勞退新制下個人帳戶與年金保險制最適轉換時點與轉換價值分析

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(1)Journal of Financial Studies Vol.] 5 No.1 April 2007. *~~MT.A~PM.~~~~M~~#.*D .#~~1l1A 11'-~1T. Analysis of Swi~ch Option under New Labor Pension Plan. Ii1Jt'. Jennifer L. Wang. .fIt~;t.". Sharon S.Yang. -.w.t''''. H.C. Huang *,.j:.J;i;..... Yung-Tsung Lee (Received: Nov. 30,2005; First Revision: March 15,2006; Second Revision: April 10,2006; Accepted: April 14, 2006). ~. *. ft~*1.#*~4._~.*#~.M.#*~#~ •• aff~4~~#~.A4~ •• ~·~. ~.* •• ~~.~T'~~*1~.A.~tiA.*G~~~M.~.~.,.~~~ti4.~L~ ~~,.t*1~~~.~~~~*MAa.C~T~.~4~a*fu ••#*~.·~;t..~~.*. G.~T.~ •• ~.4~~#ti#.~~n.* •• 'M*•• ti~~ •• tiM~.~*1- ••4. ~ •• tiA~ro4~~#ti~ •• ~~.·*;t..~*1~.A.~tiT~.~.*G.ti~ •• ~. *~,~~#~.ti4 ••• #M~~ •• ·~RM ••a*1•• ~ ••* •• ~A.A.~ti~a .:mAlltJf..l.JI.*~.~ ~4*~ ,1t~~i!l&~ ••~4iti'Jl'fiM9:.Jil..AJffJu.#M~~ ~ ~ .. ••. ~M.:*1.#*ti4·~~~#.·~~ •• ~·.A.~~·.*G.·~.~. Abstract Recent pension reform in Taiwan has changed our Labor Pension Plan from defined benefit plan into defined contribution plan. To mitigate the risks under defined contribution plan, this paper develops a theoretical framework to analyze the switch option design between Individual Retirement Account and Annuity Insurance Plan under new Labor Pension Plan. We estimate the optimal timing to exercise the switch option and calculate the increase in the retirement wealth after employees switch their pension plan choice. Our research results show if employees were to exercise the switch option optimally, the switch option design could help to increase the retirement wealth and decrease investment risk under new Labor Pension Plan. Keyword: Labor Pension Plan, defined benefit plan, defined contribution, Individual Retirement Account, Annuity Insurance Plan, option. • I/jLit~€r*"Jil..i'nt"~i'Jtttt. (Corresponding author) ,(t;ll:.iJi;t.J..1i4B,f]J3..::..$1 64 ft(NO.64, Sec.2, ZhiNan Rd., Wenshan District, Taipei City, 11605, Taiwan) , E-mail: [email protected] • Tel:+886-2-29393091 ext.81235 • " t.~*"illimit"~;'Jtttt, (t;ll:.iJi.l'Ii~t-ll 56 ft(N0.56, Kueiyang St., Sec I, Taipei City, Taiwan) , E-mail: [email protected] ' Tel:+886-2-231Il531 ext.3627 • ... IIjLiti€r*"Jil..'i'nt"~.Qbnttttt ' t;!l:.iJi;t.J..1i4B,f]J3..::..a 64 ft(NO.64, Sec.2, ZhiNan Rd., Wenshan District, Taipei City, 11605, Taiwan) , E-mail: [email protected] ' Tel:+886-2-29393091 ext.81214· ...·11 jLiti€r *"Jil..'i'nt" ~ if±.~R1.' t;ll:. iJi;t. J..16AB ,f]J3..::..& 64 ft(NO.64, Sec.2, ZhiNan Rd., Wenshan District, Taipei City, 11605, Taiwan) , E-mail: [email protected] ' TeI:+886-2-29393091 ext.81046 •.

