is of primary interest to portfolio managers who systematically monitor the co-movements of asset markets. However, the relevant literature on real estate securities markets is very thin. Our study extends the literature by using the flexible symmetrized Joe-Clayton (SJC) copula to estimate the tail dependences for six major global markets (U.S., U.K., Japan, Australia, Hong Kong, and Singapore). In implementing the SJC copula, we model the marginal distributions of returns through a semi-parametric method which has never been applied to real estate returns. Our major findings suggest that international markets display different strength and dynamics of tail dependence. We extensively discuss the implications of our findings for financial practices such as portfolio tail diversifications, portfolio selections, portfolio risk management and hedging strategies. Our study also demonstrates that the widely used linear correlation is an inadequate measure of market linkages, especially during periods of crisis.

The Tail Risk of Emerging Stock Markets

This paper investigates tail risk in emerging stock markets by comparing the investable and noninvestable segments in terms of the expected shortfall of standardized returns and tail dependence on the world market. Employing the skewed Student-t GJR-GARCH model and the symmetrized Joe-Clayton copula, we show most investable portfolios have lower tail risk but higher tail dependence than noninvestable ones, and emerging markets are likely more dependent on the world market during large joint losses than large joint gains. In addition, tail dependence of the aggregate and investable markets on the world market varies across countries and across regions.

Dynamic Asymmetric Dependencies between Equities and Exchange Rate Markets

This paper investigates the dynamic relationship between exchange rate and equity return differentials, for ten developed countries relative to the US, by employing a time varying copula methodology. Most of the time, this relationship is empirically found to be positive with statistical significance: e.g., when a foreign country equity index has a higher return than S\&P500, it is accompanied with the appreciation of the foreign (local) currency relative to the US dollar. Evidence of structural breaks (dramatic drops) is found in the conditional copula during the 2008 global financial crisis but not in the 2002 bear market. Asymmetry is also tested for the estimated dynamic dependence by the symmetrized Joe-Clayton copula. For most of our samples, the upper tail dependence tends to be smaller than the lower tail dependence. This demonstrates that the exchange rate and equity return differentials against the US are less dependent when the local currency appreciates against USD and the local equities outperform the US equities, than vice versa.