Levy copulas are the most general concept to capture jump dependence in multivariate Levy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Levy copulas, is to find flexible but still applicable models for higher dim…
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48 results for “copula concepts”
GCMM improves clustering and fits un-synchronized data.
problem Improving clustering performance with copulas.
method Mathematical definition, copula concepts, Expectation Maximum algorithms, nonparametric estimation.
result GCMM outperforms GMM in goodness-of-fit and data analysis.
A Natural Copulaq-fin.RM
A new copula minimizes distance between distributions.
problem Arbitrariness in copula choice.
method Minimizes Wasserstein distance; linear programming estimation.
result Natural copula provides parsimonious estimation.
Copula models have become popular in different applications, including modeling shocks, in view of their ability to describe better the dependence concepts in stochastic systems. The class of maxmin copulas was recently introduced by Omladič and Ružić. It extends the well known classes of Marshall-Olkin and Marshall co…
A new copula, the checkerboard copula, maximizes entropy and preserves dependence.
problem Choosing copula for non-continuous marginal distributions.
method Introducing the checkerboard copula, maximizing Shannon entropy.
result Checkerboard copula maximizes entropy and preserves dependence.
We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be minimal in concordance ordering in the sense that no copula exists which is stric…
This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same probability space, whereas a copula is a function that joins a multivariate distributi…
Copulas and time series with long-ranged dependencesphysics.data-an
We review ideas on temporal dependences and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework…
When choosing the right copula for our data a key point is to distinguish the family that describes it at the best. In this respect, a better choice of the copulas could be obtained through the information about the (non)symmetry of the data. Exchangeability as a probability concept (first next to independence) has bee…
The exclusive or (xor) function is one of the simplest examples that illustrate why nonlinear feedforward networks are superior to linear regression for machine learning applications. We review the xor representation and approximation problems and discuss their solutions in terms of probabilistic logic and associative …
This paper is devoted to the quantification and analysis of marginal risk contribution of a given single financial institution i to the risk of a financial system s. Our work expands on the CoVaR concept proposed by Adrian and Brunnermeier as a tool for the measurement of marginal systemic risk contribution. We first g…
Proposes a copula-based method to interpret neural networks.
problem Neural networks lack interpretability due to ambiguity in decision-making.
method Uses pair copula correlation coefficients to reveal feature importance and decision paths.
result Consistent results with Random Forest's feature importance values.
We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the conte…
This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spea…
This paper develops copula-based models for forecasting multivariate realized volatility.
problem Forecasting multivariate realized volatility matrices with hidden dependence structure.
method Copula-based time series models to capture hidden dependence structure and ensure positive definiteness.
result Copula-based models achieve significant performance in volatility matrix forecasting.
We propose to use nonparametric Bernstein copulas as bivariate pair-copulas in high-dimensional vine models. The resulting smooth and nonparametric vine copulas completely obviate the error-prone need for choosing the pair-copulas from parametric copula families. By means of a simulation study and an empirical analysis…
Impact of non-stationarity on estimating and modeling empirical copulas of daily stock returnsq-fin.ST
All too often measuring statistical dependencies between financial time series is reduced to a linear correlation coefficient. However this may not capture all facets of reality. We study empirical dependencies of daily stock returns by their pairwise copulas. Here we investigate particularly to which extent the non-st…
Extends insurance-finance arbitrage concept to include model uncertainty.
problem Evaluating hybrid insurance products in uncertain financial markets.
method Introduces robust asymptotic insurance-finance arbitrage and -evaluations.
result No robust asymptotic insurance-finance arbitrage exists under certain conditions.
Copula is a powerful tool to model multivariate data. We propose the modelling of intraday financial returns of multiple assets through copula. The problem originates due to the asynchronous nature of intraday financial data. We propose a consistent estimator of the correlation coefficient in case of Elliptical copula …
Paper compares MCMC-based copula methods for exchange option pricing.
problem Pricing exchange options using copulas and MCMC.
method Risk-neutral pricing, copulas, and MCMC algorithm.
result Different copula models provide similar option prices except Gumbel.
A new copula estimation method using classification.
problem Estimating copula density from joint and marginal distributions.
method Train a classifier to distinguish joint density from product of marginals.
result Empirically outperforms existing copula estimators.
We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient co…
Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulasstat.ME
The study models insurance dependence using Bernstein copulas.
problem Modeling dependence structures in nonlife insurance data.
method Review and suggest fitting Bernstein copulas to empirical data.
result Monte Carlo simulation and PML estimation for aggregate losses.
In this paper we introduce some new copulas emerging from shock models. It was shown earlier that reflected maxmin copulas (RMM for short) are not just some specific singular copulas; they contain many important absolutely continuous copulas including the negative quadrant dependent part of the Eyraud-Farlie-Gumbel-Mor…
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…
Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, i…
Paper uses a new copula to model risk aggregation and capital allocation.
problem Modeling dependence between risks for risk aggregation and capital allocation.
method Uses a generalized Archimedean copula (mixed Bernstein copula) to define dependence structure and derives closed-form risk measures.
result Closed-form expressions for tail value-at-risk and allocations are derived.