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(10) 10. Journal of Financial Studies Vol.l5 No.1. Lachance, Mitchell. ~. Smetters. April 2007. (2003) ,J:J..&.. Milevsky. ~. Promislow. , 1G-1I"j~Jl:I:.#t .H~1t~4~~#.JJ.@]l!.:ff* (Buy-Back Option) AA"'ifiJ~ , Jl:1:..$l!p ~**~~~~4Jttt~~T~ • • M~*._.44Jt~#~.o.@] l!.:ff.~~- • • ~4~tt~~*.~~~.~~~~t~,~~#.@] • • ~Q*.~.@]4Jt~#~*.~~o~.@] • • ~Q~-Jt¥~(~m A~e~+~) .~_~~'t~~4~tt~.1T1*P tf{/.]J:lA-'£Mli 't.~. (2004) it;\::A;t.ili 1iJ4~tt~-$tJf.t.@]4Jt~-ft.JJ:t.l!.:ff*.$ 0. 0. ®~~*4~~~~ifiJ.M~'.~~ffi~~*:t.._ff.l!.:ff.·.@]. l!.:ff.~~.~4m4Jttt~~**~#~.~4Jt~#{/.]**~#~~. {/.]. tf {/.] J: lA-f.t.~.fo~.@]1•• (efft~ DC(t)- P{t») it{/.] X ~ 11!!~.~ -~l!.:ff* ~ P]~ Margrabe's (1 978)PiTtt ili {/']l!.:ff~l.$ t ~ ~A.@]l!.:ff.tf'~*.x.{/'].A~~&~~{/.]~ •• 1t,.~.~ ~t~D~~_ffl!.:ff*{/.]~Jt'.~~.~ •• A{/.] ••• 1t~.*_ff J:.4Jttt~~P. 0. l!.:ff.{/'].~~~.~ffi¥~~*~D*.~.o ~T~.-~. •••. @]l!.:ff.PiTA~{/.].1t'a-1l"j#.T~ ••••. • @]l!.:ff•• 1t~ * •• ®*~~~T: , - ,. i!*~#.~~.@]l!.:ff*1.1t. 'DB{t)f(.*- t a:fJ5J:.,J:J..~iJf*.&.Jlfl;fi1!=1t Jf. ili {/']4~~1tltt1~*.~-ftJJt1t · 'Jl'l!p DB{t)~. ~~*J:lA-~# .l;fiJJt1t (Accumulated Benefit Obligation, ABO) P];fl.~ • DC(t)ft.*-~ t ~DJ:.t4~tt~~~tftt~4*.&.a.~~{/'].J: ••1t'ift.*-4Jttt ~~~tf{/.] • •a •• ~o~ 1~~4Jt_#~~~4Jttt~~~{/'].M 1rH~.~~~D t=0 ~.,4.m. 0. i!*~#~.;fi1!=-.{/']~.I·~ft~.;fi1!=-.{/'].Mt4Jttt~~~{/.]. ••• ~.~~*~M'~~4 ~_#ttl1 tf _#tt J. ~ ~ {/.];it tiAt j:{backloaded)# 'jf IS '-fit. ~. @]l!.:ff.. ~*-#.1t_~4Jt_##~:~ifiJ' ~~J!.~.1t0.

(11) II. Journal of Financial Studies Vol.l5 No.1 April 2007. i! #. J€t #. ~;t J€t# -$Hfi $I i! #.J€t#. E[DB(T)]. $I. E[DC(T)]. ti. --- --. _______ -------1----------- ----o. III .::... '. ,,. ~ ;t t{ :I~UHfi jlJl i! #.J€t.ft. Y.. I. 1. :2. J. 4. 5. IS. 7. 8. '). 10 11. 12. n. 14. lS 16 17 18 )9 20 21. 22. :n. 14 2~ 16 27 28 29 30 31. J1. , ,,. ,,. 13 14 ]~. hi ft~1t;,M ahi ft~Ai;'Mttt'l hi1*~1t $tJJ!l~1f- 'i .t:.n~ if. III. hiftjf;1tAA-@1~:f3.. hiftjf;NAA-@11Jt:f3.-P(t).t:.tt .JJ:.:f~ 't~hi Jtjf;NififF ;f:;.*i!1*jf;N1£ t *.~I ••• ~*·1£ •• ~&*.L~~~NAA-@1.:f3.*.*.@1hi ftjf;Ni!1*~~~O~ •• L~hift •• ~P •• ~~~~.hift.NAA @1~:f3.'.Lm~~~~A~'i~~.~~~.~;~ •• L~hift •• ~P • • ~~~.hiJt~NAA-@1.:f3.POO'm1£ •••• L~~~~ DC(t)-P(t)~ i! 1*~ 0. ~. ,. ~1T. AA- @1 UHf:ffi.t:. f,} t!. a~ •• Ll£i!1*.~1T.~~~1T •• :ffiffl~~~i!1*.N •• ~. ~~*2·1£~~~1T •• :ffi~~~~'.Ll£i!1**(*M.T)ffl~~ ~i!1*.1t1•• ~hift ••"1.t:.1*P •• ' I!p DC(T)· :f~1t~ , 1£. L~1T. •• :ffi~~~~'.L1£i!1**ffl~~~ ••N~.M~~1T*Mt~. it L ~~.l'lhiJt.1t"*'l.t:.i!1*.N ' I!p DB(R) , /]tIJ:.hiJt••1*P • •• hiftjf;NAA-@1~:f3.4.~*~~·.~~4.~.A£.4~ •• · ~A~~.~t*.~R*.'S ••hift• •~~~a'i.~i •• ~~ • • 1!1~ • • L1£ t<R *.I.!;~1Tl!.:ffi * ' 1i!!.3t~ ~l!~l!.:ffi>t ~ A~ pq (in the money) 41.1!- (outthemoney) AT*5~l!-iV1t~AA-@1lJ!. 0. •. 0. :ffi'a~.ft1£~.*M.t'.L~.+ffl~~~.M~i!1*ffl.'i.' j:~:f.iA1t.'Jr~~.~;t ~*i~ ft"-~ ~ .J.~1TAA-@1l!.:ffi. '. t~a1iif*.~.

