Asymmetric Copulas Research Articles

Stochastic dominance and statistical preference for random variables coupled by arbitrary copulas

Recently, results have been published showing that first order stochastic dominance implies statistical preference and diff-stochastic dominance, when the copula relating the compared variables is either Archimedean, the product copula, or one of the Fréchet-Hoeffding bounds.In the present paper, we rely on known results on multivariate stochastic orders to extend these results and simplify the proofs. The results are expanded in two directions: First, we show that it suffices for the copula to be symmetric. Second, we reveal that first stochastic dominance entails a wider range of stochastic preferences beyond statistical preference and diff-stochastic dominance.We further analyze whether first stochastic dominance implies statistical preference for the case of asymmetric copulas. We observe that, when at least one of the marginal cumulative distribution functions has no discontinuity jumps, the family of asymmetric copulas for which the implication holds is at least as large as the one for which it does not.

Unveiling Portfolio Resilience: Harnessing Asymmetric Copulas for Dynamic Risk Assessment in the Knowledge Economy

Unveiling Portfolio Resilience: Harnessing Asymmetric Copulas for Dynamic Risk Assessment in the Knowledge Economy

Analysis of asymmetric financial data with directional dependence measures

The increase of the product variety in the financial markets requires a clear understanding of the dependence between such instruments for the decision-makers. For a few decades, such dependence structures were often modeled with symmetric copula families. How- ever, financial data may reveal an asymmetric structure, which can be determined via directional dependence measures in the context of copulas. Previously, some asymmetric copula models were proposed in different ways using Khoudraji's device. But they are merely used for financial time series data in a broader sense. In this study, a new set of asymmetric copulas were defined by using one parameter of Archimedean copula families. For this aim, widely used copula families were studied and the corresponding directional dependence measures were analyzed. To illustrate the efficiency of the parameter estimation method, a small simulation scenario consisting of an asymmetric dependence pattern was carried out. Thereafter, the proposed asymmetric bi-variate copulas with directional dependence coefficients were investigated for two different stock market data. The study's primary findings suggested that the newly generated asymmetric models might be useful for directional dependence. Especially, the estimated directional dependence coefficients can serve as an indicator to explain the variability of one stock in terms of the other.

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.

Property analysis and application in biomedicine of two kinds of copula related to FGM

ABSTRACT FGM copula is widely used in correlation analysis because of its simple form and excellent properties, but its application in asymmetric correlation analysis is limited by its symmetrical function form. This paper mainly analyzes the properties of two kinds of asymmetric copulas related to FGM copula-generalized FGM copula and three-section copula. As two kinds of asymmetric copula related to FGM copula, they retain many excellent properties of FGM copula, such as closure under convolution operation and the relation between Spearman ρ and Kendall τ , etc. The closeness of convolution operation provides convenience for the calculation of Copula dependence coefficient. Finally, the generalized FGM is selected to analyze the asymmetric dependence between variables in biomedicine, which lays a foundation for its application in biomedicine.

A multivariate model to estimate environmental load on an offshore structure

Offshore structures such as oil platforms are subjected to significant environmental loads caused by wind, waves, and current. The complexity of offshore environment requires robust and reliable models to capture dependencies among environmental variables. A vine copula is a powerful tool that can be used to construct multivariate models by decomposing the complex structure into a series of simple pair copulas. Previous studies have shown that simple and symmetric copulas can be used as building blocks to construct vine copula models. In this study, symmetric and asymmetric copula functions are considered building blocks to capture all possible dependency structures. The c-vine model is then used to estimate the total environmental load on an offshore structure. Estimated loads are compared with those using the traditional independent variable approach and a multi-Gaussian distribution function-based method. The results reveal that both symmetric and asymmetric copula functions can be fitted to build c-vine copula models for the trivariate case. C-vine copulas, constructed using asymmetric copulas, provide a better estimation of the total environmental load than the independent and multivariate Gaussian methods. The result of this study is useful in probabilistic structural analysis of offshore structures for design and resilience analysis.

