條件獨立假設下合成型擔保債權憑證之評價與避險

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(1)Journal of Financial Studies VoL17 No.1 March 2009. .#.ft~aT~4~~~~.~.~W«~.~. The Pricing and Hedging of Synthetic cnos Under the Conditional Independence Assumption ~5Ili+t. Mi-Hsiu Chiang' lliI1Lift if; J;." i:-~" * National Chengchi University ~ '" MI. J.t" *. Meng-Lan Yueh. !i111LifLf; J;." Mfi -f. National Central University #.~-'f. An-Ping Lin. !i111L,ti;f; J;."i:-~" *. National Chengchi University. #j.t 4;..;t-tEi!!.I1J.1'f~~1Hij.n:.(conditional independence}fl!J1FH1r ' iHfl Hull and White (2004) 1'If~:I:l z~2f.f14)i;Il'J(probability bucketing method}Jt.1i'!Ii. ~tti*fA" t# i! ~1it#:IlH.II.(reference pool}zlA 1<.. 5}i!ic. ' i! m:,# if.:I:l m~). J.5}4-1~ m ft ~fl!J.f:M# s\(semi-analyticH. ~~ ~ • 4;..;ti1 m .f: M# s\ H-1. flit ~ ¥tf 5} 4-M m 1. ~ , jt~.gt. JitM' ~ -f 11 tt(factor loadings}~ @1.fI2f. (recovery rate)z~~5}4-1; m 1. ~fl!J~~lt 5}# • 4;..;t~A 'tfi~l'If.f*m fl!J;..ti5}~JitM'.ftjf:4IH~. tt. .1f,. *"5}#1i'!Ii. ~~ilf.1i t#i! ~~5}4-zfo 1t JitM'#ttt·tt it.*UlilliJ.t1A"t#:lI'fj.ll.z e..'t J.t4lt $It(realized loss) lt~~5}4-fl!JfoltJitM'~:::f:MfJ.ltfl!J~t'!· e..'tJ.tlA$lta~ltt#~5}4-il!li.1HI' {jpM*~ ATt#~5}4-*±.$ltfl!J:::f:~~tl·~.~~5}4-,.e..'tJ.ta$lt • • A~*&Mm~ • • (subordination levelH! ' ~.k. ~5}4-* 1:Alt $ltfl!J:l!it2f.J!ihtt ' #! 1t Jitl'it~ m:,~;i" • 4;..;t~{!¥J.5} 4-i!!i l'it.ttjt~.gt.i!!iM'5}#·~~.J.tflmMmatti!!iM'zi!!iM'!li.4;.;i".~~.5}4-~~.5}4--tEi!!i #f -'t 1t .. Delta it-+1;i"zf.- j a1t m i!~'J 3''-44 ' 1AJR.i!!i#. M'1! fl!J it~tA~ ~ , .t!:.*5} 4-41 'if. A.. ~Mm.fl!Jzft~~.JitI'it*"4~ltifJ.ltfl!Ji!!iI'it~.·. ruli.t:fO"l):. 1i'!Ii.~tti*1A"t#i!~' ~-fit~Jt., 5}4-i!!iI'it~t.M. '4I1$1t5}i!ic.·. Abstract In this paper we investigate the valuation and hedging issues of synthetic collateral debt obligations (CDOs) under the conditional independence assumption. The probability bucketing method of Hull and White (2004) enables us to construct the loss distribution, and we characterize the correlation structure between defaults based on the factor-copula formalism initiated by Laurent and Gregory (2003) to arrive at a semi-analytic valuation framework. We consider risk measures that are adequate for assessing the relative risks of tranches. Efficient calculation of the hedging parameters is demonstrated, and we provide an in-depth analysis for the relevant hedging implications fol1owed from our numerical results. Keywords : synthetic COOs, factor copulae, tranche Deltas, loss distributions. ·ft~~.~~.~~.A.~. 1'Hf:. •• *~'.~.4~J;."i:-~"*4a~.ft.*~~ • • ·*~~.. ~5Ili1'} ·!iII1Lifti~J;."i:-~"*' :I::ll:."'~J,~ 1164lirfJ~.::..ji.6Ht,. Address: No. 64, Sec. 2, Zhi-Nan Road. Wen-shan District. Taipei. Taiwan. Tel: 4;886 9393091 Ext. 81265 Email: mhchiang@nccu.edu.tw ..

