Pricing Equity-Indexed Annuities under Stochastic Interest Rates Using Copulas

Table 1

Point-to-point with term-end 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%	62.17	56.27	68.58	59.94	58.38	63.08	59.59	70.28	69.98	70.05
	4%	62.17	55.85	69.17	59.79	58.07	63.12	59.46	70.27	69.40	70.64
	8%	62.15	55.44	69.75	59.63	57.75	63.15	59.31	70.25	68.83	71.23
30%	0%	48.95	43.20	55.15	47.02	45.63	49.79	46.54	55.46	55.14	55.25
	4%	48.95	42.93	55.54	46.93	45.43	49.82	46.45	55.45	54.74	55.68
	8%	48.94	42.66	55.93	46.83	45.23	49.85	46.37	55.45	54.35	56.11
3% Minimum guarantee on 100% premium
20%	0%	44.58	41.32	47.87	43.45	42.65	45.06	43.20	53.25	53.12	52.88
	4%	44.57	40.93	48.38	43.32	42.36	45.09	43.07	53.25	52.56	53.46
	8%	44.55	40.53	48.89	43.18	42.07	45.12	42.94	53.24	52.00	54.03
30%	0%	32.20	29.12	35.38	31.25	30.56	32.63	30.96	39.27	39.13	38.98
	4%	32.20	28.89	35.69	31.18	30.40	32.65	30.89	39.27	38.77	39.36
	8%	32.19	28.65	36.00	31.10	30.23	32.67	30.81	39.27	38.41	39.75