Pricing Guaranteed Annuity Option with Surrender Rates Consideration

Transcription

1 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

2 Agenda Moivaion Inroducion Models Numerical Illusraions Summary

3 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

4 Moivaion (con.) Life annuiy Guaraneed annuiy opion Dynamic surrender model Fair pricing

5 Life annuiy due Life annuiy due y a 1 p 1i y y 0 Age(y) Annuiy purchase rae (APR) annuian insurer 1 a y ay

6 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

7 Guaranee annuiy opion Guaranee annuiy opion (GAO) APR ay T10 1 GAR ay T GAR Accumulaion period Guaranee Annuiy Rae (GAR) 0 T T+1 T+2

8 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 T T+1 T+2 Age y y+1 y

9 Surrender 1 ax T Surrender? GAR 0 T T+1 T+2

10 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 ) 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 P(65,65 ) A 65,65 exp B 65,65 r B65,65 = ˆ r 2e 1 e ˆ ˆ ˆ 2 r Time T T+1 T+2 Age y y+1 y

11 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

12 Surrender model (con.) Sandard Scenarios of AG 43

13 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, ITM -1 H Holding value a ime where, ITM F Accoun value a ime H?

14 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 ime age Conrac value Holding value Max F APR a, F GAR a r3 e p J q DB H 3 J 4

15 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 ime age Conrac value Holding value J3 F3 r2 H2 e p63 J3 q63 DB3

16 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 Premium amoun 1, 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.

17 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, Accumulaion period (T): Correlaion coefficien :-0.5, 0, Asse price volailiy : 0.1, 0.3, Iniial ineres rae :0.025, 0.05, Moraliy:Life able 100%, Life able 90%, Life able 80% 1 GAR, T 10, 0.3, r , q 100% s x life able 9 ˆ 0.014, 0.026, r 0.06 r 0 S

18 Single premium GAO Charge: 7% Scenarios SPA SPA(s) Raio 1/ % GAR 1/ % 1/ % % T % % % % % % S % % % r % % % 死亡率 % % SPA() s SPA Raio SPA Raio 1.86% ~ 3.87%

19 Single Premium GAO (con. 1)

20 Single Premium GAO (con. 2)

21 Single Premium GAO (con. 3)

22 Monhly Premium GAO Charge 12% Scenarios RPA RPA(s) Raio 1/ % GAR 1/ % 1/ % % T % % % % % % S % % % r % % % 死亡率 % % Raio 1.61% ~ 3.58%

23 Monhly Premium GAO (con.)

24 Single Premium GAO+GMDB Charge: 7% Scenarios SPAD SPAD(s) Raio 1/ % GAR 1/ % 1/ % % T % % % % % % S % % % r % % % 死亡率 % % Raio 1.42% ~ 4.23%

25 Single Premium GAO

26 Monhly premium GAO+GMDB Charge: 12% Scenarios RPAD RPAD(s) Raio 1/ % GAR 1/ % 1/ % % T % % % % % % S % % % r % % % 死亡率 % % Raio 1.60% ~ 2.83%

27 Monhly premium GAO+GMDB(Con.)

28 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

29 Thank you for your lisening!