Modeling and Risk Analysis Using Parametric Distributions with an Application in Equity-Linked Securities

Table 6

The estimated parameters of the eight distributions and maximum log-likelihood for the filtered residuals from EURO STOXX 50’s log return.

Model	No.	Parameters					Log-L.
Cauchy	2	μ	σ				−3513.7
		0.0474	0.5384
Laplace	2	μ	σ				−3250.4
		0.0302	0.2817
Normal	2	μ	σ				−3258.3
		−0.0001	0.9959
Student’s t	3	μ	σ	ν			−3222.1
		0.0226	0.8485	7.1443
Skew normal	3	μ	σ	α			−3249.4
		−0.0079	0.9944	−0.0007
Skew Cauchy	3	μ	σ	α			−3511.5
		0.1279	0.5418	−0.1494
Skew Laplace	3	μ	σ	α			−3247.4
		0.103	0.3750	0.5332
Skew Student’s t	4	μ	σ	α	ν		−3216.1
		0.2383	0.9860	7.6407	−0.2387
Hyperbolic	4	μ	σ	α	β		−3213.6
		0.2168	0.9871	−0.2179	1.7874
NIG	4	μ	σ	α	β		−3214.2
		0.2274	0.9859	−0.2274	2.2103
Variance gamma	4	μ	σ	α	λ		−3213.1
		0.2052	0.9872	−0.2052	2.4650
G. hyperbolic	5	μ	σ	α	β	λ	−3213.1
		0.2072	0.9861	−0.2075	0.2689	2.4395