Pricing Equity-Indexed Annuities under Stochastic Interest Rates Using Copulas

Table 3

Annual reset with term-end point design 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%	38.91	37.19	40.51	38.42	38.02	39.16	38.19	43.26	43.25	43.27
	4%	38.91	37.27	40.41	38.44	38.07	39.15	38.21	43.26	43.31	43.21
	8%	38.91	37.35	40.32	38.46	38.12	39.14	38.23	43.27	43.37	43.17
30%	0%	28.23	26.72	29.59	27.86	27.54	28.42	27.65	31.39	31.38	31.39
	4%	28.23	26.79	29.50	27.88	27.59	28.41	27.67	31.39	31.43	31.34
	8%	28.23	26.87	29.41	27.89	27.63	28.41	27.69	31.39	31.50	31.30
3% Minimum guarantee on 100% premium
20%	0%	35.42	33.93	36.74	35.04	34.71	35.62	34.82	40.59	40.57	40.55
	4%	35.42	33.92	36.76	35.03	34.70	35.62	34.82	40.59	40.52	40.60
	8%	35.41	33.90	36.77	35.02	34.69	35.61	34.81	40.59	40.49	40.66
30%	0%	25.19	23.87	26.36	24.91	24.65	25.35	24.71	28.89	28.86	28.87
	4%	25.19	23.88	26.34	24.91	24.66	25.35	24.72	28.89	28.85	28.89
	8%	25.19	23.89	26.32	24.91	24.67	25.34	24.72	28.90	28.85	28.91