TY - JOUR
T1 - Multi-tail generalized elliptical distributions for asset returns
AU - Kring, Sebastian
AU - Rachev, Svetlozar T.
AU - Höchstötter, Markus
AU - Fabozzi, Frank J.
AU - Bianchi, Michele Leonardo
PY - 2009
Y1 - 2009
N2 - In the study of asset returns, the preponderance of empirical evidence finds that return distributions are not normally distributed. Despite this evidence, non-normal multivariate modelling of asset returns does not appear to play an important role in asset management or risk management because of the complexity of estimating multivariate non-normal distributions from market return data. In this paper, we present a new subclass of generalized elliptical distributions for asset returns that is sufficiently user friendly, so that it can be utilized by asset managers and risk managers for modelling multivariate non-normal distributions of asset returns. For the distribution we present, which we call the multi-tail generalized elliptical distribution, we (1) derive the densities using results of the theory of generalized elliptical distributions and (2) introduce a function, which we label the tail function, to describe their tail behaviour. We test the model on German stock returns and find that (1) the multi-tail model introduced in the paper significantly outperforms the classical elliptical model and (2) the hypothesis of homogeneous tail behaviour can be rejected.
AB - In the study of asset returns, the preponderance of empirical evidence finds that return distributions are not normally distributed. Despite this evidence, non-normal multivariate modelling of asset returns does not appear to play an important role in asset management or risk management because of the complexity of estimating multivariate non-normal distributions from market return data. In this paper, we present a new subclass of generalized elliptical distributions for asset returns that is sufficiently user friendly, so that it can be utilized by asset managers and risk managers for modelling multivariate non-normal distributions of asset returns. For the distribution we present, which we call the multi-tail generalized elliptical distribution, we (1) derive the densities using results of the theory of generalized elliptical distributions and (2) introduce a function, which we label the tail function, to describe their tail behaviour. We test the model on German stock returns and find that (1) the multi-tail model introduced in the paper significantly outperforms the classical elliptical model and (2) the hypothesis of homogeneous tail behaviour can be rejected.
KW - Generalized elliptical distributions
KW - Likelihood ratio test
KW - Risk management
KW - Varying-tail parameter
KW - t-Distributions
KW - α-Stable distributions
UR - http://www.scopus.com/inward/record.url?scp=68149157171&partnerID=8YFLogxK
U2 - 10.1111/j.1368-423X.2009.00290.x
DO - 10.1111/j.1368-423X.2009.00290.x
M3 - Article
AN - SCOPUS:68149157171
SN - 1368-4221
VL - 12
SP - 272
EP - 291
JO - Econometrics Journal
JF - Econometrics Journal
IS - 2
ER -