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An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family. 1

In this article, we describe qregsel, a community-contributed command that implements a copula-based sample-selection correction for quantile regression recently proposed by Arellano and Bonhomme (2017, Econometrica 85: 1–28). The command allows the user to model selection in quantile regressions by using either a Gaussian or a one-dimensional Frank copula. We illustrate the use of qregsel with two examples. First, we apply the method to the fictional dataset used in the Stata Base Reference Manual for the heckman command. Second, we replicate part of the empirical application of the original article using data for the United Kingdom that cover the period 1978–2000 to compare wages of males and females at different quantiles.

The Copula approach for continuous variables is highly developed, while discrete ones are underdeveloped due to computational difficulties and sometimes algorithm failure to convergent. Therefore, providing an alternative method for discrete variables becomes an essential issue. In this paper, a simple method is proposed to answer the problem by applying the Continuous Extension Technique (CET). This is carried out by adding random independent perturbations in the form of either Uniform distribution U(0,1) or (U(0,1)−1), and the discrete variables are treated as continuous. Subsequently, a Copula model for resulted variables is estimated based on the Copula theory for continuous variables. This method is called a Copula continuous extension technique. Our analytic and simulation approaches show that both random perturbation forms produce the same Kendall’s Tau measure and the selected Copula bivariate model. As illustrations, the proposed method is applied to the seismicity data obtained from the annual frequencies of earthquakes that occurred in the Sumatra megathrust of Indonesia, from January 1971 to December 2018, with magnitudes ( Mw ) of at least 4.6. Based on the selected Copula models, our simulations confirm the evidence of dependence seismic activity in each of the two adjacent large earthquake sources. These results provide new information regarding the seismicity behavior in the Sumatra megathrust.

The paper analyzes the morphosyntactic status of a copula no as part of complex verbal predicates of Guinean Pular. A locative copula no, combined with various forms of lexical verb, adds up to three verbal constructions. Morphological and semantic non-compositionality of no in such constructions questions its morphosyntactic status as a free word and suggests that it might be an affix or a clitic. Pular data has been subjected to a series of tests using a set of phonological, morphological, and semantic criteria. The results of the phonological tests show that no in complex verbal predicates cannot be a free word, whereas the morphological tests deny it the status of an affix. It is, therefore, concluded that this copula is a clitic, which is confirmed by the language data complying with general morphological and phonological criteria.

Agriculture is one of the main pillars of economic growth in Indonesia. Failure in this sector can result in faltering economic stability of the country. Thus, to minimize these failures, mapping of areas with particular commodity potential is needed. One of the main factors affecting the growth of crops is rainfall. Therefore, this paper aims to model the potential distribution of commodity growth based on rainfall precipitation using dynamic copula. The modeling results are then used as a basis for grouping the potential of food crop commodities in Indonesia. The determination of the group was carried out using the k-means clustering method. We expect that the result of the modeling can provide an overview for farmers or the government to make policies related to the optimization of Indonesia's agricultural sector. This result will enable the government to offer facilities that can minimize agricultural losses, such as superior seeds that are resistant to weather changes and the provision of training for enhancing farming skills. In addition, it is also suggested to diversify farm areas to reduce the failures due to dependence on a single agricultural product.

This study deals with the stochastic comparison of extreme order statistics from random samples with FGM copula or FGM survival copula. For general marginal distributions, several sufficient condit...

The objective of this work is to estimate the patterns of dependence between the yields of the stock prices of the main banks of the United States (US) and Mexico. We estimate the patterns of absolute dependence and tail dependence through copulas of the Archimedean family and the use of rolling windows of 245 days. The data employed come from the daily share prices at closing from January 2, 2015, to December 31, 2020, for seven banks. Our results show that: i) there are patterns of high dependence among the main banks in the US, ii) there are patterns of very low dependence among the main banks in the US and Mexico, and iii) there are patterns of low dependence among the main banks in Mexico. These results have several implications, among them that the high-dependency patterns obtained among major US banks limit the joint selection of these US bank equity assets in an investment portfolio. Although this paper focuses on a small sample of banks, they represent an important portion of the banking sector in both countries. Given the limited literature on this subject in Mexico, our paper contributes to expanding this literature with a novel approach.

