Pricing Guaraneed Annuiy Opion wih Surrender Raes Consideraion Shing-Her Juang Deparmen of Financial Engineering & Acuarial Mahemaics, Soochow Universiy, Taiwan Shu-Chuan Chen Acuarial Deparmen, Bank Taiwan Life Insurance Chih-Hua Chiao Deparmen of Financial Engineering & Acuarial Mahemaics, Soochow Universiy, Taiwan Po-Kai Shen Produc Developmen & Managemen Deparmen, Nan Shan Life Insurance
Agenda Moivaion Inroducion Models Numerical Illusraions Summary
Moivaion Aging sociey Low birh rae, improving medical echnology, longer life expecancy Taiwan becomes an aged sociey in 2017 Economical safey is a major concern for older generaion Economic burden for younger generaion
Moivaion (con.) Life annuiy Guaraneed annuiy opion Dynamic surrender model Fair pricing
Life annuiy due Life annuiy due 1 1 1 y a 1 p 1i y y 0 Age(y) 0 1 2... Annuiy purchase rae (APR) annuian insurer 1 a y ay
Single premium deferred life annuiy Risk facors - Life able - Ineres rae Accumulaion period 1 ay T 0 Age (y) Age (y)+t T T+1 T+2
Guaranee annuiy opion Guaranee annuiy opion (GAO) APR 1000 1 1 100 ay T10 1 GAR 111 9 1 ay T GAR Accumulaion period Guaranee Annuiy Rae (GAR) 0 T T+1 T+2
Level premium Accumulaion period Benefi period c h a r g e Accoun Value c h a r g e c h a r g e c h a r g e F T E Cash inflow - Cash ouflow =0 Max F APR a, F GAR a T 65 T 65 1 F F GARMax a T T 65,0 GAR Liabiliy from GAO Time 0 1 2 T T+1 T+2 Age y y+1 y+2 65 66 67
Surrender 1 ax T Surrender? GAR 0 T T+1 T+2
Model Building Yang and Tang (2006) - Risk neural measure S: r: Asse price a ime ineres rae a ime 65 a 1 p P(65,65 ) 65 65 0 ds S rd QS, S dr ˆ ˆ r d r dw Qr, r QS, Qr, dw dw dw d ˆ 2 2 e A65,65 ˆ e 1 2 65 P(65,65 ) A 65,65 exp B 65,65 r B65,65 = ˆ 2 2 2 r 2e 1 e ˆ 1 2 2 ˆ ˆ 2 r Time 0 1 2 T T+1 T+2 Age y y+1 y+2 65 66 67
Surrender model AAA and Min 1, Max 0.5,11.25 ITM 1.1 Guaraneed value a ime : adjus coefficien, ITM = Accoun value a ime ITM Surrender rae l l base q Surrender rae a ime q Experience rae x x
Surrender model (con.) Sandard Scenarios of AG 43
Proposed surrender model During Surrender charge period w 0.05 if ITM 1 q 0.03 if ITM 1 Beyond surrender charge period w q Min 0.1, Max 0.02, 0.1-0.4 ITM -1 H Holding value a ime where, ITM F Accoun value a ime H?
Surrender ime If q w 3 3 Hold ile ime 4 H F 3 3 w 3 q vs.. 3 If q w 3 3 Surrender before ime 4 r r r r 0 1 2 3 ime 0 1 2 3 4 age 61 62 63 64 65 Conrac value Holding value Max F APR a, F GAR a 4 65 4 65 r3 e p J q DB 64 4 64 4 H 3 J 4
Surrender ime (con.) If q w 2 2 Hold ile ime 3 H F 2 2 w 2 q vs.. 2 If q w 2 2 Surrender before ime 3 r r r r 0 1 2 3 ime 0 1 2 3 4 age 61 62 63 64 65 Conrac value Holding value J3 F3 r2 H2 e p63 J3 q63 DB3
Assumpions - Gender:Male Numerical Illusraions - Premium pay:single premium, monhly premium - Accumulaion period:10, 15, 20 years - Premium Single premium:120,000 Monhly premium: - Annuiy dae:he 65 h BD Accumulaion period 10 15 20 Premium amoun 1,000 666 500 - Benefi: Surrender during accumulaion period, reurn he accoun value. Wih GMDB during accumulaion period, deah benefi = max(accoun value, oal premium) No GMDB during he accumulaion period, deah benefi = accoun value. Choice of APR or GAR a he annuiy dae.