Sibuya copulasmath.PR
The standard intensity-based approach for modeling defaults is generalized by making the deterministic term structure of the survival probability stochastic via a common jump process. The survival copula of the vector of default times is derived and it is shown to be explicit and of the functional form as dealt with in…
Copula Analysis of Risk: A Multivariate Risk Analysis for VaR and CoVaR using Copulas and DCC-GARCHq-fin.RM
Study uses copulas and DCC-GARCH for multivariate risk analysis of VaR and CVaR.
problem Multivariate risk analysis for Value at Risk (VaR) and Conditional Value at Risk (CoVaR).
method Copulas and Dynamic Conditional Correlation (DCC)-GARCH models applied to historical financial data.
result Comparison of different copula families for goodness-of-fit and effectiveness.
Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the `right' copula is not an easy task, and the temptation to prefer a tractable rather than a meaningful candidate from the encompassing…
A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copul…
Adaptive Bernstein copulas improve risk management by preventing overfitting and reducing simulation effort.
problem Overfitting and high simulation effort in estimating dependence models.
method Constructive approach to Bernstein copulas with an admissible discrete skeleton.
result Comparison of different copula approaches in risk management shows improved accuracy and efficiency.
Testing the Gaussian Copula Hypothesis for Financial Assets Dependencescond-mat.stat-mech
Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with…
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of…
New copula models learn to forget dependencies, improving data representation.
problem Restrictive assumptions and poor scaling in existing copula models.
method Diffusion and flow-based copulas that progressively forget dependencies.
result Provable valid copulas at all times, superior performance in complex dependencies.
Paper proposes copula-based models for analyzing multivariate zero-inflated continuous data.
problem Challenges in analyzing multivariate zero-inflated continuous data with mixed discreteness and continuity.
method Proposes two copula-based density estimation models and rectified Gaussian copula.
result Demonstrates superior performance compared to conventional methods.
New copulas based on general partitions-of-unity (part III) - the continuous case (extended version)q-fin.RM
In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of …
Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?q-fin.RM
Copulas outperform marginal models in multivariate risk forecasting, reducing model risk by narrowing down the set of models.
problem Model risk in multivariate risk forecasting, especially during crises.
method Comprehensive empirical study comparing Copula-GARCH models with fixed marginals, copulas, or neither.
result Model risk is almost entirely due to copula choice, not marginal models.
Characterizes symmetric Bernoulli distributions with minimal convex sums.
problem Understanding minimal dependence among Bernoulli random vectors.
method Geometric and algebraic representations of multivariate symmetric Bernoulli distributions.
result Characterizes extremal negative dependence and builds minimal dependence copulas.
Bayesian VI copula models capture asymmetric intraday equity dependence.
problem Modeling asymmetric and extreme tail dependence in financial data.
method Bayesian variational inference for skew-t copula models in high dimensions.
result The copula captures substantial heterogeneity in asymmetric dependence over equity pairs and time.
The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capabilit…
The study evaluates financial risk using copulas and statistical tests.
problem Validating bivariate forecasts in risk evaluation.
method Using copulas to characterize dependencies, applying statistical tests to validate forecasts, removing heteroskedasticity.
result A Student copula accurately describes financial time series dependencies.
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be inaccurate when there are covariates that cou…
Study proposes a method to construct copulas using corrected Hermite polynomial expansion for estimating foreign exchange volatility.
problem Estimating cross foreign exchange volatility with complex correlation structures.
method Applying corrections to the finite sum of multivariate Hermite polynomial expansions to construct copulas.
result The proposed copula method accurately reproduces the volatility smile of cross currency pairs.
This paper improves tail dependence analysis by introducing a path-based approach.
problem The classical tail dependence coefficient fails to capture non-exchangeable features of tail dependence.
method The paper introduces a path-based maximal tail dependence approach to capture the most pronounced feature of dependence over all possible paths.
result The paper proves the existence and provides an explicit characterization of the path-based maximal TDC, improving analytical and computational tractability.
A novel stepwise VI method using vine copulas for complex latent dependence.
problem Modeling complex latent dependence structures in probabilistic models.
method Stepwise estimation of vine copula parameters using Rényi divergence and a stopping criterion.
result Our method outperforms mean-field VI and is more parsimonious in complex applications.
We present a constructive and self-contained approach to data driven general partition-of-unity copulas that were recently introduced in the literature. In particular, we consider Bernstein-, negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data.
Paper introduces a new test for conditional independence using weighted partial copulas.
problem Testing conditional independence between variables.
method The approach uses a weighted partial copula function and a bootstrap procedure to compute regions of rejection.
result The proposed test has competitive power compared to existing methods.