New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

Abstract New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.

Maximal asymmetry of bivariate copulas and consequences to measures of dependence

Abstract In this article, we focus on copulas underlying maximal non-exchangeable pairs ( X , Y ) \left(X,Y) of continuous random variables X , Y X,Y either in the sense of the uniform metric d ∞ {d}_{\infty } or the conditioning-based metrics D p {D}_{p} , and analyze their possible extent of dependence quantified by the recently introduced dependence measures ζ 1 {\zeta }_{1} and ξ \xi . Considering maximal d ∞ {d}_{\infty } -asymmetry we obtain ζ 1 ∈ 5 6 , 1 {\zeta }_{1}\in \left[\frac{5}{6},1\right] and ξ ∈ 2 3 , 1 \xi \in \left[\frac{2}{3},1\right] , and in the case of maximal D 1 {D}_{1} -asymmetry we obtain ζ 1 ∈ 3 4 , 1 {\zeta }_{1}\in \left[\frac{3}{4},1\right] and ξ ∈ 1 2 , 1 \xi \in \left(\frac{1}{2},1\right] , implying that maximal asymmetry implies a very high degree of dependence in both cases. Furthermore, we study various topological properties of the family of copulas with maximal D 1 {D}_{1} -asymmetry and derive some surprising properties for maximal D p {D}_{p} -asymmetric copulas.

Dependence structure between the international crude oil market and the European markets of biodiesel and rapeseed oil

Being an environmentally friendly fuel obtained from rapeseed oil, biodiesel is used extensively in Europe. However, the dependence structure between global crude oil prices and the European prices of biodiesel and rapeseed oil is understudied and unclear. In this paper, we address this gap by utilizing asymmetric copulas and cross-quantilogram approaches on daily data. The results of the DCC-Student-t copula indicate that during bearish periods the conditional connectedness between crude oil prices and biodiesel (rapeseed oil) prices are stronger than during bullish periods, indicating increased co-movement with a decline in crude oil prices. The application of cross-quantilogram indicates that an increase in crude oil price positively influences biodiesel prices reflecting an asymmetric dependence structure among the assets. There is evidence of shifts in the dynamics of quantile dependency during periods of financial and economic turmoil. Overall, the results show a significant dependence between the global crude oil market and the European markets of biodiesel and rapeseed oil in specific periods and under specific market conditions, which have important implications for policymakers and investors.

Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables

This paper considers the difference of stop-loss payoffs where the underlying is a difference of two random variables. The goal is to study whether the comonotonic and countermonotonic modifications of those two random variables can be used to construct upper and lower bounds for the expected payoff, despite the fact that the payoff function is neither convex nor concave. The answer to the central question of the paper requires studying the crossing points of the cumulative distribution function (cdf) of the original difference with the cdf's of its comonotonic and countermonotonic transforms. The analysis is supplemented with a numerical study of longevity trend bonds, using different mortality models and population data. The numerical study reveals that for these mortality-linked securities the three pairs of cdf's generally have unique pairwise crossing points. Under symmetric copulas, all crossing points can reasonably be approximated by the difference of the marginal medians, but this approximation is not necessarily valid for asymmetric copulas. Nevertheless, extreme dependence structures can give rise to bounds if the layers of the bond are selected to hedge tail risk. Further, the dependence uncertainty spread can be low if the layers are selected to hedge median risk, and, subject to a trade-off, to hedge tail risk as well.

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.

Copula-Based Estimation Methods for a Common Mean Vector for Bivariate Meta-Analyses

Traditional bivariate meta-analyses adopt the bivariate normal model. As the bivariate normal distribution produces symmetric dependence, it is not flexible enough to describe the true dependence structure of real meta-analyses. As an alternative to the bivariate normal model, recent papers have adopted “copula” models for bivariate meta-analyses. Copulas consist of both symmetric copulas (e.g., the normal copula) and asymmetric copulas (e.g., the Clayton copula). While copula models are promising, there are only a few studies on copula-based bivariate meta-analysis. Therefore, the goal of this article is to fully develop the methodologies and theories of the copula-based bivariate meta-analysis, specifically for estimating the common mean vector. This work is regarded as a generalization of our previous methodological/theoretical studies under the FGM copula to a broad class of copulas. In addition, we develop a new R package, “CommonMean.Copula”, to implement the proposed methods. Simulations are performed to check the proposed methods. Two real dataset are analyzed for illustration, demonstrating the insufficiency of the bivariate normal model.