(2) Journal of Financial Studies Vol.17 No.1 March 2009. 2. a. 1;- ~ 1i! ~ iKdiUl i! tt(synthetic. collateralized debt obligations):Jt -;ft m .J4H·~ ~ tr.J~;fl(Special Purpose Vehic1e)jflT 1;.- ~ - Jf?H~ ffl.i!~ 3(A:~ (credit default swaps) , ~A**~1t ffl *'~ Jf ~(credit protection buyer)PIT*-~.t:. ~ffl.~tr.J*M.£'R~._A(~~ffl*,.Jf~).J4~~~tr.J~;fl. (Special Purpoe Vehic1e).t:.M j[~. J 1l *l WA..t:.~** J-A. -t~1t.et***~Jt ~-t Jf#J:.1. *l ~f1tl ' ~JtM~1.*llf~ll(reference pool). ~**~ tfj ~ -t*j.~ ~ tr.J ~;fl(Special Purpose Vehicle) , • -t ~1tay l!;jf.J4~;t~ ~ tr.J #UJ4:iftr1i *l • • .t:..i!~~M·~1t~M~M~~~~M~#~~~tr.J~;fl-~ • • ~ *(protection premiums);/J!1J:.1l*llfft.Jl.PIT A. .i...t:.m*5tit -I (:fIJ ,~) , mJ~~ ~ tr.J ~;fl~. *-~ • •If • • .i...i!~tr.J~M~~o~~~tr.J~;fl.1l.If • .t:.~ffl.~t~~.~~~ ffl¥ • .t:.~.,j[tfj~-tft.Aom~~ffl l! ~ ~ .f~~JtJl;fJJ j[ ~** ~ .f~(not funded) , Jt PIT JIlt ~ .t:.JJl.*ifrt -1(. :fIJ *;f!1 :f'J.~)j[~~~A~~it~.t~ A.t:..~7~~ R Jl:t.~~ ~ tr.J~;fl--At"M~ tfj .~ • .t:.~A**ft ~~~ffl~¥1l.'~R.l!~. ~fi*,~Jf~PIT 11; 4lAt .t:. ~ ~ 0. 0. 0. it ffl -M .i..'I:1.. J'a ' irH(u- il --fit ffll!#J ~ .f~(basket credit default swaps) &'*5tPlT.f*tt .t:.~i;j!;1l.i! l!t(collateralized debt obligations) , Jt. £~Iti~ - J!. f t:f~ tr.J(multi-name).t:.1i *l.~JI.(reference pool) , Ji.~ll.t:.;fl~ ay ~. *. ~f1l.~.A.tt.fu.t:..tr.Jo~M~~.A.l!~~Mtl~~~.1i!.t:.. ~'A • • ~.J4.~~#~M~tr.J.Mo~.M~~*, • • • tt.~.t:.5t a.t~~&.Jt~ • .t:.5ta,m~~.~ffl~.i..tl.£J!.~~.~~~..

(3) Journal of Financial Studies Vo1.17 No.1 March 2009. 3. .~#~'.~~.*~A~~W~~.~&~.t~.M4.~.~m. ~~~ •• &~ •• '*~ .~~~~~. ••~~.~£~&~~'~«aw.~·. • • _.fu~£~*AM~ ••••. '4M~~ •. T W._.it:.~.t~~~*".i«-f<:: 0 ~~w ••• it:.~~ .fa ' e!A! T ~ Jft1t.it:.~ £(MBS), m1- J.tqt'l*;t,U1t.it:.~ £ ' ~ 't J.t qt'l*,f,t••it:. (ABCP)' 1•• t1t~it:. ~ £(CBO) '1£-'t Jf;t,tt1t.it:. ~ £(CLO) ~ ~ • J.t ~ 1. 0 .ft. 4' CBO (collateralized bond obligations) ~ CLO (collateralized loan obligations) '§' l ~1.f~3t! ~.f4i*1. {tl :~_(CDO) 0 ~ 0'1-* IAm~~A.~'~« •••••• LAM.«,~rnO~« •••• ~.~«~M.«,~ao~« ••• M. ~.~.ffJfa••M. «0 it:.{~~~jft*1lit:.. ~~CDO~£~*ff'~~+~.&.~.$A •• 1.~~.