Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1], the distortion Cψ : [0, 1] → [0, 1], Cψ(x, y) = ψ(C(ψ−1(x)), ψ−1(y)), is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ which ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in...

Motivated by the wide applications of distortion function and copulas in insurance and finance, this paper generalizes the notion of deterministic distortion function to a stochastic distortion function, i.e., a random process, and employs the defined stochastic distortion function to construct a so-called stochastic distorted copula. One method for constructing stochastic distortions is provid...

Modeling short and long time dependence in univariate time series may be successfully accomplished through existing time series processes. In the multivariate setting just a few complex models exist to take care of the di®erent marginal dynamics as well as of the dynamic covariance matrix. The copula approach factors the joint distribution into the marginals and a dependence function, its copul...

Abstract T his paper empirically examines the impact of dependence structure between the assets on the portfolio optimization, composed of Tehran Stock Exchange Price Index and Borsa Istanbul 100 Index. In this regard, the method of the Copula family functions is proposed as powerful and flexible tool to determine the structure of dependence. Finally, the impact of the dep...

In this paper we investigate a new approach of estimating a regression function based on copulas. The main idea behind this approach is to write the regression function in terms of a copula and marginal distributions. Once the copula and the marginal distributions are estimated we use the plug-in method to construct the new estimator. Because various methods are available in the literature for ...

Abstract. Tail order of copulas can be used to describe the strength of dependence in the tails of a joint distribution. When the value of tail order is larger than the dimension, it may lead to tail negative dependence. First, we prove results on conditions that lead to tail negative dependence for Archimedean copulas. Using the conditions, we construct new parametric copula families that poss...

Recent literature on semiparametric copula models focused on the situation when the marginals are specified nonparametrically and the copula function is given a parametric form. For example, this setup is used in Chen, Fan and Tsyrennikov (2006) [Efficient Estimation of Semiparametric Multivariate Copula Models, JASA] who focus on the efficient estimation of copula parameters. We consider a rev...

This paper develops a novel approach to modeling and forecasting realized volatility (RV) measures based on copula functions. Copula-based time series models can capture relevant characteristics of volatility such as nonlinear dynamics and long-memory type behavior in a flexible yet parsimonious way. In an empirical application to daily volatility for S&P500 index futures, we find that the copu...

Arthur Charpentier (see Arthur’s blog) was recently contacted by some researchers willing to test if a multivariate copula is or not Gaussian. They use a test proposed in Malevergne and Sornette (2003) stating that one should simply test for pairwise normality. This test may be of importance in finance, in actuarial science, and in risk management in general: for example, given 120 financial as...

Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it is heavily a↵ected by boundary bias issues. In addition, most common copulas admit unbounded ...