Gram-Charlier Processes and Applications to Option Pricing

Table 1

Comparison of ratchet option values computed with the Black-Scholes formula and Gram-Charlier distributions. Rows A to F are based on the four-parameter GC , while row G is based on a six-parameter GC .

									B-E	%		%		%
A	−0.0042	0.1685	0	0	0	0	0	0	0.419	0	109.26	0	100.00	0
B	−0.0035	0.1685	0	0	−0.1150	0.0360	−0.6898	0.8634	0.443	5.5	107.60	−1.5	98.92	−1.1
C	−0.0034	0.1685	0	0	−0.1749	0.1021	−1.0493	2.4508	0.478	13.9	105.42	−3.5	97.50	−2.5
D	−0.0051	0.1685	0	0	0.1749	0.1021	1.0493	2.4508	0.446	6.3	107.39	−1.7	98.78	−1.2
E	−0.0043	0.1685	0	0	0	0.1667	0	4.0000	0.493	17.5	104.59	−4.3	96.96	−3.0
									B-E	%		%		%
F	0.0027	0.1595	0	0	0	.0	0	0	0.441	0	107.69	0	100.00	0
G	0.0451	0.1595	−.3054	.09542	−0.12384	0.06120	−0.5437	0.5091	0.438	−0.7	107.90	0.2	100.14	0.14