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

Table 8

Kolmogorov–Smirnov test statistics and its values.

	HSCEI	KOSPI 200	S&P 500	EURO STOXX 50
Cauchy
Statistic	0.4404	0.3197	0.2891	0.3382
p value	≤0.0000	≤0.0000	≤0.0000	≤0.0000
Laplace
Statistic	0.2162	0.1999	0.1836	0.2035
p value	≤0.0000	≤0.0000	≤0.0000	≤0.0000
Normal
Statistic	0.0316	0.0471	0.0547	0.0471
p value	0.0192	≤0.0000	≤0.0000	≤0.0000
Student’s t
Statistic	0.0128	0.0306	0.0391	0.0304
p value	0.8344	0.0262	0.0016	0.0270
Skew normal
Statistic	0.0308	0.0352	0.0460	0.0370
p value	0.0241	0.0063	0.0001	0.0034
Skew Cauchy
Statistic	0.0654	0.0667	0.0579	0.0642
p value	≤0.0000	≤0.0000	≤0.0000	≤0.0000
Skew Laplace
Statistic	0.0381	0.0315	0.0201	0.0319
p value	0.0023	0.0201	0.3013	0.0178
Skew Student’s t
Statistic	0.0116	0.0143	0.0173	0.0184
p value	0.7244	0.7244	0.4871	0.4080
Hyperbolic
Statistic	0.0132	0.0121	0.0102	0.0137
p value	0.8060	0.8895	0.9674	0.7745
NIG
Statistic	0.0371	0.1463	0.1237	0.1122
p value	0.0034	≤0.0000	≤0.0000	≤0.0000
Variance gamma
Statistic	0.0136	0.0121	0.0090	0.0130
p value	0.7821	0.8791	0.9914	0.8225
G. hyperbolic
Statistic	0.0114	0.0121	0.0092	0.013
p value	0.9221	0.8808	0.9879	0.8257