(12) 12. Journal of Financial Studies Vol.15 No.1 April 2007. i!#'~1t1J:. 1.i. l!!=J '. tJtAt ~ @J l! ~ *fl. :f: tJtAt ~ @J .i! ~ *fl. OB(T)+[OC(t)-P(t)]( 1+i)R-t. OC(T). J!4 @J .i!~*fl J& 1&tJt..ftllif M .ar~*I~tJt.ff~@Jl!~.~.1&*M·~.al~ • • • ~~~. • • • *~~.1&tJt.ff~Mo.- • • • *~I~~t*~tJt.ffl!~.*ffl .*~M~~1.i* ~~~tJt.ffl!~.~ffl.*~M~.1.i·.~ • • • *~ I ~~i!;-~i"1 tl:! ~ $.-ft!:.tJt.ff*MJ'!; t*>t ,~~g;*M .'l'!;J:[email protected]!~ • • • ~.~~~M~1.io!~a~~ffl~~~~~*~r: r. = min{t~R:. $.- tp. Et(BB(t»> Et (OC) and Et(BB(t»> EtCBB(t*», 'II t*>t}. Et(BB(t*)=E[OB(T)+[OC(t*)-P(t*)]( 1+il-t·\Ft)]. Ji Et (OC)=E[OC(T) 1Ft]. ... ~~~.~~.~'*~~~~ AMP~_.*~~~T~i!#' *1 • • ~~&" ~~~M~.~'~~fflM • • •a*fu~.*'. ••. • • tl:!.~~.AMP~T".L.*~~~~ • • • • *~.'_.~ ~tJt.ffi!#'*.4.l!~*fl1lffl A~"4.~1.i~*+. 0.

(13) Journal of Financial Studies Vol. 15 No.1 April 2007. 13. ~l~~~~~£~#~~~*~.~'*X~~ffl~*~~*~~ ~~~*~~~~A~?~'~~~~W~~~~#~~~*~~~'~ Jl:f:~*~1*1Jil~lWl~aJ/RA~ #~@HIJA~?~l~.ItVl.. 200. AJ-:t.J:..~m..l' jt~~~w~*f,(.~.1.j1j.. 0. - , ~#.*M'i" ltt~~~lt~ *btf-1E ~ ~~ 1!.! lt~~ i!~ ~ (Continuous) 'iF1 tt T '. **. ~ ~ ~ ~ ~ 'f ~~' •• $~a'm~~.W4~$~g'~*f,(.~~~~fm$~LD ~~.~A~?~.~.f,(.~~~~~£A~*~aW.~.~a~~f m$T '~II1-M.J.5k~~A~?~ (DCt ) I .~.i~fk.1~lft#J) (INS,) ~M'i"lft.a~~~~~T~A~~~:. DC". r r. ei(k-t)aIoe gt dt. :=. INSk :=. (1). ,. (1- L)ej("-t)aIoegt dt. (2). Atiaj~~_~~A~?~T.~ •• ~~T~m~~aW&h (ForceofInterest)' e.f.t~.t~W.~$~tt~~J-:t.i!~:fi~1~;;7A D. *M-(l)Aa(2)Att~1t.AA1i~j;).~4~A(3)a(4) DC,. al0. ( ell' _e'k) =__. (3). g-l. alo(l-.L) (e sk INS. =. 1. g- ]. _elk). .. a/o(l- L)(kesk). '~T:. ifg,;:j. (4). if g==j. ~~~f,(.~~T'**~~~#.~~lttM~tll1-'ffl~~~~~? •• '~~'~lttMII1-'~A.?~*f,(.~~~.~~~,~~~ .i!~.~~.~*~~l.M~M'i"'M~.~~.~~~~f,(.~~~ ~.M~tt~.~A~?~~~~'*btf-1E~~~.~~~tt~~~~4.

(14) 14. Journal ofFinancial Studies Vol. 15 No.1 April 2007. A~4~.#.~~~U fJi~;fIJ$tAlii..*'. ••. tA•. .J.t:.~)lIJ. .J.~U • •1;'iHk.:t...#.U16. ~*'. '~~'. •• L~~_'~.~P. ...•. (Equivalence Principle) ~"$*1t. 0. ••• ~ ••• ~ •••• '*~~M~.~.A~P~ ••. ..._.. ..... o._M.k.A••. A.~~~~~.~~~A' ~'~~~~.~.L. ••. L._M.k •.. ........ A~P~.A.~~~. ~~~~T.~~~. ..... AM.~.~.~7,t.A~P~~.U~~.~ •• '~~ili~_~ •. •. ~I. •• A~PtJ.~~~'~*.A~P~~.U.~.~ •• '. ~~~.L.~.~. M.TJ •. '.~~_. .:t..M$~aA ••• ~~T.:t..M$~~.A~P~t • • ~&. .M~~ • •. *jF , )1IJ. '~~'.L~_~. ~~~.'.L~~~M$*~~W. WT (k) -- INST +(DCk -INSk )*ei(T-t) . (5). a 11"1 tA• • • .:t...4~. it f;t. $( V (k) )'f'(.*.4~~J li~t • LM. 91-~ /;a T. ~~~Ma • • A~ ~(6). •• ~4TM$.it.:t..~it'M~ • • ~~~A~~. : (6). =- ' :l:.i!.4~ _ ra, .:t..;ff! !J. .t.L.•... ~~~_M. ..... ~4~.*fu~~~ • •. #.. it' ~Jtt. • .Ma.*1t.~~)lllT • :l:.i!.4._ra' .... i.~1f1+A • • 1~. 16 . ilUUtJ.::til:1f.fl-lA'161JJt$' xHf.:t.~;fiiJil<ft T lJ'-i!#-' i!#-q.:ot.iJil< ... .fIitltINSr ' .(Ht~fl1i r ' i!#-4t:lJ'--ar4Ul:ot.lJ'--t-AiU (Ii NS ) ttJ.*"r :. It-.,, a..r .\.{£.lt~fl1ir 4t:lJ'-"'lfll"'~lJ'--t-:ot." J.J.tit •. 11. 111 A+ll' +J .... AlJ'--t-iJf."~....I6IJ 1IItI!l.fl*3-Jt$.~t.r iPJI/f~ P(t)6IJJt$'.{£. k q.J6....*lq. P(k) = lNS(k),.

