Conditional Copula Research Articles

Systematic Market Risk Adjusted for Liquidity Cost in the Banking Sector

The emergence of one or more risks in the financial markets during a specific period causes a financial crisis. Financial crises impact financial stability, which is a key concern for all financial authorities, including central banks. One way to mitigate the risks any economy faces is to understand the origin of risk and how it spreads through the financial system. Liquidity risk goes hand-in-hand with market risk, as they affect each other during a crisis. After the 2007-2008 global financial crisis, banks showed that they need monitoring and efficient liquidity management during both stress and normal conditions; that is, they require better integration of bank liquidity and market risk management. In this study, we present a new methodology to forecast the systematic market risk adjusted for liquidity cost based on the Conditional Value at Risk (CoVaR) risk measure and asymmetric conditional copulas. We analyze a sample of international banks based on asset size in the US, EU, and Asia. Our hypothesis confirms that liquidity risk goes hand-in-hand with market risk, as they affect each other during a crisis. The results show dependence in the tails of the banks’ returns and the market returns. These are very high generally, and even higher for the Covid-19 period than for other periods. The effect of both market risk and liquidity risk on banks during a crisis period is less than in non-crisis periods because banks are well informed institutions and can anticipate a financial crisis and mitigate risk, which explains our results.

Approximate Bayesian conditional copulas

Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem, any multidimensional absolutely continuous distribution function can be uniquely represented as a copula, i.e. a joint cumulative distribution function on the unit hypercube with uniform marginals, which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the conditional copula, especially when one does not have enough information to select the copula model. Several Bayesian methods to approximate the posterior distribution of functionals of the dependence varying according covariates are presented and compared; the main advantage of the investigated methods is that they use nonparametric models, avoiding the selection of the copula, which is usually a delicate aspect of copula modelling. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.

Testing the simplifying assumption in high-dimensional vine copulas

Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observations and check constraints on high-dimensional distributions. So far, corresponding tests have been limited to single conditional copulas with a low-dimensional set of conditioning variables. We propose a novel testing procedure that is computationally feasible for high-dimensional data sets and that exhibits a power that decreases only slightly with the dimension. By discretizing the support of the conditioning variables and incorporating a penalty in the test statistic, we mitigate the curse of dimensionality by looking for the possibly strongest deviation from the simplifying assumption. The use of a decision tree renders the test computationally feasible for large dimensions. We derive the asymptotic distribution of the test and analyze its finite sample performance in an extensive simulation study. An application of the test to four real data sets is provided.

The Role of Economic Contagion in the Inward Investment of Emerging Economies: The Dynamic Conditional Copula Approach

Contagion has been one of the most widely studied and challenging problems in recent economic research. This paper aims at capturing the main impact of contagion risk of the U.S. on foreign direct investment inflows in 18 emerging countries. To quantify the degree of contagion, the time-varying tail dependence copula is employed. Then, the Granger causality test and time series regression analysis are used to investigate the temporal and contemporaneous effects of contagion risk on investment inflows, respectively. Overall, the results confirm the time-varying contagion effects of the U.S. economy on 18 emerging economies. The size of contagion effects gradually increases for all countries, except Thailand, the Philippines, Argentina, and Chile. Furthermore, the results of the Granger causality test and regression reveal that temporal and contemporaneous effects of contagion risk on investment inflows exist in 8 out of 18 countries.

Conditional copula models for correlated survival endpoints: Individual patient data meta-analysis of randomized controlled trials.

Correlations among survival endpoints are important for exploring surrogate endpoints of the true endpoint. With a valid surrogate endpoint tightly correlated with the true endpoint, the efficacy of a new drug/treatment can be measurable on it. However, the existing methods for measuring correlation between two endpoints impose an invalid assumption: correlation structure is constant across different treatment arms. In this article, we reconsider the definition of Kendall's concordance measure (tau) in the context of individual patient data meta-analyses of randomized controlled trials. According to our new definition of Kendall's tau, its value depends on the treatment arms. We then suggest extending the existing copula (and frailty) models so that their Kendall's tau can vary across treatment arms. Our newly proposed model, a joint frailty-conditional copula model, is the implementation of the new definition of Kendall's tau in meta-analyses. In order to facilitate our approach, we develop an original R function condCox.reg(.) and make it available in the R package joint.Cox (https://CRAN.R-project.org/package=joint.Cox). We apply the proposed method to a gastric cancer dataset (3288 patients in 14 randomized trials from the GASTRIC group). This data analysis concludes that Kendall's tau has different values between the surgical treatment arm and the adjuvant chemotherapy arm (p-value<0.001), whereas disease-free survival remains a valid surrogate at individual level for overall survival in these trials.

