Multi-Tail Elliptical Distributions
نویسندگان
چکیده
In this paper we present a new type of multivariate distributions for asset returns which we call the multi-tail elliptical distributions. Multi-tail elliptical distribution can be thought to be an extension of the elliptical distributions that allow for varying tail parameters. We present a two-step random mechanism leading to this new type of distributions. In particular, this mechanism is derived from typical behavior of financial markets. We determine the densities of multitail elliptical distribution and introduce a function which we label the tail function to describe the tail behavior of these distributions. We apply multi-tail elliptical distributions to logarithmic returns of German stocks included in the DAX index. Our empirical results indicate that the multi-tail model significantly outperforms the classical elliptical model and the null hypothesis of homogeneous tail behavior can be rejected.
منابع مشابه
The Tail Mean-Variance Model and Extended Efficient Frontier
In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of r...
متن کاملCredit Risk Modelling and Estimation via Elliptical Copulae
Dependence modelling plays a crucial role within internal credit risk models. The theory of copulae, which describes the dependence structure between a multi-dimensional distribution function and the corresponding marginal distributions, provides useful tools for dependence modelling. The difficulty in employing copulae for internal credit risk models arises from the appropriate choice of a cop...
متن کاملMultivariate Extremes, Aggregation and Dependence in Elliptical Distributions∗ Henrik Hult and Filip Lindskog
In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the ta...
متن کاملMultivariate Extremes, Aggregation and Dependence in Elliptical Distributions
In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the ta...
متن کاملTail Conditional Expectations for Elliptical Distributions
Significant changes in the insurance and financial markets are giving increasing attention to the need for developing a standard framework for risk measurement. Recently, there has been growing interest among insurance and investment experts to focus on the use of a tail conditional expectation because it shares properties that are considered desirable and applicable in a variety of situations....
متن کامل