(15) Journal of Financial Studies VoLt 5 No.1 April 2007. -1l~JT ~M 'SWr(k) ft~M{tt-:.x~;t{t-t-:j\..~~. ~OCT' • • ~.*'. ••. ·. 15. Jl.,::,:,X~;t+~~{fJ. *.~M{fJ._~T;. -;.x~;t{fJ.{~ : -t-dWr(k) =0. die. , _dINS, )e,(r-ll -(oc, (dOC dk dk. dWr(k) dk. M~~(3)&'(4H~A(7)~,. INS. )ie,(T-». (7). }llJ. dWr(k)=(aIO(gest_Ml) aloO L)(gest_jei'»)e;tr.ll dk g-l g-}. -r. alo (est -e") aIo(l-L) (est _ei'»)ie,(T-ll. ,g-I. :j\. tp. g-}. , dINSk = a1o{l- L)(eft' + jkeJk ). -t-1}i{.(8).~ (l! p dWr(k);:O). '. }lIJ'if*-*Jjk.*~~~M.J.!;k· '~T:. dk I. k =-.-Iog( }-g. k'. if g = j. dk. . !. (8). i- j+L'(g-i). . . »0 (I-L)'(I-}). L. (I-L)(j-i). if(i-j+L.(g-i»<Oandj~g. if. I. (9). .. g=}. ~~~.A~PM&..*~~MT'*~ • • • A~PM*A.*. ~M{fJ~ • • ~*~.*.~M{fJaf.M.'if.*~.A~P~'~ ~I:. ' 1}~(9)18{fJ *-Ni-{t;f--f~*~ i < j {fJ·m-vt ' Ia.J ~ , JIH htt t L {fJ fUll ~. /fl.. 0-1 ~r.., 19 m*~.t.;t{fJ* ' *b1f1L{fJ*.-1l~'J*1tl.t4~*~ifH*-{fJM'S~ *-fI:.T' ~~, • • **.~:r6"'-i-1.~'f.A~f'~1{fJ!t;tA*~~@11.~ 0. ~ .~KM.~~·#~~.~.A#~*~~~m~.· •• ~ •••• ~ ••• ~.*e.~M. IIl.J . l!lJlt.{I.ot1tl!!l • • {t~#: (lock in) filJPU1T' iHt1.:ai!#!l*r., (k'H.~4~'It1B'M .;a#!l*r.,•• ~ 4·. H••.. w • • • • • ~' • • ¥~~~~M.'~.M.~: l.bit: '~.~·fHlll!~.'~1i.~'. .'~M.~+ •• :'~.~~~lI!~.'~A'1i.~'. .'~~ ••+1i.•• :'~.~~~lI!~.'~~.1i.~'. .'~Mjl¥;+1i..*: '~.~~~lI!~.'~+-%'.

(16) 16. Journal of Financial Studies Vol.15 No.1 April 2007. ~'~ttka'.~~.A~P~.~.~.~ ~. >'/- '. ~~t~1}~(9).i!:..M-~M1'~.k.1t;r. raH\t;:..:;;:'1ltt~. ,. ;:..:;;:'1ltt~+~. 0 ~1if-1t-J(or. •• ~~OCM~.*~o. ' a1l"1l1!-3VJlfWr (k). 1t~. :. -J(o-* g:t-j • M. (i). d'WT(k) =~(dWd~)<o. dk' dk dk. (10). ~(g_i)_.!:L(i_g)'}eg. +~~((i- j)'eP)<O g-). ~. ~. (. 0 - g)(j . g-}. i+ Li - Lg)} (g_j)'. e. g-j. 1- L (. j-g. ')'. <-l-}. k' > _I_log (_<!.-=-~'2(i j)' } • g- j (g-I)(j-i+Li-Lg). if g > i. .. k =k . g:5.i. -. j. if. (ii) -J(o -* g = j , JlIJ k' >. ;tR:Jll1}~(9). ,. ,. (1- 2L) (1- L)(i j). (11). 1}~(10).& 1}~(l1) l:i!!.ft.~~~M k' ~M-. '. 1\A/~~(5). '&1}~~'M~*~.ft. • • •.&.ft.• • • ~.·.~aS~k·.*~~ ~ • •#.r·l:i!!.ft..~M.l:i!!n • • • ~ • • ~~W.M.'Mf J£i&.:.t).'&lf-1i.-1*~j!jt:lJuf!fl. (i,j,g,L ) ~%!f.. '. r1iJ~~fU~-M;.:L1'flf. ~~~~lf-~~%¥,m~'a1l"1Jlf~r-&l1!rr~~¥~.~. ~T~.~.M-.rr.~.~r~n. •• ~~·. •••••• '*~# • • A~. P.1r{~W.M. (i) ~~M '.L-A.&lf-*i'f-~.1r{~W.lIII. (j) ~R1:1Ju.