~~. W•• ~#T~A~.'£~.'4'n.'~~~L.oM*ff~~£~ A.~3t!mO'A~.~.~~~M •• '§'~~ • • • • ~W~~1+0 *ff•• A.kAT~~~~ •• 3t!£~~M •• M~'.~MM.«t M~.«rno,~~'~aWAo~4"~~~L.~£~~'t.ff'M. .~ .#.t:t"1.#.t*~9Htff~~~ ~,ti. CDO. I ' ig1J]~~ 9t-1}«3t! CDO t).. CDO ~£ ' jft~*« ~~{~1fit:.~i•• tl:f.A.ft.4·Hi~ raJ -~~.«. 0. -*:)(PlT ~# ~ 1f ~ , ~p k t). ~ ~ .1fit:. A#'ti ~ 1}«3t! .f41*1.:ttl:~ (synthetic CDO) 0'8.k 1.f~3t! CDO ~1t ml!~ xA~(credit default swaps)~ £ ~M*~0~~:)(M~IW ••• ~nm&~k •• nml!~x.8.». nm~.I~·. •••• 4'~W.~~*1.~1.8'.~~l!~.** ~~~~~~nm~ •• ~~ ••••• o~.~£~*ff ••• ~~ Jt : k~~ • • {~~ .~~~{~1fit:.*~tf-1.f~>t3t!tti*1•• i~.~{~~ w. ir.t.,ti ~ Jt.~ r",,~ ; .1•• tl:f.A{~1fit:.qt~1t m&~.t~ttA4}. • ~1t ml!~~ ~A4~ ~~~Ji1..,ti~ I ~1J(1!~~tR.l~~ 1f.~~4aJHt:. I 1ft ~~ ill m~ ~.1jt ~ SL. ~ 4}.{~ ~ W• ~ 1tm db ~( credit curve) , ~ fIJ ~ ~J\ iU ~1• • ~~ 4' ~~ill. db ~ 0 ~ ~~ ~{~1fit:.Jttt T .~~t,fd~ , A1. {tltl:f~Jl4' ~W.~*1.~1.8~M~ •• ~~ •• ~Jfa~p~M~ •• 'raJ~ .~T.I« •• 8~~~*~.~~*~~m~M~0 ~.ft.&~#.~~'.~ •• ~.~&~*.£~~.~A~.:~.

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(5) 5. Journal of Financial Studies Vol.17 No.1 March 2009. 1:. * ~ ~~ $IJ Jt,ij a ~ 1~1 ~t ' JE :1'11 m it:.k li i§ B~ r", fJt 12 (first passage time model) , ft Ait,~ lH~~g.. 1:.~ 'f ,t11" 1t*$IJ M a ;i(Jit :.kMj-lil$lj- r,~ ~re~~o~~.~~.12t'it~.#~g..1:..~ft*-*. wa·~. ~m&~~.11"3~it~~.~m11"£a3*~.+~it~ • • &~ • •. (recovery rate)J:..U !1t1t m &~~1t1t Jt t Jarrow and Turnbull (1995)& Jarrow, Lando and Turnbull (1997)J:J..~M raJ W(time-homogeneous)~.~~ A£t (Markov Chain) ~.ft.ft mlt$-~""~~.(transition matrix) . m *-.f~id£--0-.3J ~~mW$-~""~i§.'.~*.~raJnmw$-~.*~it~ • • o~~ and Singleton (1997) ~;f~. ,it~~ • • &~1t.~.=..1mlfr1:.~&i.i§.~ .t~·g..~~~m&~ • • ~W11"-0-A~A&~ • • ~11"-0-~~.~· 0. R.M#~~~~~A&~~.~~-nm&~.~~,~~~~~it~. • • • ~1t.~J51a. 0. ;.t. ml! iHt:f14:J51a(copula).f~id£it~~ .{~~ {ij IUH1** Li (2000) ,fi m (l$It..~A;fl12 t .I-Ait ~ B~J.5(default time)*- ft A - it ~~ .1~ ~ ~f • ~ , ~~:f14:4ij:--~~ 1f ,t~it~~ ~ ll.J51a (default intensity function)' .~ *1l!i:t 1f ,t~it~ :il~~~e.l it~~ ~ ll.J51a • -hU1}~~1t m db.