Pricing Equity-Indexed Annuities under Stochastic Interest Rates Using Copulas

Table 4

Annual reset with term-end point 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%	42.49	38.58	45.86	41.35	40.44	43.04	40.86	52.63	52.62	52.65
	4%	42.49	38.78	45.65	41.39	40.56	43.02	40.91	52.64	52.76	52.53
	8%	42.49	38.98	45.44	41.44	40.69	43.00	40.97	52.66	52.91	52.44
30%	0%	35.80	33.10	38.12	35.02	34.40	36.18	34.69	42.82	42.80	42.83
	4%	35.81	33.28	37.93	35.06	34.50	36.17	34.73	42.83	42.94	42.72
	8%	35.81	33.47	37.75	35.09	34.60	36.16	34.78	42.84	43.09	42.62
3% Minimum Guarantee on 100% Premium
20%	0%	35.42	33.93	37.69	35.04	34.71	35.62	34.82	47.46	47.45	47.35
	4%	35.42	33.92	37.73	35.03	34.70	35.62	34.82	47.46	47.36	47.46
	8%	35.41	33.90	37.77	35.02	34.69	35.61	34.81	47.47	47.28	47.60
30%	0%	30.40	27.60	32.72	29.73	29.17	30.75	29.36	39.41	39.45	39.34
	4%	30.40	27.63	32.66	29.74	29.19	30.75	29.37	39.42	39.45	39.36
	8%	30.40	27.67	32.62	29.75	29.22	30.74	29.38	39.43	39.48	39.40