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(18) Journal of Financial Studies Vol. 15 No.1 April 2007. 18. (i=3%,j=4%, g=2%). I ---"-"_. I. 0,12. ----~-.. 0,10. .... L=0,05 L=0,1 L=0.15. ~8 1i. ~t.. 4"06 M_" , _ ,. w. ~.. _. ~"_. 0,04. ~. - ~-'-. ~. .. 0,02 0.0. 30. 35. 40. 45. 50. 60. 55. "'~Jf-it. !Il2. *,,~1f-~~*"~1.1t ~t.!f. U~.~IUIIl1:~~. 1%). I. ~*'A~.-~~ • • A~~~~1f-.~~~~1:~.A~2%_~. ·tfvt, {rl~1~A~~1Ii'J~1f-.{*~1Ii'J~4~f~IUIIl!f.1t)}'j~ 3%a 5%_ ~ ~ • • 'A~.*,,~1f-~~*,,~.1t~!f.~M.A~~!Il3'~~M*. ~·~1f-.~~~~af • • !f..~'*L.*"A1f-.~~~~A.~*" ~_M • • • '~_A.~*,,~.1t~!f.~ • • ~o~.!Il2a!ll3'~m ~tffl!f.~%~*~'A.~*,,~_M.~35 • • • ~31.'A.*,,~ 1t1t~t.!f.~ 12%.~!tJ 33%E.ti ; j:).m~t ffl!f.~ lO%~·tfit. ' A.~*" ~_M.~ 40 • • •!,j35. ' A.*"~.1t~t.!f.~ 8%.~!tj28%E.ti ; j:).m~t ffl!f.~ 15%~'tfit. ' A.~*,,:i~_rll'.~ 45 • • •!tj37 • ' *" 0. ~1t1t~!f.,f:t 12%.~!tJ. 20%E.ti. Q.

(19) Journal ofFinancial Studies Vol. 15 No.1 April 2007. 19. (i=3%,j=5%, g=2%). 0.30 0.25. L=O.05 L=0.1 L=0.15. "". I. 0.20. .... ~. fJ 11i. 0.15. ~. $. 0.10 0.05. 0.0 30. 35. 40. 45. 60. 55. 50. .... ~1f-i» ~3. ••••••••• ~.(ft •• ~.AA2%). ::""~J.!J.t~* ~.*~ffl~~~~~~*'~~.~*M~~~~J.tT~ft •• ~. . ' ••4*.na••• ~~~ffi~tm.~M'~~.~ ••• *m ~M~~it~i,j,g,L. •. ~. 0. tt;jf~~it5tX.:f.}.T 'ffl~ff'J:l~. ••*.rJ;' •. •••••• ~.~~J.!J.t~#t~~T:. (-)• •1*,~*1~;fi • • ~.. U). ~l}~. ••• &~~~ • • ~ • • • • • ~• • ~.~M~o~a ~A~p~~ft •• ~.A3%'~~4~~.*.&~~~ •• ~ ••• ~4*~. • ~.~.X~MM~'.*.~~~~ •• ~.~~'~ ••• *~ffl ~~~. ••••. ~.~.k~o~*,a~~. •••. &~~ft. •• ~.~. .~J.t~#~~~~~*3,a~~~~.*.&~~ft. •• ~.~4%~. 1t.J'J 10% • • • • • ~.~.~~. 0. 7.68%~1t.J'J. 223.00%. mJ ~ • ..(£• • ~. ". I.

(20) Journal of Financial Studies Vol. 15 No.1 April 2007. 20. .~T,.~ • • ~~~a. •• ~.*a**(~.A~P~A~ • • ~. _~~.f~ • • ~~,J.~k)' *-'f~lt"'ti~lJ.i. , ... ti1tffl:ifhu~il!#'ffl~l ,l/f~1if'" 1J1J:lto ' .~.1*,~~J~.f~ • • ~.ltjIJ 8%* (l!r.A~P_~A ~*.~~~a • • ~~,J • • 5%),"'ti~J.i.~il!#'M$1if~lt~~ ...ti _IJ J.iT {(.J !if;J fl} ,I:.-LI:. 0. (i=3%, g=2%, L=lO%). 2.0. 0,5. 0.0 0.04. j j-i. k' W,(J:'). ¥T(k). 0.05. 4% 1% 10.03 If. 1,482685 7.68%. 5% 2% 5.14 If. 1,737162 26.16%. 0.06. 6% 3% 3.45 If. 2,063,856 49.88%. 0.07. 7% 4% 2.60lf. 2473,565 79.64%. 0.08. 8% 5% 2.09lf. 2,986760 116.91%. 0,09. 9% 6% 1.74lf. 3,630,978 163.69%. 0.10. 10"10 7% 1.49lf. 4442,039 ' 223.00%. tt : s~*.i!IIf~~lf.*~rtt,*,J1;;IUUII BlJPIl~ • IS JIt-...fi:t 4l!91¥-JJ1t.il" (lock in) BlJPIl,*,lT • ~HH l!.... (k·)+~4~ft~· .~I:l! .... *r.'A.~4·. .•. *r.'.