~(credit curvei'~.ft. l' ;f~~1t m 1f ~it~tj~.r.5.it~ • • ~r,,'-1t-~n~~·!i:t n~ 1~#j.~~it~ • • ~Jt,ij M.ttllt ' Jt ~ ~.1J;{*;flj.;fl12 t ~§i;fIJ. db Mt m1t1t-0-.3J({?'jica Moody)1H~ 1f ,t~1I 'K.it~ • • 1f*4 ' ~ m &~1• • 0. 0. 0. ~.11"&1f,t~.~11"£.~a3*~d1f,t~nmdbMt°~~.12t' it~.#~~~tl~unm1f,t~Mit~~.~~~tl*-_~·~m~~ tl!~.tt:f14:J51a~§~'~.~,fim~.~l!~:il~~~~~.~ • • ~ ~e.~4~,t1. ' *-,t 1:..;flj:f$Ji(reference pool)~lf~1;-it~tj • • ~~e.. 0. ~ J:J..{tm. ~raJ~l!~.tt:f14:J51.~'f*.~»ftit~~.~M~~~tl.tt:f14:· Li(2000)fJt~~it1.1t. mH1:.,t1iSJ J'oB~ . ~~Ht1.;ff{j:f$Ji t ~1f ,t~..t §*~,it~~ • • ,it~ • • U&it~~~tl$-.af~~raJ'A~~ A~.~raJ~iSJ£.a'ica~~*~.;i(J~*$-·.~~~~tl,~'f. ;ff{j:f.t~1f,ta§~f~,~m.~~ • • • ~,t1:.~Mtlit~~ • •. .1~ '*" ftB~. 0. ~!i:t · ~~ 11~1~~ij .ft.(conditional independence)34~·t1 ~ ~ ~;fl12. (latent factor modeIHtli.itJr:ftA m ~~1t1. ~ f. ,. m -f5t 1:.,t1iSJ £. 0. I'ITt~t¥.I~itjlJa;f,J.lit¥.l;tMi!:#!:$~lliG(marginaldistribution ofdefaulttime) Jl:1::.~r~AA.1f;jdHIT '!'(survival analysis)l'ITiJlt¥.IJ!r.t$.il'Jit(hazard rate function) :t ~r 1F~ t~ it jlJ :J 1'1- {It .tUli j t. • ili'Hull.' itf-J;tI!iHtlliG' 2. ~~1t. 0. 0.

(6) r. Journal of Financial Studies Vol. 17 No.1 March 2009. 6. ~~~.~~T'. •. •• ~.~.~~~ •• ~~~.&~~~.~. ~ • • ~~,~~~ti • • • • • ~~~~a~~~~. .. •• ~~~·~. 1t4':'- Li(2000)~ ~it!!.+GlA~~tJtAt .l.filTii1i?Ji;~ ~M!&M~' 1~t.B~1t~ti~~1l~ .~~~ • • ~~U.M!&~~~~.~~'~~~~m • • *M~~~ ~ • {~(Fourier transform) , ~ • • ~ ~ it. .j(u ~ .ltIT ~ ~ it. (Gaussian quadrature) , *-11 ~ ~ ~ .;~ ~ 0. •.. ~.*.~.a~.~.A~~ ~,~~a.l.- • • ~A.~# J\(semi.analytic)ft ~ , Jt# ~ ,16 A;1:IJ m f'f,14=-~*,~ • • Jt~•• ~ti~.~1f,14= {fi ~ ~~c.(conditionalloss distribution) , ~1t ~ ~'l1.J!l ~~~ , J..:.qllHt ~ti~ .~;JH,*14=-{fi ~ ~~c.(unconditionalloss distribution) _:fi ~ J!l ~ it ~~t~.~ 1fl. t~1t~ti~jJi~lf~~~*,~ • • ~~c. e..1i.~ 1t:.!&-'-t.f!&~~~~ J\ ' ffiLl:t.{fi ~~ ~c.:jf ~#~~. Of.;~. • ~t.~tf1.ft~ ~* 7 Laurent and Gregory (2003) , Andersen et al. (2003) , 1i Hull and White (2004) _ Jt tp Laurent and Gregory (2003);1:IJ m -r,,=l! 14f.~ ~.{~(Fast Fourier Transform, FFT)' ~ ft.~~ll{fi ~~ ~1tt~.(characteristic function)1ll'J • • ~~Ji~{fi ~~t§c. • ~t.