For a typical insurance portfolio, the claims process for a short period, typically one year, is characterized by observing frequency of claims together with the associated claims severities. The collective risk model describes this portfolio as a random sum of the aggregation of the claim amounts. In the classical framework, for simplicity, the claim frequency and claim severities are assumed to be mutually independent. However, there is a growing interest in relaxing this independence assumption which is more realistic and useful for the practical insurance ratemaking. While the common thread has been capturing the dependence between frequency and aggregate severity within a single period, the work of Oh et al. (2021) provides an interesting extension to the addition of capturing dependence among individual severities. In this paper, we extend these works within a framework where we have a portfolio of microlevel frequencies and severities for multiple years. This allows us to develop a factor copula model framework that captures various types of dependence between claim frequencies and claim severities over multiple years. It is therefore a clear extension of earlier works on one-year dependent frequency-severity models and on random effects model for capturing serial dependence of claims. We focus on the results using a family of elliptical copulas to model the dependence. The paper further describes how to calibrate the proposed model using illustrative claims data arising from a Singapore insurance company. The estimated results provide strong evidences of all forms of dependencies captured by our model.

In this paper, we seek to examine the relationship and dynamic dependence structure between the Australian dollar (AUD), euro (EUR), and the British pound (GBP), expressed in American dollars (USD) using a multivariate fractional cointegration model. Our empirical analysis reveals several important findings. First, the main advantage of this approach is to detect the long-term relationship as well as the short-term dynamics and to represent the interdependence between the variables. We further estimate a multivariate GARCH type model that enables us to examine the dynamic conditional correlations (short-run links) among the considered variables under the effects of long-run interactions and volatility persistence. We determine that the volatility transmission was time-varying and that influence from the crisis. Moreover, the joint distribution is explored using the Gumbel copulas in order to describe the nonlinear structure of dependence between the variables. The empirical results provide evidence of fractional cointegration between the exchanges rates and show long-run causal links between the variables and we find significant bidirectional causal links. In particular, we show a positive dynamic correlation and the dependence structure is represented by the optimal copula coefficient used for measuring the risk spillovers between the exchange rates.

Copula model has applied in various hydrologic studies, however, most analyses conducted does not considering the non-stationary conditions that may exist in the time series. To investigate the dependence structure between two rainfall stations at Johor Bahru, two methods have been applied. The first method considers the non-stationary condition that exists in the data, while the second method assumes stationarity in the time series data. Through goodness-off-fit (GOF) and simulation tests, performance of both methods are compared in this study. The results obtained in this study highlight the importance of considering non-stationarity conditions in the hydrological data.

An efficient sieve maximum likelihood estimation procedure for regression models with endogenous regressors using a copula-based approach is proposed. Specifically, the joint distribution of the en...

These last years the stochastic modeling became essential in financial risk management related to the ownership and valuation of financial products such as assets, options and bonds. This paper presents a contribution to the modeling of stochastic risks in finance by using both extensions of tail dependence coefficients and extremal dependance structures based on copulas. In particular, we show that when the stochastic behavior of a set of risks can be modeled by a multivariate extremal process a corresponding form of the underlying copula describing theirdependence is determined. Moreover a new tail dependence measure is proposed and properties of this measure are established.

We model the recursive moments of aggregate discounted claims, assuming the inter-claim arrival time follows a Weibull distribution to accommodate overdispersed and underdispersed data set. We use a copula to represent the dependence structure between the inter-claim arrival time and its subsequent claim amount. We then use the Laplace inversion via the Gaver-Stehfest algorithm to solve numerically the first and second moments, which takes the form of a Volterra integral equation (VIE). We compute the average and variance of the aggregate discounted claims under the Farlie-Gumbel-Morgenstern (FGM) copula and conduct a sensitivity analysis under various Weibull inter-claim parameters and claim-size parameters. The comparison between the equidispersed, overdispersed and underdispersed counting processes shows that when claims arrive at times that vary more than is expected, insured lives can expect to pay higher premium, and vice versa for the case of claims arriving at times that vary less than expected. Upon comparing the Weibull risk process with an equivalent Poisson process, we also found that copulas with a wider range of dependency parameter such as the Frank and Heavy Right Tail (HRT), have a greater impact on the value of moments as opposed to modeling under FGM copula with weak dependence structure.

The application of copula has become popular in recent years. The use of correlation as a dependence measure has several pitfalls and hence the application of regression prediction model using this correlation may not be an appropriate method. In financial markets, there is often a non-linear dependence between returns. Thus, alternative methods for capturing co-dependency should be considered, such as copula based ones. This paper studies the dependence structure between the four largest African stock markets in terms of market capitalization and other developed stock markets over the period 2003 to 2018 using copula models. The value at risk was used to determine the risk associated with the stock. The ten copula models were fitted to the log returns calculated from the data, two countries at a time of the twenty-eight pairs and examined. The Gumbel copula gives the best fit in terms of log-likelihood values, value of the Akaike information criterion, value of the Bayesian information criterion, value of the consistent Akaike information criterion, value of the corrected Akaike information criterion, value of the Hannan Quinn criterion and p-value of the information matrix equality of White. Estimates of value at risk with probability p for daily returns were computed using the best fitted copula model, from these value at risk, it is seen that SA/FTSE100 have the least risk while EGY/KEN has the highest risk. Prediction is given in terms of correlation and value at risk.