Copula methods for evaluating relative tail forecasting performance

PurposeThe authors apply their method to analyze which portfolios are capable of providing superior performance to those based on the Sharpe ratio (SR).Design/methodology/approachIn this paper the authors illustrate the use of conditional copulas for identifying differences in alternative portfolio performance strategies. The authors analyze which portfolios are capable of providing superior performance to those based on the SR.FindingsThe results show that under the Gaussian copula, both expected tail ratio (ETR) and skewness-kurtosis ratio portfolios exhibit remarkably low correlations respecting the SR portfolio. This means that these two portfolios are different respecting the SR one. The authors also find that copulas which focus on either the upper tail (Gumbel) or the lower tail (Clayton) render significant differences. In short, the copula analysis is useful to understand what kind of equity-screening strategy based on its corresponding performance measure (PM) performs better in relation to the SR portfolio.Practical implicationsCopula methods for evaluating relative tail forecasting performance provide an alternative tool when forecast differences are very small or found non statistically significant through standard tests.Originality/valueOur copula methods to evaluate models' performance differences are significant because when models' performance is rather similar, conclusions on statistical differences, can be defective as they may hinge on the subsample type or size used, leading to inefficient investment decisions. Our method based in copula is novel in this research topic.

Spatial contagion between financial markets: new evidence of asymmetric measures.

The objective of this paper is to identify the presence, direction and time at which the pure contagion effect occurred between financial markets. In so doing, the aim is to prove the existence of both spatial and temporal asymmetries of pure contagion effects. Firstly, a new empirical framework is proposed in order to define a spatial contagion index using the conditional cumulative distribution function as a parameter to estimate a conditional copula. This methodology enables us to estimate a dynamic conditional copula, providing information about how the market sent pure contagion effects and when. Secondly, in addition to detecting the direction of contagion, the real-time contagion effect is determined, enabling us to calculate the delay of contagion effects (spillover) between financial markets. The present empirical results show the existence of both spatial and temporal asymmetry for bilateral contagion effects for 16 mature and emerging stock markets during the 2001–2018 period. This proves the importance of taking temporal asymmetry into account when we want to detect the contagion effect of every crisis and to estimate the period of pure contagion relating to investors’ behaviors. Finally, these findings highlight the fact that contagion effects were more intensive during the subprime crisis than they were during the European debt crisis.

Omnibus test for covariate effects in conditional copula models

Conditional copulas describe the conditional dependence and the influence that covariates have on the dependence structure between two (or more) variables. Of interest is to test the null hypothesis that the covariates have a specific effect. This paper proposes an omnibus test for testing the null hypothesis of a specified effect of the covariates. The test statistic is designed for having power against many alternatives, and can be used to test for a variety of covariate effects (no effects, linear effects, partial effects, etc.). A special case is the testing problem that the covariates do not affect the dependence structure. In this semiparametric framework the marginal distribution functions are estimated using nonparametric kernel techniques and the parametric dependence model is estimated using maximum likelihood estimation. We establish the asymptotic distribution of the test statistic under the null hypothesis, and evaluate the finite-sample performance of the test via a simulation study, which also includes comparisons with alternative tests. A real data analysis illustrates the practical use of the test.

Using Conditional Copula to Estimate Value at Risk

Value at Risk (VaR) plays a central role in risk management. There are several approaches for the estimation of VaR, such as historical simulation, the variance-covariance (also known as analytical), and the Monte Carlo approaches. Whereas the first approach does not assume any distribution, the last two approaches demand the joint distribution to be known, which in the analytical approach is frequently the normal distribution. The copula theory is a fundamental tool in modeling multivariate distributions. It allows the definition of the joint distribution through the marginal distributions and the dependence between the variables. Recently the copula theory has been extended to the conditional case, allowing the use of copulae to model dynamical structures. Time variation in the first and second conditional moments is widely discussed in the literature, so allowing the time variation in the conditional dependence seems to be natural. This work presents some concepts and properties of copula functions and an application of the copula theory in the estimation of VaR of a portfolio composed by Nasdaq and S&amp;P500 stock indices.

Tail Dependence between Crude Oil Volatility Index and WTI Oil Price Movements during the COVID-19 Pandemic

This study investigates the dependence between extreme returns of West Texas Intermediate (WTI) crude oil prices and the Crude Oil Volatility Index (OVX) changes as well as the predictive power of OVX to generate accurate Value at Risk (VaR) forecasts for crude oil. We focus on the COVID-19 pandemic period as the most violate in the history of the oil market. The static and dynamic conditional copula methodology is used to measure the tail dependence coefficient (TDC) between the variables. We found a strong relationship in the tail dependence between negative returns on crude oil and OVX changes and the tail independence for positive returns. The time-varying copula discloses the strongest tail dependence of negative oil price shocks and the index changes during the COVID-19 health crisis. The findings indicate the ability of the OVX index to be a fear gauge with respect to the oil market. However, we cannot confirm the ability of OVX to improve one day-ahead forecasts of the Value at Risk. The impact of investors’ expectations embedded in OVX on VaR forecasts seems to be negligible.