~~~ Jt.1/H~ ~ • • ~~*'~ 53i&A &1#k(stochastic default intensities)' ~ § *'~~~*'~ @]11.. ~~*.~·AOf.m~~~~M~M • • t4':'-.~tp,~Jt • • ~_ • •. 'A~m~l!~~~ • • *ffl*~ • • ~~.ti.~_*Mu1i~~~. ~c.~;f."At& -Andersen. et al. (2003)~4J.. • • ~ § *,~A{fi ~.1il.~*.~. t~ T ' ;#t ~ tJ.ltl@it.Jl'J(recursive method):4f" J.t 100 IN .1t{jf IJu A. ft ~ti~#JifilT • .1.~~*'~,tij-*; • tJ..;~_ft~ti~~Ji~1,*14=-{fi~~t§c.~. _ Hull and White (2004)J..X Andersen et al. (2003)A£.r;Jt~ a~1;f-:jf Laurent and Gregory (2003)1t 4':'- • • ~ § *' ~ , @] ~l. • • 11 ~ ~ ,ti . ;#t ~ • • /;J 4- it. IN (probability bucketing method)*-Jt~• • • ~.~4fi ~ ~~c. Jt£*,m;t;1:u Andersen et al. (2003)~M~ , ~~:4f" J.t •• 1t{jflJuA.1t~ti~jll~~~,tij-*; _ Hull and White (2004)~~{fi ~ ~ A tum ~ M ' ~~Alf,f,14=-~f-."J • •1llIJ ~1m • • ~jll{fi ~ ~~ .~~1OO~M~ • • ,~~Jt• • *~~~~~.· ~ 4':'-~~~ a~~~~ff • • ~~U~~ • • ~.~~~~~.·~~*~Jt.~~~ @]11..Af~.(random recovery rate) , A Of-r,,=l! ,*,_;j:j} 1;f-ft. f~1~~~~M!! 0. ~~. •.. •• ••. • ~#J\.~4':'-.~&~~#1iM!!~ • • ~~_.l.:jf~.~.*.~ • • a~A~~a~~*~~.'Mu;#t~ • • ~.~~~ftm. 'ft.

(7) J oumal of Financial Studies Vol.17 No.1 March 2009. ~~. •• ~4*M. .. •.. .~.«.~.~~~~~,~.#. ~M~~ • • ~ • • ~~.'.¥~~~. «.~. 7. ~.~.. ••••• ~~.~. Mf.tli ~ *.~ .~il?!Fitlt.{7>J(tranche Delta) ~1oo}N1t Jij Jf A.~l!~JiLFit A • • • 'MRa.~~~.~~~Jij.£'I*.~ • • • • • • • Jf A. • • • • ~~.~M.Ii,~.~~*~~.~.JfA..£~M~il?!~ 0. l;C11'J. 0. !J.. ' Is. *-1Kttt l4;f~ ?l:! 1t ~. *- ~ :±. -I-~ A -=-100 'J' ~ , 1ft - + ~ -tf. {lhd!f~ij .1L(conditional independence) ~1~J.. t1 T ' :f'l Jij IN + it ~ jt ;f4{)t 1:! (factor copula) , ~;fJ4; 1;- 11£ 12 ~ 1*1. ~l i~ ~f ~ .(tranche)~f.Mlfj- i<. ~f1'{)t 12 " 1ft..::..+ iP ~! 1;- 11£ 12~1*.~li~ ~f-ffU't JiL ~ ~ ilLI" ~~ {~ , I -tyt !l}j ~~~ {~~ :t! 1ft -=- + ip ~IJ ~ ! 1;- 11£ 1:! ~ 1ifd. {j i~ -tf~ .~il?!~ 1-it ' I ~a~ ~1iiJ:f1 Jij 1ft - + ip P1Ttt~~f. M# i<. ~f.~)t 0. 12**.~.~il?!~1-it° ~a~~*-~P1T*m~~.~!~T:. sUi :. ~.j ~1;-lJ.1tm.£' j=.~~.' ;.k1t~.' ' l.. ' .t'J.&~. 1t~. 8H.i : !f;;J-ft.~ El. ti-l • ti M~8:t MrIO' J%. B ( t;) : tb 11 .~ El ti.tJf JJL~_ itA:fJJ ~# JJt IN + AU) : ~. j ~£ EI *-~. L.