Numerical Illusraions (con.) Assumpions - Life able:1997 Taiwan Insurer Annuiy Life Table - Fracion age assumpion:udd assumpion - Sandard scenario: - Ineres rae model:chang(2010) Scenarios: - GAR: 0.1, 0.111, 0.125 - Accumulaion period (T):10 15 20 - Correlaion coefficien :-0.5, 0, 0.5 - Asse price volailiy : 0.1, 0.3, 0.5 - Iniial ineres rae :0.025, 0.05, 0.075 - Moraliy:Life able 100%, Life able 90%, Life able 80% 1 GAR, T 10, 0.3, r 0 0.05, q 100% s x life able 9 ˆ 0.014, 0.026, r 0.06 r 0 S
Single premium GAO Charge: 7% Scenarios SPA SPA(s) Raio 1/10 0.0302 0.0293-3.10% GAR 1/9 0.0405 0.0394-2.63% 1/8 0.0532 0.0522-1.88% 10 0.0405 0.0394-2.63% T 15 0.0242 0.0237-2.10% 20 0.0157 0.0152-3.21% -0.5 0.0405 0.0394-2.63% 0 0.0310 0.0303-2.49% 0.5 0.0219 0.0213-2.79% 0.1 0.0341 0.0335-1.86% S 0.3 0.0405 0.0394-2.63% 0.5 0.0457 0.0439-3.87% 0.025 0.0518 0.0505-2.57% r 0 0.05 0.0405 0.0394-2.63% 0.075 0.0299 0.0294-1.58% 1 0.0405 0.0394-2.63% 死亡率 0.9 0.0446 0.0434-2.58% 0.8 0.0489 0.0477-2.39% SPA() s SPA Raio SPA Raio 1.86% ~ 3.87%
Single Premium GAO (con. 1)
Single Premium GAO (con. 2)
Single Premium GAO (con. 3)
Monhly Premium GAO Charge 12% Scenarios RPA RPA(s) Raio 1/10 0.0589 0.0577-1.98% GAR 1/9 0.0799 0.0785-1.80% 1/8 0.1067 0.1050-1.58% 10 0.0799 0.0785-1.80% T 15 0.0523 0.0510-2.57% 20 0.0373 0.0366-1.82% -0.5 0.0799 0.0785-1.80% 0 0.0713 0.0697-2.19% 0.5 0.0624 0.0607-2.70% 0.1 0.0742 0.0730-1.61% S 0.3 0.0799 0.0785-1.80% 0.5 0.0865 0.0834-3.58% 0.025 0.1118 0.1093-2.18% r 0 0.05 0.0799 0.0785-1.80% 0.075 0.0554 0.0542-2.20% 1 0.0799 0.0785-1.80% 死亡率 0.9 0.0881 0.0866-1.70% 0.8 0.0978 0.0957-2.22% Raio 1.61% ~ 3.58%
Monhly Premium GAO (con.)
Single Premium GAO+GMDB Charge: 7% Scenarios SPAD SPAD(s) Raio 1/10 0.0329 0.0322-2.15% GAR 1/9 0.0435 0.0422-2.91% 1/8 0.0559 0.0546-2.31% 10 0.0435 0.0422-2.91% T 15 0.0275 0.0268-2.56% 20 0.0189 0.0186-1.42% -0.5 0.0435 0.0422-2.91% 0 0.0342 0.0330-3.44% 0.5 0.0251 0.0244-2.74% 0.1 0.0356 0.0349-1.87% S 0.3 0.0435 0.0422-2.91% 0.5 0.0504 0.0492-2.31% 0.025 0.0557 0.0547-1.81% r 0 0.05 0.0435 0.0422-2.91% 0.075 0.0320 0.0313-1.95% 1 0.0435 0.0422-2.91% 死亡率 0.9 0.0475 0.0454-4.23% 0.8 0.0513 0.0504-1.69% Raio 1.42% ~ 4.23%
Single Premium GAO
Monhly premium GAO+GMDB Charge: 12% Scenarios RPAD RPAD(s) Raio 1/10 0.0628 0.0615-2.12% GAR 1/9 0.0838 0.0821-1.93% 1/8 0.1109 0.1090-1.76% 10 0.0838 0.0821-1.93% T 15 0.0569 0.0554-2.64% 20 0.0427 0.0420-1.60% -0.5 0.0838 0.0821-1.93% 0 0.0749 0.0733-2.18% 0.5 0.0659 0.0645-2.12% 0.1 0.0770 0.0758-1.62% S 0.3 0.0838 0.0821-1.93% 0.5 0.0914 0.0888-2.83% 0.025 0.1164 0.1145-1.61% r 0 0.05 0.0838 0.0821-1.93% 0.075 0.0585 0.0570-2.53% 1 0.0838 0.0821-1.93% 死亡率 0.9 0.0916 0.0894-2.39% 0.8 0.1000 0.0984-1.62% Raio 1.60% ~ 2.83%
Monhly premium GAO+GMDB(Con.)
Summary Single premium or monhly premium, GAO or GAO+GMDB - Guaranee cos m C GAR T S r 0 Moraliy - Guaranee cos reduced wih our surrender model
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