Bayesian sequential stock return prediction through copulas

In this paper we perform density prediction for the equity returns in a non-linear manner by employing a copula-based approach. The use of asymmetric copulas allows to model asymmetric predictive densities and non-linear dependencies between equity returns and some predictor variable. In our proposed approach, the copula parameter and the marginals are estimated simultaneously by using Sequential Monte Carlo techniques. We apply proposed models to daily log returns of 20 assets traded at the NYSE. Among other findings, we show that in terms of predictive log Bayes Factors the asymmetric copula is preferred by more assets than the symmetric copula, advocating the use of non-linear models. Also, dividend yield is a better predictor variable than the lagged returns overall, but this result is reversed if we consider a volatile period only. These results have major implications for the investors when making portfolio decisions or measuring tail risk.

Copula-Based Assessment of Co-Movement and Tail Dependence Structure Among Major Trading Foreign Currencies in Ghana

This paper examines the joint movement and tail dependence structure between the pair of foreign exchange rates (EUR, USD and GBP) against the GHS, using daily exchange rates data expressed in GHS per unit of foreign currencies (EUR, USD and GBP) between the time range of 24 February 2009 and 19 December 2019. We use different sets of both static (time-invariant) and time-varying copulas with different levels of dependence and tail dependence measures, and the study results reveal positive dependence between all exchange rates pairs, though the dependencies for EUR-USD and GBP-USD pairs are not as strong as the EUR-GBP pair. The findings also reveal symmetric tail dependence, and dependence evolves over time. Notwithstanding this, the asymmetric tail dependence copulas provide evidence of upper tail dependence. We compare the copula results to DCC(1,1)-GARCH(1,1) model result and find the copula to be more sensitive to extreme co-movement between the currency pairs. The afore-mentioned findings, therefore, offer forex market players the opportunity to relax in hoarding a particular foreign currency in anticipation of domestic currency depreciation.

Copula diagnostics for asymmetries and conditional dependence

ABSTRACT Vine copulas are constructed from a sequence of trees to represent dependence and conditional dependence, and a set of bivariate copulas that are applied to univariate distributions in tree 1 and to conditional univariate distributions in subsequent trees. Diagnostic methods based on measures of dependence and tail asymmetry are proposed to guide the choice of parametric bivariate copula families assigned to the edges of the trees in the vine and to assess whether a copula is constant over the conditioning value(s) for trees 2 and higher. The measures are conditional measures applied to bivariate conditional distributions in trees 2 and higher. If the diagnostic methods suggest the existence of reflection asymmetry, permutation asymmetry and possible asymmetric tail dependence, then three- or four-parameter bivariate copula families might be needed. Moreover, if the conditional dependence measures or asymmetry measures in trees 2 and up are not constant over the conditioning value(s), then non-constant copulas should be considered. We illustrate the use of the diagnostic methods for a gamma factor model and two real datasets. The examples show that better models are attained by using asymmetric and non-constant copulas under the guidance of the diagnostic tools.