(21) 90'0. SO'O. £0'0. G'O ~-------------------------------,. V'O. W. ¥r. Iro. ':M. 9'0. O'~. l!. ...¥f ~. :JLr. n. S'I f;t}.:L ~f# ± 4t !t fil'"# ~~ Lllf ~f .wlb~U*1f ' ~fti il '* ~ l~ -$- f:i:t rlf ±.:L ~dWY.~T.'~4t~ •••• ¥~~dwY.no*WW#il'** .~T.'¥ •• VW ••• ¥~~~~~-$-V~dWY.*'.:L~.f;t} Wti~ ''1fl.¥J %S£'II flf*'%8CZSI M.1-1lY¥r~ftiiF~ '%L flf'1hi%Z ~ •••• ¥~~dfiy.&,t.~ •• *W#~W9.~ •••• ¥ ~d~Y •• ~.,~~o.~~~.1-1lY.W#iF~'~~~.W •• •• ¥~~d~Y.&~~S~.,~4t •••• ¥~~~~~-$- • .:L~ 0. ~~o.~~.1-1lY.W#iF~V •••• ¥~~d~Y.~.S~. Ii§t~ (!) • • • • ~f~fl*d~Y.(-:::). IZ.

(22) 22. Journal of Financial Studies Vol.1S No.1 April 2007. i j-i. 2% 6% 1.761f. 2,984,659 152.78%. k· WT(k). Vr(lc). 3% 5% 2.091f. 2,986,760 116.91%. 4% 4% 2.571f. 2,990,430 84.84%. 5% 3% 3.34 1f. 2,997,317 56.53%. 6% 2% 4.791f. 3,0 Il,922 31.94%. 7% 1% 8.511f. 3,051,768 I 11.35%. tt: lb~*.i!RJf"J~+~f,Yd'k"J;ij"i>!~MIli.Jm."J. • ~.tt.{f.:t1tl!9+;Ht+.Ut (lock in) 1li.Jm...JT· *it .1.Rt;a#:ttBilr., (k'H~4 ~tt~ . 'I'JRt;a#:ttBilr.'fl.l.~~4·. ('=")JlftJJu f m*. (L ) .:t..;%~. 006.~MJJufm*A. •••••• ~*.:t..M.·.OO6~~MJJuf. m*A•••• ~*I.~M.o~~'a~.mJJufm*.:t...~&~# M*~.~*5,~*5~~*~,$.AMPM.:t..a •••*.m'A .~.~M.:t..a ••• *.~~.tT'.~.~.~M.:t..a •••*. ~,.~MJJufm*~5%~JJu~W%~'*1~ • • • • • M~JJu~~*. 1'1T1l ' 1!!.••• ;f~1• • ~*~N~ 12.1%,* £. 1.79% ' AJlil;f.~1~i';Fk~J.:t..Jlft JJufm$~~'*1~~~~~~.A.~.~M'~~$5%.:t..MJJufm. *T' •••• ~M • • ~JJu.AMPM.£.,~$2~.:t..mJJufm* T' •••• ~M • • ~JJu.A~PM.~+.· (i=3%, j=4%, g=2%) 0.16 0.14. it 1&. ...#i:. 0.12 0.10. 11. 1i.. t.t.. if.. 0.08 0.06 0.04 0.02 0.05. 0.10. 0.15. 0.20.

(23) Journal of Financial Studies Vol. 15 No.1 April 2007. 23. *- 5 RtiJuf m$~."'li~l1T (i=3%,j=4%, g=2%) L. 5%. 10%. 15%. 20%. j-i. 1%. 1%. 1%. 1%. k Wr(k) Vr(k). 5.00 1f.. 10.03 1f.. 15.11 1f.. 20.271f.. 1,543,591. 1,482,685. 1,435,271. 1,401,610. 12.1%. 7.68%. 4.23%. 1.79010. (W)M.~k$(g)~#. ••••••• ~$~M.o.17~~,.ft ~~'M.~k.~iJu~*MS' •• ~ •••• ~$_I.~M.·~ 17*-~M.~k$. *'a~.M.~k$~."'li~l1TM*~.~*-6·~*-6~~*a'~ •• ~k$.~iJul%'.~*~.~.-.*.A.*.~~' ~k~ A*~M.a. TM• •. •• $Am~' •• M.~~k'~~~ •• m~ •• ~$. *••. ~.f,.~.*.~~~a. M~~iJu~ ••• *·.ft~~·. •••. $.~'. • • • •A. •• ~~~~.~~· •• ~k$ ••. ••• *M~ti •• li.~~~.~· (i=3%,j=4%, L=10%). . 4A -1l'. .. ii.. 0.08. 0.07. It 0.06. 0.05. 0.04 0.01. 0.02. 0.03. 0.04. 0.05. 1h1fJ£-& .. ~7. •• ~k$ ••••• ~.~$~M.. 0.06.