Right-truncated Archimedean and related copulas

The copulas of random vectors with standard uniform univariate margins truncated from the right are considered and a general formula for such right-truncated conditional copulas is derived. This formula is analytical for copulas that can be inverted analytically as functions of each single argument. This is the case for Archimedean and related copulas. The resulting right-truncated Archimedean copulas are not only analytically tractable but can also be characterized as tilted Archimedean copulas, one of the main contributions of this work. This characterization now allows one to not only immediately obtain a limiting Clayton copula for a general vector of truncation points converging to zero (an extension of a result known in the special case of equal truncation points), but to work with an exact model instead of an approximate limiting model in the first place. As tilted Archimedean copulas have been studied in the literature, the characterization allows one to obtain various analytical and stochastic properties of right-truncated Archimedean copulas. Further contributions include the characterization of right-truncated Archimax copulas with logistic stable tail dependence functions as tilted outer power Archimedean copulas, and an analytical form of right-truncated nested Archimedean copulas.

Semiparametric estimation and model selection for conditional mixture copula models

AbstractConditional copula models allow the dependence structure among variables to vary with covariates, and thus can describe the evolution of the dependence structure with those factors. This paper proposes a conditional mixture copula which is a weighted average of several individual conditional copulas. We allow both the weights and copula parameters to vary with a covariate so that the conditional mixture copula offers additional flexibility and accuracy in describing the dependence structure. We propose a two‐step semi‐parametric estimation method and develop asymptotic properties of the estimators. Moreover, we introduce model selection procedures to select the component copulas of the conditional mixture copula model. Simulation results suggest that the proposed procedures have a good performance in estimating and selecting conditional mixture copulas with different model specifications. The proposed model is then applied to investigate how the dependence structures among international equity markets evolve with the volatility in the exchange rate markets.

Quantile association regression on bivariate survival data.

The association between two event times is of scientific importance in various fields. Due to population heterogeneity, it is desirable to examine the degree to which local association depends on different characteristics of the population. Here we adopt a novel quantile-based local association measure and propose a conditional quantile association regression model to allow covariate effects on local association of two survival times. Estimating equations for the quantile association coefficients are constructed based on the relationship between this quantile association measure and the conditional copula. Asymptotic properties for the resulting estimators are rigorously derived, and induced smoothing is used to obtain the covariance matrix. Through simulations we demonstrate the good practical performance of the proposed inference procedures. An application to age-related macular degeneration (AMD) data reals interesting varying effects of the baseline AMD severity score on the local association between two AMD progression times.

Stochastic Simulation of Daily Suspended Sediment Concentration Using Multivariate Copulas

An estimation of daily suspended sediment concentration (SSC) is required for water resource and environmental management. The traditional methods for simulating daily SSC focus on modeling the SSCs themselves, whereas the cross-correlation structure between SSC and streamflow has received only minor attention. To address this issue, we propose a stochastic method to generate long-term daily SSC using multivariate copula functions that account for temporal and cross dependences in daily SSCs. We use the conditional copula method to construct daily multivariate distributions to alleviate the complications and workload of parameter estimations using high-dimensional copulas. The observed daily streamflow and SSC data are normalized using the normal quantile transform method to relax the computationally intensive model of building daily marginal distributions. Daily SSCs can thus be simulated through the multivariate conditional distribution using previous daily SSC and concurrent daily streamflow values. The proposed method is rigorously examined by application to a case study at the Pingshan station in the Jinsha River Basin, China, and compared with the bivariate copula method. The results show that the proposed method has a high degree of accuracy, in preserving the statistics and temporal correlation of daily SSC observations, and better preserves the lag-0 cross correlation compared with the bivariate copula method. The multivariate copula framework proposed here can accurately and efficiently generate long-term daily SSC data for water resource and environmental management, which play a critical role in accurately estimating the frequency and magnitude of extreme SSC events.

How Does the Conditional Quantile Dependence in the FOREX Market Change Depending on the Time of Day? Analysis Based on Ask and Bid Prices

In the paper, we show that estimates of the strength of linkages between the exchange rates EUR/USD, AUD/USD, GBP/USD, and NZD/USD below small or above large quantiles de-pend on the time of day, at which the daily returns are calculated. We argue that this is due to the activity of traders in different parts of the world, and the impact of the information flow. We use daily returns calculated for each hour of the day. The analysis is performed separately for bid and ask prices. We model the conditional dependence by means of bivari-ate Markov-switching copula models. Then, quantile dependence probabilities are calculated for the fitted conditional copulas. The models include copulas that can capture different types of asymmetry and tail behavior. Our results show that the applied dynamic dependence measures change significantly, depending on the hour of the day. The rankings of the strength of the dependence below small or above large quantiles, which we obtain using the model confidence set methodology, can be useful in portfolio risk management.