Modeling asymmetric dependences among multivariate soil data for the geotechnical analysis – The asymmetric copula approach

Multivariate information of soil parameters is quite important for the design and risk assessment of geotechnical engineering problems. It is necessary to have an accurate and realistic statistical multivariate model for representing the soil properties and thus evaluating the soil conditions. Thus, advanced multivariate modeling of soil parameters could help to improve the geotechnical engineering practice. In this paper, the asymmetric copulas are introduced to model the geotechnical soil data. Compared to extensive previous research on the use of symmetric copulas on the modeling of engineering data, this study is focusing on capturing asymmetric dependencies among the natural soil parameters, which are critical for engineering design. A copula-based multivariate probabilistic model is built based on a set of collected samples from a granite residual soil from Portugal. Several asymmetric copula functions, capable of capturing nonlinear asymmetric dependence structures, are tested and analyzed. The fundamental information on tail dependencies and measures of asymmetric dependencies are also exploited. To demonstrate the advantages of asymmetric copulas, its concept is compared with the traditional copula approaches for modeling site soil data. The performance of these asymmetric copulas is discussed and compared based on data fitting and extreme value characterizations.

Rendimiento y volatilidades de los mercados mexicanos bursátil y cambiario

Se analiza la relación entre los rendimientos del mercado bursátil mexicano y los rendimientos (tasa de apreciación) del dólar estadounidense, así como la relación entre sus volatilidades. La evidencia al respecto, incluyendo el ámbito internacional, no es concluyente. El análisis se lleva a cabo mediante la metodología de cópulas, las cuales se seleccionan con base en los criterios de información de Akaike y Schwarz. Las volatilidades fueron estimadas por medio de modelos GARCH asimétricos con parámetros variantes en el tiempo de acuerdo con un proceso de cambios markovianos. La evidencia sugiere que las dinámicas bursátil y cambiaria no siempre están asociadas, pero existe asociación entre los rendimientos accionarios y la apreciación/depreciación del peso frente al dólar y una asociación positiva cuando las volatilidades son altas en ambos mercados. Una consecuencia obvia es que el riesgo cambiario puede ser un riesgo importante para la inversión bursátil, tal como lo asume la teoría financiera convencional, por lo que, aunque no es posible establecer que las dinámicas bursátil y cambiaria estén siempre asociadas, es conveniente establecer políticas de inversión bursátil considerando dicho riesgo.

Asymmetric dependence in international currency markets

We find new channels for the transmission of shocks in international currencies, by developing a model in which shock propagations evolve from domestic stock markets, liquidity, credit risk and growth channels. We employ symmetric and asymmetric copulas to quantify joint downside risks and document that asset classes tend to experience concurrent extreme shocks. The time-varying spillover intensities cause a significant increase in cross-asset linkages during periods of high volatility, which is over and above any expected economic fundamentals, providing strong evidence of asymmetric investor induced contagion. The critical role of the credit crisis is amplified, as the beginning of an important reassessment of emerging currencies which lead to changes in the dependence structure, a revaluation and recalibration of their risk characteristics. By modelling tail risks, we also find patterns consistent with the domino effect.

Dependence properties and Bayesian inference for asymmetric multivariate copulas

We study a broad class of asymmetric copulas introduced by Liebscher (2008) as a combination of multiple – usually symmetric – copulas. The main thrust of the paper is to provide new theoretical properties including exact tail dependence expressions and stability properties. A subclass of Liebscher copulas obtained by combining comonotonic copulas is studied in more detail.We establish further dependence properties for copulas of this class and show that they are characterized by an arbitrary number of singular components. Furthermore, we introduce a novel iterative representation for general Liebscher copulas which de facto insures uniform margins, thus relaxing a constraint of Liebscher’s original construction. Besides, we show that this iterative construction proves useful for inference by developing an Approximate Bayesian computation sampling scheme. This inferential procedure is demonstrated on simulated data and is compared to a likelihood-based approach in a setting where the latter is available.

On structural properties of an asymmetric copula family and its statistical implication

Constructing new copulas by transforming a given copula is necessary to enhance the flexibility of the existing copula family. Among various copula transformations, the Khoudraji transformation (K-transformation), described in [16], provides a promising way to create asymmetric copulas. In this study, we completely characterize the invariance property of the K-transformation and discuss how the K-transformation changes measures of association or asymmetry of a copula. In particular, this study explores the identifiability issue of Khoudraji-transformed copula families. Some conditions for guaranteeing identifiable transformed copula families are provided.