(24) Journal of Financial Studies VoLl5 No.1 April 2007. 24. g. j.j. k W,.(k'). VAk'). .=.. '. 1% 1% 9.59 Sf. 1,301,755 8.61%. 2% 1% 10,03 Sf. 1,482,685 7.68%. 3% 1% 10.54 Sf. 1,701,318 6.74%. 4% 1% 11.1 1 Sf. 1,966,932 5.82%. 5% 1% II. 78 Sf. 2,291,301 4.92%. 6% 1% 12.57 Sf. 2,689,415 4.05%. I I !. I. .f~ jl~~~.:t...xJl ~#. ~~.6~~#.:t...~~~4k.#I.-~.a~*.*~~~M~ .:t...~.,*aM*~.~xJl~#~~~.#~.AMP~ • • ~.~~. T.f~jl~~~ (i,j ) ~ r;q*1t*~~:i&*f~fff:*M.:t...~.. 0. ~8k~r;q~~~~~.~:i&*f~*M.:t...xJl~#i'i9k~r;q~ ~~~~.~:i&*f~ • • ~ • .:t...xJl~#~'~M#~.~a~*m~~7 .~8o.~8&~9a~~~.~~j.~:i&*f~*M.~:i&*f~ •• ~. .~t~.tt~::l~~ '1f.~r;q (i,j ). • *j,,#J 45. fo.ll-f}T '. ~.:t...A*. ~:i&*f~fff:*M.*f~fff:1l.~t.. ' Jt.1{~ ~ (i, j ) ~ ~JJHl.i~1t..* ' ~:i&*f~fff:*"" .*flfff:1l. ~t.. ::l-l->F *- *1;.J *-~ , ~ ( i, j ) ~ >Jlj ~ (2% ' 3%) '(3% ' 4%)' ... (8% ,9%) ~::lllf~ 1%~·tt*t.*, ~:i&*flfff:*M~$-;ba.AM P ~Hl#J 10.54 .R. 8.22 .;f,.t"'*fA.iti%~~l · mJ ~l!*f~fff:1l.~t.~.R'l ~ 6.74%R. 12.22%' i!!..t,.tk~*flfff:{l~:it;ba 6.74%R. 12.22%.:t...i!~M~ ; 1§.~ (i,j ) ~>J'l~ (2% · 4%)' (3%' 5%), .... (8%, 10%) ~::lJE.~ 2%~,tt*t.*, ~:i&*flfff:*M #J~4:-;ba1mAMP ~lHl~ 5.27 • .f. 4.60 .J.!i*f A.iti%~~11' mJ~l!*flfff:1l.~t.~MJ.b 24.21%R. 35.58%' i!!..t,.tk~*flfff: {l ~:it;ba 24.2I%R. 35.58%.:t...~~Jij ~ I!'I ~t., 1f..:fij r;q ~.fi jl~~ ~ ::lllfT ' ~~jl~~.~.*~'*~~*~#~.# • • • ~~i!!..**-'~~.:t... ~·~~jl~~.::lllf*.~·*~~*~*f~·#~ • • ~~*~o 0. 0.

(25) Journal of Financial Studies Vo1.15 No.1 April 2007. 25. 0.10. ~. *. 1lI< I'k. 4. 2. 6 8. 0.08. i<1 .:t. ~i. Jl :til iHl $. 006. j. 0.04. I. ~O 0.02. 0.03. 0.04. 2,4,6,8, lO. 005. ~:l:l&.;f.a;fr.,. 0.06. 0.D7. 0.08. 1m A. ~ l' i<1.:t.fi Jl :til iHl $. Ji)8. $..7. ~~M&ft • • • • • • • • • *M~~~#Ji). ~~ft • • • • • • ~ • • *M~~~#$... ~. 0.03. 0.04. 0.05. 0.06. 0.07. 0.08. 0.09. 0.02. 10.54. 5.27. 3.51. 2.63. 2.11. 1.76. 1.51. 1.32. 1Q,Q3. 5.14. 3AS. 2.60. 2;09. 1.74. 1.49. 9~59. 5.02. 3.40. 2.57. 2.01. 1.73. 9.19. 4.90. 3.34. 2.54. 2.05. &84. 4.79. 3;29. 2.51 •. 8;$.1. 4.69. 3.24. 8~22. 4.60. I. 0.03. NA. i. 0.04. NA. NA. I. 0.05. NA. NA. NA. 0.06. NA. NA. NA. NA. 0.07. NA. NA. NA. NA. NA. I 0.08. NA. NA. NA. NA. NA. !. NA. 0.1 I. !.

(26) 26. Journal of Financial Studies Vol.IS No.1 April 2007. The contour plot of the ratio of the transfer value, i and j g=20/0,L=10% 0,10 0,5. 0.5, 1,1.5,2.2.5 ~ I: ~ ,fUl:1I1B. hl:.. *". 0.04. 0,03. 0.02. IX I I. 0.02 0.03 0.04 0.05 0.()6 0.07 0.08. 0.04. 0.05. 0.05. 0.06. 0.07. 0.08. 0.09. 0.1. 0.7446. 1.0926. 1.5278. 2.0738. 2.7609. Q.49,,88. 0.7964. ·1~l()9.l. 1.6369. ~I~~@J. O~~. 0.8484. ~. 1.7470. 0.3004. I).!M. 0.9002. Jt~. mtUD.. 0.3194. iIlm. 0.9512. 0.03. 0.04. 0.()674. 0.2421. 0.4656. Q.;Q7,Q8. 0.2616. Q;~t. 0.2811. NA NA NA NA NA NA. NA NA NA NA NA. NA NA NA NA. tt: (l)NA f\:../df.:L'f: ..... ~~£ ; ~*r.,. .. O,OS. 0,07. OJJ6. ct«l_ NA NA NA. ,,~.~. NA NA. IiIl NA. 0.3379. Q;.,. Jf;~. 0.3558. I. f.t il itf\:. ...... :ft.j,·Mt-..JIHliIA.tlf' "J.iIlill.:.t..l.J!!.-M~r :.t.:all.... (2)e~*i!,f/f~:.t. ... :ftf,'f."'~1;i!lUUllillJm"I' IiHt'(£'~4l!.9"'''{!'~#'. "U:.:all... ~*r.' (k·H~4 :.t.tl~ • Jtl:all ... ~*r.'.!1"~4·. Oockin) illJPUJr·. *.