Estimation of the Value at Risk Using the Stochastic Approach of Taylor Formula

The aim of this paper is to provide an approximation of the value-at-risk of the multivariate copula associated with financial loss and profit function. A higher dimensional extension of the Taylor–Young formula is used for this estimation in a Euclidean space. Moreover, a time-varying and conditional copula is used for the modeling of the VaR.

Bayes theorem–based and copula-based estimation for failure probability function

The failure probability function (FPF), aiming to decouple the nested-loop reliability-based design optimization solution into a single-loop optimization problem, has attracted a great deal of interest from designers and researchers. It is defined as a function of failure probability with respect to the design parameter. Among the estimation methods for the FPF, the Bayes theorem based on probability distribution function methods is competitive. It transforms the FPF as the estimation of the conditional joint probability density function (PDF) of design parameters on the failure event and the augmented failure probability. The augmented failure probability can be estimated by Monte Carlo simulation, while for the joint multi-dimensional PDF, the existing estimation methods are unavailable. To alleviate this issue, a novel FPF estimation method is proposed by Bayes theorem and copula. In the proposed method, the FPF is derived as a product of the conditional copula density and the augmented failure probability, in which the vine copula is employed to disassemble the multi-dimensional conditional copula density into several bivariate copula density functions, and they can be completed by the existing PDF estimation methods. In contrast to the existing Bayes theorem–based estimation methods for the FPF, the proposed method interprets the FPF as the dependence function between design parameters and the augmented failure probability in terms of copula, which involuntarily breaks the limitation of the multi-dimensional design parameters. In addition, the adaptive Kriging surrogate model is embedded in the proposed method to improve the efficiency of the proposed method. The presented examples demonstrate the efficiency and accuracy of the proposed method.

Reflection of government performance from foreign exchange market through engineered mechanism using conditional copula model

This paper investigates governments’ performance in the country. We achieved this objective differently. We employed an inverse method of assessment, with the utilization of factor copula modeling technique, to study the dependence relationship of exchange rates returns as auxiliary variables, the performance of political and army government tenures in the country in the last two decades are evaluated. Through factor analysis, common factors for the exchange rate are obtained. The analysis shows that conditioned on the common factors, the dependence amongst the elected currencies are strongly asymmetric in most of the tenures except the term of Pakistan Muslim League-Nawaz, and condition on common factor Clayton copula demonstrating hypothesis is more suitable. However, we perceive high left tail reliance among foreign currency returns during Pakistan Muslim League-Nawaz tenure, and the condition on common factor Gumbel copula molding assumption is more appropriate. We are signifying the foulest government performance in the country among all occupancies under consideration.

Asymmetric Dynamic Conditional Copula Correlation and Fundamental Determinants of Interest Rate Comovement

Asymmetric Dynamic Conditional Copula Correlation and Fundamental Determinants of Interest Rate Comovement

Conditional dependence structure between oil prices and international stock markets

PurposeThe purpose of this paper is to analyze the optimal hedging strategy of the oil-stock dependence structure.Design/methodology/approachThe methodology consists to model the data over the daily period spanning from January 02, 2002 to May 19, 2016 by a various copula functions to better modeling the dependence between crude oil market and stock markets, and to use dependence coefficients and conditional variance to calculate optimal portfolio weights and optimal hedge ratios, and to suggest the best hedging strategy for oil-stock portfolio.FindingsThe findings show that the Gumbel copula is the best model for modeling the conditional dependence structure of the oil and stock markets in most cases. They also indicate that the best hedging strategy for oil price by stock market varies considerably over time, but this variation depends on both the index introduced and the model used. However, the conditional copula method with skewed student more effective than the other models to minimize the risk of oil-stock portfolio.Originality/valueThis research implication can be valuable for portfolio managers and individual investors who seek to make earnings by diversifying their portfolios. The findings of this study provide evidence of the importance of stock assets for making an optimal portfolio consisting of oil in the case of investments in oil and stock markets. This paper attempts to fill the voids in the literature on volatility among oil prices and stock markets in two important areas. First, it uses copulas to investigate the conditional dependence structure of the oil crude and stock markets in the oil exporting and importing countries. Second, it uses the dependence coefficients and conditional variance to calculate dynamic hedge ratios and risk-minimizing optimal portfolio weights for oil–stock.