(8) r. 8. Journal of Financial Studies Vol. 17 No.1 March 2009. D(j) :. ~~j ·~.AJL$I;;.Jl::..~J5(detachmentpoint). CU) : ~~ j i!:.~JL$I;;.~~J5(attachment point). • • • • • • i!:.W~,~~k~ • • • • • • • ~~~j~~.~A (Premium Leg )i!:.JJt-fiPLU)~i1H~i.l:I:I(Defau1t Leg )i!:.JJt-fiDL(J) , j..~.>~l:I:I1m1tJ£ it mitt ~(fair spreadHt~~~~ ~qtA~ i.l:I:I i!:.JJt-fi7t1:-:.ffil1l 0. L;:l = min (max (Lt, - C(j) ,0 ),D(;) -. -1t tf ' Lti. d ll ). (1). ~. :tll:Bfk~. ti lli-J.!;i!:.l~1$~l!k. ' eli) ~ ~ ~ j i!:.~ji !k.~~ J.!;(attachment point) , ifiJ DU) Jllj ~ ~ ~ j i!:.~l !k.Jl::..~J'!;(detachment point) ( D(i) _ eli)) .t@- ~ ~ ~ j ~ ~ ~J] ~ § -*-1t( notional amount )A(j) Jt '" F;, (-) ~ ti lli-J.!;~la.~!k.4i!:. • • ~~~a'M~~ji!:..~~!k.~.~~: 0. 0. .~A~~~~ji!:.~~~!k..~1m~~fflk~'I-1m~~~4# • • :Bf. k~I~~!k.4*~dnlli-'~~j~~§-*-1t7t1:-~!k.~~&~,-1ttf (d i ) -C(j)) ~~l !k.i!:.~t1t~ , ifiJ Q( L" > 01 11 ) ~ ~c..14-~~1:.i!:. • • ; I ..:A~~ ~ 4 #1. :tll:Bfk ~ I ~~ji!k. L, 1'r~ CUJ ~ D U) iii- ' ~~~~l !k.1t~ ~. (x- eli)). 0. '. .1*1.;flli~.~~i!:.~~::If A. ' -tf~1m1t.~. E1 *,~#i~*1t~*+4~~ ~.o~.~IIi-J.!;ffl~~i!:.~.~~-fi.'~~~~~.~Ai!:.~-fi°.. ~1t. mitt ~~1f.~ a -tf ~ ~~~J]JJi1t e..i* Jt. ' ~ ~C.~~i1t.~ PLU) i!:.Ji1.~~.

(9) 9. Journal of Financial Studies Vol.I7 No.1 March 2009. ~*~~#. B~#~*.~~4~lio.~m~M*~~~.j~.~d. ~'~~#.~#~B~~~.j~#~* •• ~.·~~4~#~B~# ~*.M~*~ •• ~Am.~#.~T:. PL(J). =sU) x L~ ~_ f. (3). U ) _CUI) £[L(;)]J .B(t.)[(D r I,. L1. ;=1. $.+tl~~#JiHtI)B. 4~-1iifiJ' ~.j ~4A~~~m.DL(j)~;f'l m(2)~~~.j ~1'ii;ltJWt~tt.~I1T : DL(J) =. 0. I B(t) [ £(L::))-£(L;~;)J. (4). 1=1. •• ~A.~#J~~~m•• '+~A.~~~m.~.'M ~ :i!:i&T 911IUH~~-,jt*~~~.j ~1t m1J.l. in *~~~.j. 0. . ±B(tJ[E(L\/) ) E(L;~; )]. sU) =. (5). ,=1. ±~i-l.iB(ti)[(dj) cl;))-E(L;~;)J 1=1. .w~~~,a*~-~.j~+.1J.l.·~~~*~~.j~1'iiMd. ~(tranche expected loss). E[L;,il] , iiiJ~~j ~1'iiM4A~~:t~N~~1tm1t#i. •• ,. ~.~I.d~~Eo~~~ • • #i~.~d~~~ • • k~.~~~.. ~.~.#i~.+-. ~~.qo4.#.~~.tT'*~:i!:i&~~. l! ~ #.t.~ ~ ;fIlm Hull and White (2004)M ~ ~ ~. ~ ~ 4- it: ~IJ. *. ~.1t. #i~.~d~~E'A~~~&.#.~~~~~A.d~~m.'~iiiJ *~+4~.~.#i~.~~.~+.1J~o. .:::.. '. {l1~~ij ~~1FH~(The. .t.~~.+~N ~*~~T:. .•. Conditional Independence Assumption). Xi = aiM +~1-ai2 Zi. L. ~.A'. ••• ~.Ai~ •• ,~ •• ~a (6).