Copulas have recently emerged as practical methods for multivari- ate modeling. To our knowledge, only a limited amount of work has been done to apply copula-based modeling in context analysis. In this study, we generalized Clayton copula under the appropriate weighted function. In some examples, bivariate distributions by using the weighted Clayton cop- ula are generalized. Also the properties of generalized Clayton copula are provided. The Clayton copula and weighted Clayton model cannot be used for negative dependence. These have been used to study left tail depen- dence. This property is stronger in weighted Clayton model with respect to ordinary Clayton copula. It will also be shown that the generalized Clayton copula is suitable for the probable modeling of the hydrology data.

We investigate the dependency, risk spillovers, and systemic risk between the sectoral indices returns of the Bombay stock exchange (BSE) and oil prices using recently developed empirical technique...

To quantify variations in seismic hazard assessment, a large number of scenario earthquake shaking maps (hereafter referred to as s-EQ maps for short) are required. In this article, we propose a method to easily generate a large number of s-EQ maps by combining modal decomposition and empirical copula. First, by applying modal decomposition to a set of existing s-EQ maps, we identify a scenario set with a parameter space to reduce the dimensionality of models. Next, we model a probability distribution of the modal coordinates, which we regard as random variables to allow us to induce a probability measure on the parameter space. By applying an empirical copula for modeling the probability distributions, the dependence structure between modal coordinates and the probability distribution of an individual modal coordinate can be discussed independently. Some simulations show that the dependence structure between modal coordinates is important to not distort the seismic hazard assessment. The proposed method can be applied to actual existing s-EQ maps to easily generate a large number of new s-EQ maps that follow the original probability distribution. We also show that variations can be added to the newly generated s-EQ maps by adjusting the empirical copula. Furthermore, we give a generalization of the proposed method to cases with nonequal probabilities of occurrence of existing scenarios.

Value at Risk (VaR) plays a central role in risk management. There are several approaches for the estimation of VaR, such as histori- cal 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 distri- bution. 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 allow- ing 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&P500 stock indices.

Vine copula, constructed from bivariate copulas, provides great flexibility in modelling complex high-dimensional dependence. When applied to multi-population mortality modelling, vine copula yields significant improvement over traditional multivariate copulas. In this paper, we propose to capture time-varying features in mortality dependence with dynamic regular vine (R-vine) copula which is built from bivariate copulas with time-varying dependence parameters. We develop two dependence dynamics for R-vine copulas and illustrate the selection and estimation of dynamic R-vine copulas using mortality data from eight populations. The estimated R-vine copulas using the proposed dependence dynamics are shown to yield better goodness of fit than both static and regime-switching vine copulas. We further demonstrate the simulation of mortality paths using dynamic R-vine copulas and examine the impact of vine copula choice on the assessed effectiveness of longevity hedge.

In the modeling of multivariate extreme risks, the tail dependence and the heavy tailedness are the two key factors. Heavy tailedness are usually defined through the regular variation. Tail dependence can be modeled by copulas with the so-called tail order property. In this paper, we propose a new risk measure called the Joint Expected Shortfall (JES) as an alternative of quantifying extreme risks. The JES, which can be viewed as a consolidation of both Expected Shortfall (ES) and Marginal Expected Shortfall (MES) risk measures, has the desirable property of measuring risk by jointly capturing both tail dependence and heavy tailedness. The asymptotic analysis of JES is conducted to provide a simple and transparent way of studying the interplay between tail dependence and heavy tailedness. Various examples are presented to illuminate our results. In particular, risk measures such as ES and MES that ignore the joint effect of dependence and heavy tailedness may severely underestimate the underlying risk.

