176 research outputs found
Construction of asymmetric copulas and its application in two-dimensional reliability modelling
Copulas offer a useful tool in modelling the dependence among random variables. In the literature, most of the existing copulas are symmetric while data collected from the real world may exhibit asymmetric nature. This necessitates developing asymmetric copulas that can model such data. In the meantime, existing methods of modelling two-dimensional reliability data are not able to capture the tail dependence that exists between the pair of age and usage, which are the two dimensions designated to describe product life. This paper proposes two new methods of constructing asymmetric copulas, discusses the properties of the new copulas, and applies the method to fit two-dimensional reliability data that are collected from the real world
The joint distribution of stock returns is not elliptical
Using a large set of daily US and Japanese stock returns, we test in detail
the relevance of Student models, and of more general elliptical models, for
describing the joint distribution of returns. We find that while Student
copulas provide a good approximation for strongly correlated pairs of stocks,
systematic discrepancies appear as the linear correlation between stocks
decreases, that rule out all elliptical models. Intuitively, the failure of
elliptical models can be traced to the inadequacy of the assumption of a single
volatility mode for all stocks. We suggest several ideas of methodological
interest to efficiently visualise and compare different copulas. We identify
the rescaled difference with the Gaussian copula and the central value of the
copula as strongly discriminating observables. We insist on the need to shun
away from formal choices of copulas with no financial interpretation.Comment: 12 figure
Intermediate Tail Dependence: A Review and Some New Results
The concept of intermediate tail dependence is useful if one wants to
quantify the degree of positive dependence in the tails when there is no strong
evidence of presence of the usual tail dependence. We first review existing
studies on intermediate tail dependence, and then we report new results to
supplement the review. Intermediate tail dependence for elliptical, extreme
value and Archimedean copulas are reviewed and further studied, respectively.
For Archimedean copulas, we not only consider the frailty model but also the
recently studied scale mixture model; for the latter, conditions leading to
upper intermediate tail dependence are presented, and it provides a useful way
to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur
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