(10) 10. Journal of Financial Studies VoL1? No.] March 2009. :!t- <p ' M ~ Xi tt-.J ~ AAAi.1il.Fft ~ q-(common factor) , Zj ~ Xi ..t~Af ~ #di.1il.Fft ~ q- (idiosyncratic factor)' ai ~ ~ ~!t. ·ti.1il. Fft ~ q- Xi tt-.J ~ ~ ~ tt (factor loadings) 1¥Hl1il.Fft~ q- M 1f Zi 1i.:ff!l~ 1L' ...El. M 1f Zi ar)Jli;HI:-1"Ii~tt~ 0, ~.tt~l~ • • ~~o~~.~W1il.Fft~q-M1f~tt-.J~~.a'ar~~ jIj illt. ~tt Xi ~ M ~ J1;J 1;! ~~:ff!l ~~·ti..*ttl ' ~~ ~ q-..it -f-~tlf~ 1;!(factor copula) 0. 0. 4 ~ q-..it -f- .*t tl:f~ ~ ;¥,--itj!Jr,~. 1il.Fft~. <P ' it j!J * 14 tt-.J ~ 1.. $!. ..7§ lPt iA;¥,- Jt 4 11' ~ it ..7§ +. m;¥,-1il.Fft~q-. 0. M. it~Jt4i. 'i=1,2,···N. ,¥--;ttt-.J~M,.t1.. '~~.*;¥,-¥--J1;Jtt-.J1il.Fft~q-M~T'it~** • • ~.1L'~. ~~.*.1Ltt-.J.ao4~.a~T'.m.tt-.JJt4tt-.Jit~*M~~~tt. Jt 411' :f~~illt. ~ Xi tt-.J l ti • • ~~c..~tt F,{x);t - tt - tt-.J ~ ~ , ;Jl' £!p : Q; (t) = Q( T; ~ t) = F (Xi ~ X) =.t; (X) , :!t- <P 1"{ ~ Jt 4 i 1f-1.. it ~ tt-.J *M mJlt.ar~o' Nf:-14~JJ1Ltt-.J1IIta1~)ttlAf~1;!(structural model)foilriAAA :f~~(reduced-form model)4it~*14tt-.J ;tJ\J:..3tf'J- ~ Qlt)1f1~*-. 0. 0. ~q-. M $!. Zitt-.J • • ~fJjc..~arM:f!f ' ~ 4 i tt-.Jf'*14:il~it~~~c..1~ ar m 4f ~ M,·ti.1il.Fft ~ q- Zi tt-.J l ti• • ~ ~u~.*- iF :. (7). = P(aN = P(Z;. +~l-a/ Z; ~ xlM). ~ x-aiM. M). 1. ~l-a/. =H'[~l :!t-<P. Hi~ Z{~lti • • ~fJjc..~tt. M $!. Zi~M1i.:ff!l.1L' ~JI;t. J-A If; PIT*-iF~it~ • • Q(tIM) ;Jl'1i.~.1L 4~*14~JJ1Ltt-.J1¥Hl~ T ' ~ Jt4~.*it~ • • 1i.~.1L,~~ • • • • ~.*.+it~ • • ~~ar r..~1t.~~:f~tt-.J Jt 4~1~14it~ • • ~fJjc..~*ti ' ;Jl'£!p : 0. m;¥,-~. 0. N. Q(t 1M) = I1Q;(t I M) 1=1. (8).

