Estimation of Tail Risk and Moments Using Option Prices with a Novel Pricing Model under a Distorted Lognormal Distribution

Table 3

Descriptive statistics of and .

T	Call (m)						Put ()
	Max	Min	Mean	Std	Skewness	Kurtosis	Max	Min	Mean	Std	Skewness	Kurtosis
0.03	5.15	−0.51	−0.17	0.58	5.46	39.50	−0.27	−71.41	−10.4	11.5	−2.02	8.69
0.1	4.82	−0.65	−0.17	0.54	6.99	56.60	−0.09	−48.17	−4.79	6.64	−3.09	15.90
0.2	0.30	−0.67	−0.21	0.17	−1.48	4.78	−0.05	−24.93	−3.34	4.34	−2.37	9.67
0.28	1.55	−0.66	−0.16	0.33	2.79	15.12	−0.06	−9.05	−2.62	2.65	−0.80	2.41
0.35	3.11	−0.66	−0.01	0.63	3.28	14.05	−0.08	−24.90	−4.01	4.98	−1.84	6.79
0.6	1.17	−0.62	−0.14	0.25	2.30	14.18	−0.11	−18.97	−3.02	3.70	−1.95	7.40
0.85	0.65	−0.54	−0.16	0.15	0.87	11.16	−0.13	−24.92	−3.30	4.22	−2.47	10.97
0.95	1.32	−0.58	−0.11	0.29	3.21	15.62	−0.15	−23.90	−3.01	4.04	−2.58	11.36
1.35	0.02	−0.48	−0.14	0.12	−0.71	3.47	−0.17	−19.52	−2.55	3.29	−2.82	12.63
1.87	0.03	−0.37	−0.13	0.10	0.01	1.74	−0.19	−16.26	−2.41	2.82	−2.43	10.20
2.87	0.02	−0.31	−0.13	0.11	−0.23	1.60	−0.27	−12.72	−1.84	2.04	−2.87	13.29