Pricing Equity-Indexed Annuities under Stochastic Interest Rates Using Copulas

Table 2

Point-to-point with term-end design and 15% cap rate for various interest rate volatilities.

			Decomposed approach						Unified approach
$\sigma$	${\sigma }_r(t)$	$C^I$	$C^U$	$C^D$	$C_{0.5}^{CJ}$	$C_2^{CJ}$	$C_{-0.1}^G$	$C_{0.3}^G$	$C^I$	$C^U$	$C^D$
3% Minimum guarantee on 90% premium
20%	0%	65.65	59.00	72.98	62.95	61.16	66.69	62.73	75.95	76.61	75.43
	4%	65.65	58.61	73.40	62.82	60.88	66.72	62.62	75.95	76.10	75.85
	8%	65.64	58.23	73.85	62.68	60.61	66.75	62.50	75.94	75.64	76.29
30%	0%	58.94	51.26	67.42	55.97	54.00	60.11	55.62	69.87	70.94	69.33
	4%	58.94	51.10	67.54	55.91	53.89	60.12	55.59	69.88	70.66	69.52
	8%	58.94	50.96	67.70	55.86	53.79	60.13	55.56	69.90	70.45	69.76
3% Minimum guarantee on 100% premium
20%	0%	45.20	41.85	48.58	44.00	43.18	45.69	43.78	54.60	54.93	54.10
	4%	45.19	41.44	49.07	43.87	42.89	45.72	43.66	54.60	54.35	54.63
	8%	45.17	41.03	49.56	43.73	42.59	45.74	43.52	54.59	53.80	55.16
30%	0%	34.25	30.86	37.78	33.12	32.34	34.73	32.87	43.20	43.99	42.60
	4%	34.25	30.63	38.04	33.06	32.19	34.75	32.81	43.20	43.46	42.96
	8%	34.25	30.40	38.31	32.99	32.04	34.77	32.74	43.21	42.97	43.45