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(29) 29. Journal of Financial Studies Vol. 15 No.1 April 2007. ~~5(ik. 1. £11*' ".:§fl!HJT-$Hf!#'~*~ W*.ilffl I!-~ 'f"J£" , .:§fl!HJT-$fT *"* .~.~• •I!-• •~ff.'~~*~A.a~"J£I!-.~ • • ~~~ *,,*~~~~~~.,~~~+~~o. 2. . £11*' "*l!HJT-$Htl!#.ffl.f.f:9t*-*l!#. rp~~~¥" ,. .:§fl!HJT-$'l*~. ~ff.'~~t~A*~.t~,~~t~A*4.ffl:9t~~t~A* j£~.. ' ~~~+l$~. 0. 3. £11*' :mai:St' ~i5/.#g , ".:§fl!HJT-$~r100A..1*.P-$lJ~~~1Jf;~-$'l~ffl • .f.f~1-\;'2¥)}lJf'" t;;!fIfMfi-!1I"!!:IIl.' ~liJtJJ ' 175-220 Ji ' ~~~+ li.~o. 4. #.t:L~.' ".:§f.:Ll!#'~1~1J~:if.*~**i~1~H**li{r.rtf1.~)}lJf'". ~~t~. A*M~*tt~~ffl~±~:St'~~~+~~o. 5. $e.~IUt' ".:§f.:Ll! #.~~-$llr ~l&1!!**~~*J.!;:9t**i~1. 1iUflJf", *iiJ:A*a~*tt~1Jf;~~~PJf "Jt±~:St. 6. . ~ai:St'. ):d5/.#G ,. :I~~:t. ~*T:l1it{(.J1l'"~a~J.iiffl'". '. ~~. ~Im~+l$~·. ' ".fiW1:!i%~1Jf;"ti:#Hta~~*T:I : ~tI!1a £*$-#-;111' ~ 204 ' ~":::"~JJ ' 159-181 Ji '. ~~~+~~o. 7. . ~*~.:§f.:L~I.,.:§f.:Ll!#..~.a~'~~~+I$+":::"~o. 8. Allen, Everett T., Joseph J Melone, Jerry S. Rosenbloom and Jack L. Vanderhei, 1998, Pension Planning: Pension, Profit-sharing, and Other Deferred Compensation Plans (New York: The Mcgraw-Hill Companies, Inc.) 9. Ballotta, L., Haberman, S., 2003, "Valuation of Guaranteed Annuity Conversion Options," Insurance: Mathematics and Economics, Vol. 33, No.1, 87-108 10. Boyle, P. and M. Hardy, 2003, "Guaranteed Annuity Options," Astin Billetin, 33,2, 125-152..

(30) 30. Journal of Financial Studies Vol.lS No.1 April 2007. 11. Childs, P.D., D. Fore, S. H. Ott, and C. C. Lilly, 2002, "Defined benefit vs. Defined Contribution? Determining the Optimal Benefit Plan Choice Using a Real Options Framework," TIAA-CREF Institute Working Paper. 12. Ippolito, Richard A. "The Labor Contract And True Economic Pension Liabilities, 1985," American Economic Review, Vol. 75, No.6: 1031-1043. 13. Lachance, M., O. S. Mitchell, and K. Smetters, 2003, Guaranteeing Defined Contribution Pensions: The Option to Buy-Back a Defined Benefit Promise," The Journal ofrisk and insurance, 70(1): 1-16. 14. Magrabe, W., 1978, "The Value of an Option to Exchange One Asset for Another," The Journal ofFinance, 33(1): 177-186. 15. Milevsky, Moshe A. and Promislow, S. David, 2004, "Florida's Pension Election: From DB to DC and Back," Journal ofRisk and Insurance, 71(3): 381-404. 16. Milevsky, Moshe A. and Promislow, S. David, 2001, "Mortality Derivatives and the Option to Annuitise," Insurance: Mathematics and Economics. 29(2), pp. 299-318. 17. Pelsser, A., 2003, "Pricing and Hedging Guaranteed Annuity Options via Static Option Replication," Insurance: Mathematics and Economics, Vol. 33, No.2, pp. 283-296. 18. Pennacchi, 0., 1999, "The Value of Guarantees on Pension Fund Returns," Journal ofRisk and Insurance, 66(3): 219-237. 19. Sherris, M., 1995, "The Valuation of Option Features in Retirement Benefits," Journal ofRisk and Insurance, 62(3):509-535 20. Wilkie, A. D., Waters H.R. and Yang, S. S., 2003,"Reserving, Pricing and Hedging for Policies with Guaranteed Annuity Option," British Actuarial Journal9 (2) : 263-391. 21. Wirch, lL. and Hardy, M. R., 1999, "A Synthesis of Risk Measures for Capital Adequacy," Insurance: Mathematics and Economic (25) : 337-347..

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