Skew Student-t Distribution
|
SfePCOMP |
NASCOMP |
JAPA500 |
MSACWFL | |
|
Location |
0.0062 |
0.0096 |
0.0013 |
0.0055 |
|
Scale |
0.0222 |
0.0357 |
0.0300 |
0.0196 |
|
Skewness |
0.8664 |
0.8506 |
0.9593 |
0.8593 |
|
Kurtosis |
5.4329 |
3.4153 |
4.5528 |
4.8423 |
|
LogLik |
2.fl79 |
2.0313 |
2.Ц60 |
2.5503 |
Skew Generalized Secant Hyperbolic Distribution
|
SfePCOMP |
NASCOMP |
JAPA500 |
MSACWFL | |
|
Location |
0.0061 |
0.0010 |
0.0011 |
0.0055 |
|
Scale |
0.0220 |
0.0334 |
0.0294 |
0.0193 |
|
Skewness |
0.8738 |
0.8440 |
0.9645 |
0.8599 |
|
Kurtosis |
-1.4014 |
-2.1752 |
-1.7483 |
-1.6308 |
|
LogLik |
2.fl60 |
2.0360 |
2.Ц77 |
2.5 f97 |
Skew Exponential Power Distribution
|
SfePCOMP |
NASCOMP |
JAPA500 |
MSACWFL | |
|
Location |
0.0065 |
0.0105 |
0.0020 |
0.0056 |
|
Scale |
0.0221 |
0.0330 |
0.0292 |
0.0193 |
|
Skewness |
0.8673 |
0.8416 |
0.9479 |
0.8571 |
|
Kurtosis |
0.6278 |
0.5358 |
0.6151 |
0.6166 |
|
LogLik |
24135 |
2.0332 |
2.1Ц6 |
2.5 f 67 |
5 Conclusions
In this paper we have studied the family of multivariate distributions by Koheler and
Smanowski in order to model financial returns and measure dependent risks. Fitting
the distribution to the returns of four market indices, the SfeP 500 Composite index
(SfePCOMP), the NASDAQ Composite index (NASCOMP), the NIKKEI 500 index
(JAPA500) and the MSCI AC World index (MSACWFL), with skewed Student t, gen-
eralized secant hyperbolic and generalized exponential power marginals, we have seen
that this distribution succeeds in properly interpreting the dependence structure of
data, apart from the marginals, introducing therefore some measures which can couple
the usual correlation indices in the interpretation of the strength of the link among
dependent risks. However, other important aspects of the distribution must be stud-
ied, for example the analysis of sensitivity of the parameters in presence of dependence
structures of higher order introduced by Koeheler and Symanovski (1995).
References
Ayebo, A. and Kozubowski, T.J. (2003): An Asymmetric Generalization of Gaus-
sian and Laplace Laws, Journal of Probability and Statistical Science, 1(2), 187—
210.
Caputo, A. (1998): Some Properties of the Family OfKoehler-Symanowski distribu-
tions. The Collaborative Research Center (SBF) 386, Discussion Paper No. 103,
University of Munich.
10
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