Copulas and frailty models have been two major tools for modeling dependence in multivariate failure time distributions. The objective of this paper is to investigate multivariate failure time models that include copula models and frailty models as special cases. To this end, we revisit a broad family of multivariate failure time models proposed by Marshall and Olkin (JASA 83:834–841, 1988). This family accommodates both frailty and copulas, unlike the models that accommodate only one of them. However, their work focused on very specific copulas and is limited to bivariate models. Instead, we focus more on popular members of copulas and some multivariate models. Another novel feature of our paper is to restrict our attention to the shared frailty model, and call our restricted class as the generic name “frailty-copula”. This name yields a taxonomic classification of all the members of distributions. We also consider somewhat complex frailty distributions (two-parameter gamma, lognormal, truncated-normal, and folded-normal), which were not considered in Marshall and Olkin (1988) and other papers of frailty models. To illustrate the usefulness of the proposed model, we briefly discuss maximum likelihood estimation methods with some numerical evaluations.

Given $(Z_{i},\delta _{i})=\left\{ \min (T_{i},C_{i}),I_{(T_{i}

In this article, we develop a new method based on copulas to model correlated inputs in discrete-event stochastic systems. We first define a type of correlated stochastic process, called Copula Cor...

This study examines the extent of systemic risk embedded in the credit and equity markets using a conditional value-at-risk (CoVaR) measure. We implement a copula-based CoVaR approach with differen...

In this paper, we propose a stochastic order for bivariate copulas based on their hazard rates. We study its properties and the relationships it has with some stochastic orders and dependence notions. The utility of the new order in verifying concepts and orders involving dependence notions is also discussed.

Multiple disasters induced by hurricanes such as floods, strong winds, and heavy rainfall have always been a significant threat to coastal infrastructures. However, few studies have attempted to model the dependence between hazards and study its impact on multi-hazard risks—these cognitive deficiencies inevitably affect the control of risks. This paper addresses these difficulties by first using the copulas to capture the dependence between hurricane-induced floods and strong winds based on synthetic multi-hazard events. Moreover, another two types of dependence, regression-based and mutually independent, are constructed to compare the impact of different dependence behaviors on the facility’s failure. Second, the frequency of concurrent events and a scenario-based fragility function are convolved to quantify the multi-hazard risk of storage tanks. Subsequently, the annualized failure risk (AFR) and the mean return period of failure (MRPF) are used as two metrics for the multi-hazard risk. The case study results demonstrate that the BB1 copula can accurately describe the change in dependence across the full range of the multivariate distribution, avoiding overestimation or underestimation of equipment failure risks. The application of risk zoning provides decision-makers with more intuitive and convenient tools for planning and layout, highlighting the practicability of the proposed multi-hazard risk assessment method.

Tujuan dari penelitian ini adalah memodelkan ketergantungan FDI dan GDP. Metode yang digunakan adalah copula. Tahapan yang dilakukan dalam penelitian ini adalah uji stasioner, penentuan model ARIMA, uji heterokedastisitas, transformasi residu data, uji normalitas, uji koefisien korelasi tau Kendal, perhitungan nilai parameter kelas Archimedean, perhitungan MSE. Dari rangkaian yang dilakukan, diperoleh bahwa copula clayton yang terpilih dalam pemodelan ketergantungan FDI dan GDP.

Geyser eruption is one of the most popular signature attractions at the Yellowstone National Park. The interdependence of geyser eruptions and impacts of covariates are of interest to researchers in geyser studies. In this paper, we propose a parametric covariate-adjusted recurrent event model for estimating the eruption gap time. We describe a general bivariate recurrent event process, where a bivariate lognormal distribution and a Gumbel copula with different marginal distributions are used to model an interdependent dual-type event system. The maximum likelihood approach is used to estimate model parameters. The proposed method is applied to analyzing the Yellowstone geyser eruption data for a bivariate geyser system and offers a deeper understanding of the event occurrence mechanism of individual events as well as the system as a whole. A comprehensive simulation study is conducted to evaluate the performance of the proposed method., Comment: 29 pages

This study investigates expectile Value-at-Risk (EVaR) as a risk measure in dynamic copula-based portfolio optimization, compared with the common variance and CVaR. To estimate the dependence structure between asset returns, the canonical vine copula augmented with the generalized additive models (GAMC-vine) is used. Applying multivariate conditional distributions from the GAMC-vine model, step-ahead asset return forecasts are obtained and used to construct dynamic copula-based EVaR portfolios. Using ten S&P 500 industry sectors, EVaR leads to a min-risk dynamic GAMC-vine portfolio that achieves higher out-of-sample average return and risk-adjusted ratios. Furthermore, EVaR shows a better portfolio ranking than CVaR. Moreover, the copula-based variance and EVaR portfolios show higher-order stochastic dominance compared to CVaR strategies. Finally, a subsample stochastic dominance analysis reveals that, in overall, the risk minimization does not benefit from the choice of risk modeling. However, the dynamic copula model leads to optimal portfolios that dominate the equally weighted benchmark more often compared to those from historical approach.

