Evaluation of variable annuity guarantees with the effect of jumps in the asset price process

Figures & data

Figure 1. FBMKLCI index price.

Figure 2. DARSDSEI index price.

Figure 3. SPTXS index price.

Figure 4. S&P500 index price.

Figure 5. S&P500 index returns.

Figure 6. SPTXS index returns.

Figure 7. FBMKLCI index returns.

Figure 8. DARSDSEI index returns.

Table 1. Stock market mean returns and standard deviations

Index market	Mean return (%)	Standard deviation (%)
DARSDSEI (Tanzania)	3.2	1.8
FBMKLCI (Malaysia)	9.2	9.3
SPTXS (Canada)	17.6	12.7
S&P500 (USA)	17.6	12.1

Table 2. Malaysian mortality table

Attained age	Mortality rates		Attained age	Mortality rates
	Male	Female		Male	Female
45	0.00240	0.00126	63	0.01580	0.00829
46	0.00268	0.00140	64	0.01757	0.00926
47	0.00299	0.00155	65	0.01951	0.01033
48	0.00334	0.00172	66	0.02163	0.01151
49	0.00372	0.00191	67	0.02394	0.01280
50	0.00413	0.00212	68	0.02645	0.01421
51	0.00458	0.00235	69	0.02919	0.01575
52	0.00507	0.00260	70	0.03217	0.01743
53	0.00559	0.00288	71	0.03540	0.01927
54	0.00614	0.00319	72	0.03890	0.02126
55	0.00674	0.00355	73	0.04269	0.02344
56	0.00737	0.00397	74	0.04680	0.02580
57	0.00804	0.00444	75	0.05123	0.02836
58	0.00875	0.00499	76	0.05602	0.03114
59	0.01015	0.00522	77	0.06118	0.03414
60	0.01137	0.00588	78	0.06675	0.03740
61	0.01271	0.00660	79	0.07274	0.04091
62	0.01419	0.00741	80	0.07918	0.04471

Table 3. Canadian mortality table

Attained age	Mortality rates		Attained age	Mortality rates
	Male	Female		Male	Female
45	0.00148	0.00105	63	0.01028	0.00929
46	0.00162	0.00117	64	0.01160	0.01040
47	0.00178	0.00130	65	0.01304	0.01152
48	0.00196	0.00144	66	0.01462	0.01265
49	0.00216	0.00162	67	0.01632	0.01377
50	0.00238	0.00181	68	0.01816	0.01489
51	0.00263	0.00204	69	0.02013	0.01602
52	0.00291	0.00229	70	0.02225	0.01715
53	0.00323	0.00259	71	0.02450	0.01827
54	0.00359	0.00292	72	0.02691	0.01940
55	0.00400	0.00329	73	0.02946	0.02053
56	0.00445	0.00371	74	0.03216	0.02166
57	0.00498	0.00419	75	0.03501	0.02278
58	0.00558	0.00472	76	0.03802	0.02391
59	0.00626	0.00530	77	0.04119	0.02504
60	0.00705	0.00595	78	0.04453	0.02617
61	0.00801	0.00706	79	0.04802	0.02729
62	0.00908	0.00817	80	0.05169	0.02842

Table 4. Tanzania mortality table

Attained age	Mortality rates		Attained age	Mortality rates
	Male	Female		Male	Female
0–1	0.089699	0.080493	50–54	0.015640	0.013854
1–4	0.013899	0.013899	55–59	0.021106	0.014641
5–9	0.005855	0.005504	60–64	0.028290	0.020588
10–14	0.003131	0.003070	65–69	0.038868	0.032480
15–19	0.003682	0.003392	70–74	0.060049	0.052626
20–24	0.006069	0.006159	75–79	0.095084	0.084197
25–29	0.010988	0.015461	80–84	0.164111	0.147358
30–34	0.014279	0.016065	85–89	0.250214	0.223177
35–39	0.017673	0.016012	90–94	0.365264	0.320709
40–44	0.016207	0.012830	95–99	0.511382	0.441152
45–49	0.015416	0.013037	100+	0.660961	0.582228

Table 5. Calibrated diffusion model parameters

Index	μ	σ	g
DARSDSEI (Tanzania)	0.032045	0.018269	0.027550
FBMKLCI (Malaysia)	0.092161	0.093089	0.046061
SPTXS (Canada)	0.176643	0.126744	0.088322
S&P500 (USA)	0.175795	0.121167	0.087898

Table 6. Calibrated jump-diffusion model parameters

Index	μ	σ	λ	μJ	σJ	g
DARSDSEI (Tanzania)	0.032231	0.018257	66.208454	0.000905	0.019716	0.027718
FBMKLCI (Malaysia)	0.092041	0.093049	11.114209	−0.003253	0.032613	0.046020
SPTXS (Canada)	0.177217	0.126589	19.595428	−0.005650	0.034590	0.088609
S&P500 (USA)	0.175513	0.121152	30.078617	−0.003544	0.031558	0.087757

Figure 9. M&E fee for Malaysian male annuitants for different volatility models.

Figure 10. M&E fee for Malaysian female annuitants for different volatility models.

Figure 11. M&E fee for male annuitants in Malaysian stock market.

Figure 12. M&E fee for female annuitants in Malaysian stock market.

Figure 13. M&E fee for Malaysian male annuitants in various stock market.

Figure 14. M&E fee for Malaysian female annuitants in various stock market.

Figure 15. M&E fee for Canadian male annuitants in various stock market.

Figure 16. M&E fee for Canadian female annuitants in various stock market.