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

Table 3

The estimated parameters of the eight distributions and maximum log-likelihood for the filtered residuals from HSCEI’s log return; No. means number of parameters; Log-L. means value of maximum log-likelihood.

Model	No.	Parameters					Log-L.
Cauchy	2	μ; 0.0062	σ; 0.5493				−3531.5
Laplace	2	μ; −0.0073	σ; 0.2773				−3260.5
Normal	2	μ; 0.0024	σ; 0.9982				−3263.1
Student’s t	3	μ; 0.0089	σ; 0.8539	ν; 7.4987			−3220.7
Skew normal	3	μ; −0.0002	σ; 0.9978	α; −0.0006			−3262.3
Skew Cauchy	3	μ; −0.0032	σ; 0.5492	α; 0.0171			−3531.5
Skew Laplace	3	μ; −0.0118716	σ; 0.3788268	α; 0.4957863			−3260.3
Skew Student’s t	4	μ; 0.0715	σ; 0.9960	α; −0.0690	ν; 7.5439		−3219.9
Hyperbolic	4	μ; 0.0694	σ; 0.9938	α; −0.0671	β; 2.0951		−3221.1
NIG	4	μ; 0.0718	σ; 0.944	α; −0.0693	β; 2.3546		−3220.6
Variance gamma	4	μ; 0.0551	σ; 0.9938	α; −0.0527	λ; 2.7442		−3221.7
G. hyperbolic	5	μ; 0.0564	σ; 0.996	α; −0.0503	β; 2.205	λ; −1.7451	−3220.4