A new family of copulas generated by a univariate distribution function is introduced, relations between this copula and other well-known ones are discussed. The new copula is applied to model the dependence of two real data sets as illustrations.

Conditional 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 semiparametric 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.

Copulas are a convenient tool for modelling dependencies in competing risks models with multiple spells. This paper introduces several practical extensions to the nested copula model and focuses on the choice of the hazard model and copula. A simulation study looks at the relevance of the assumed parametric or semiparametric model for hazard functions, copula and whether a full or partial maximum likelihood approach is chosen. The results show that the researcher must be careful which hazard is being specified as similar functional form assumptions for the subdistribution and cause-specific hazard will lead to differences in estimated cumulative incidences. Model selection tests for the choice of the hazard model and copula are found to provide some guidance for setting up the model. The nice practical properties and flexibility of the copula model are demonstrated with an application to a large set of maternity leave periods of mothers for up to three maternity leave periods.

Nowadays, insurance contract reserves for coupled lives are considered jointly, which has a significant influence on the process of determining actuarial reserves. In this paper, conditional survival distributions of life insurance reserves are computed using copulas. Subsequently, the results are compared with an independence case. These calculations are based on selected Archimedean copulas and apply when the ‘death of one individual’ condition exists. The estimation outcome indicates that the insurer reserves calculated by means of Archimedean copulas are far more effective than those resulting from an independence assumption. The study demonstrates that copula-based dependency modelling improves the calculations of reserves made for actuarial purposes.

In this paper, a new copula model with given unit marginals is proposed, based on Rüschendorf’s Method. A new bivariate copula family is introduced by adding a proper term to independence copula. Thus, we avoid the complexity of the proposed copula model. By choosing a baseline copula from the same marginal, we derive a new copula that can approach from above towards the independence copula. Furthermore, it is established that a bivariate copula constructed by this method allows some flexibility in the dependence measure according to Spearman’s correlation coefficient. Additionally, tail dependence measures are investigated. Illustrative examples are given taking into account the specific choices of a baseline copula.

Most previous studies that have confirmed size anomalies in U.S. bank stock returns rely on a simple OLS regression. However, empirical evidence shows that all the financial variables used in their...

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

Hurricanes are destructive forces of nature that have the ability to cause vast devastation both economically and socially. Estimating the potential damage caused by hurricanes aids local, state and federal governments as well as insurance and reinsurance companies to plan for future hurricanes. Direct damages caused by hurricanes are difficult to estimate. There are multiple factors that could contribute to the damages caused by a hurricane. Wind is typically considered the most important factor to account for when estimating potential damage. Aside from the complex physical processes, the difficultly in estimating hurricane damages is further compounded by limited data and a changing climate. Fitting models with limited data presents a series of challenges. These challenges include outliers that could form a large proportion of the data, overfitting, missing data and it becomes difficult to leave out a portion of the data for external validation. This study found a significant positive correlation using the Kendall rank correlation coefficient between hurricane damages, measured by the area of total destruction and the maximum landfalling wind speed (τ = 0.451). A copula-based approach was used to model their dependency. Both bivariate Archimedean and elliptical copulae families were assessed as potential models. A bivariate Frank copula with Weibull marginals was found to be the most appropriate fitting model based on a visual inspection of the contour plots of the fitted copulae. Simulation from the fitted copula was qualitatively similar to observation. This study demonstrated a potential method to overcome the limitation of small data facing models to estimate hurricane damages.

Efficient energy production and distribution systems are urgently needed to reduce world climate change. Since modern district heating systems are sustainable energy distribution services that exploit renewable sources and avoid energy waste, in-depth knowledge of thermal energy demand, which is mainly affected by weather conditions, is essential to enhance heat production schedules. We hence propose a mixture copula-based approach to investigate the complex relationship between meteorological variables, such as outdoor temperature and solar radiation, and thermal energy demand in the district heating system of the Italian city Bozen-Bolzano. We analyse data collected from 2014 to 2017, and estimate copulas after removing serial dependence in each time series using autoregressive integrated moving average models. Due to complex relationships, a mixture of an unstructured Student-t and a flipped Clayton copula is deemed the best model, as it allows differentiating the magnitude of dependence in each tail and exhibiting both heavy-tailed and asymmetric dependence. We derive the conditional copula-based probability function of thermal energy demand given meteorological variables, and provide useful insight on the production management phase of local energy utilities.