(11) Journal of Financial Studies Vol.17 No.1 March 2009. [!). ••• #~[!)~M.~'~~*~~_DtT~ • • _.~ • • 4~. •• ~&~T:. :or. ). II. , N. ff. (9). Q(t)= LQ(tIM)dM = LUQi(tIM}iM. or. f1j.. •• _.~• • 4~ •• ~E. - :/if Mt1f ~ It ~ J;- Mt it ~. ~ , IlI::.I'!P.f M# ~ (semi -analytic)~ ~ ~ i,l W Ji T ~!L*":)t1t {fl.a~ AAAiJi.f1t[!) ~ M~qf ~ AA..tiJi.f1t[!) ~ Zi M1l1:t WJa~ ~ ~ •• ~&'~~n.±~~Mtl~~~~~tlM.'~~.~WJa~~. it. [!)~~E.aT'[!)~~'M.~~~Mtl°. ~M. (2) [!) ~ ~ •• ~ ~Lf~l. tt. ~~~~'4**.~~.a~T'. ,J-. 0. ti. !1IJ .W.Ji.f1t[!)~~ •• ~Ea~'[!)~.'M.~~~.±~~.~. t\.. ~~~~~tlM.o*:)t.ffl~WJa[!)~~~.a~m •••• It~&~. Student-t ~~L. rt. '. ~fI"l~)J'J~t1f~M,ti~T. 0. 4~-a,ltmtf' ~fI"l.aJi.f1t[!)~M~Zi~MIl1Jt. ••• It~~Lo 4. ~.aTm.±~4~~~tl~'M •• ~~U~oo~m.~~~M~~ :f1:1~,ti~',*t*.(Gaussian copula)' 1!!:Jt.~~lfn • •. ~~L4[!)~~~~{fl.. a~T.I*~'[!)~4_ff~~.~ffl.~+.~.o_M~~~~ •. ••• It~~_' •••• ~~~~~Mtl' •• ~.~~ ••••• ~. .:. ~'[!)~.~ • • i~.#~~ •• ~*. Qi(tIM). 1,. [. P Z,. cI>. ~. f. ~. tf. S;. X-aM]. ~I_~/. (10). X-aiM] [~I-a/. <P( • ) . i~ • • It ~ iliL~ ~ ••• ~ it. liEf.. 0. 4 ~ -=-a·It*5 tf ' ~ fI"l{fHtJi.f1t [!) ~ M~ Zi J~ 1-1-. Student-t ~~L ' Ill':. I'!p Hull and White (2004)~ double-t copula Student-t ~iliL~J~.~ ~ , ~ J.. • • (e/e-2) , ~ tf § Wit(degree offreedom) _{fl.a M~ ZiJ~~.. E.. l. 0. 0.

(12) 12. Journal of Financial Studies VoU7 No.1 March 2009. Student-t ~ i!iC'-A mmIt ~ glJ ~ ~""tt~. 1 ~I~A~~.. -. ~-~ I. I. 0. (£M-2)~M + £. $!- Ez !If' 1i[;If M ll1 Zi;ff,"," 1t.~ ~ j~ tt~ 0, ;q«.t\.(6).t\.Ii[i!.t~~T7IJ*j.t\. :. Ra 2(£z-2)~Z .. M. Q,(tIM)=P Z, [. $(~)~ Ez. EM. 2. I. £. (ll). I. Z. R ' 1. x-(_M_)2 E -2.! a M. (12). l-a/. 0, ~"".~ 1 S9M..~tt xi.~mWJ 1m Student-t j)-i!iC'-S9M..~.P1T~Jl~ , 1~Jt-*-A- JE.+Jll-Vt Student-t ~i!iC'- ' ltil. 1£- double-t copula T '. Xi it}~tt~. 0. ~~ • • • • • • ~**.~~~£o 't1¥{1~! i~A1JilHt ltil-fBl-Vt Student-t ~i!iC'-!If. ' ! $)t..tiJilHtltil-f:J:: ~ti.. ~.S9.$~m';If~P1T~M..~.Xi~!If:J::~ti.~.S9.$~m'~~ ~! $)tA1.ltil-fJll-Vt Student-t ~i!iC'-!If. ' t"1!. £. ~ !lflt~ ~~ !lf1+i~S9.$. ~m. ' JIt$!-. £ M;ffl 1Ul~.J:.*P1Tlt~S9!}.!M~ ° ,*,1¥{l~Af! tJtA1.JilHt ltil-fJll-Vt Student-t ~i!iC'-!If ' 4f!l;t,t1JilHtltil-f:J::JJtti.~.S9.$~m ' ;If ~.-M..~.~:J::~ti.~.S9 • • ~m'ltilJlt.~.£ • • lt~~ • • 1+~S9 • • J:.*,JIt$!-f£M;fflIUl~.T~P1Tlt~S9 • • ~~oltil~.f £lt~*m~.~~ltil.!If,.-.£lt~JE.+t" • • Jt~.£lt~,~ .£lt~*m.~~ltil.S9 • • ~m!lf';If~.£~!lflt~$!-~!lf1+~S9 .$T'*o ~~! l;t'tiJilHtltil-fJll-Vt.$.\! ItiEl.){'~~JJ.~ Student-t ~i!iC'-!If. '. ;If~~.M*t.A~~~~m.£~.oltil~.Aj)-~a~.ffiM~~. .+ -1- S9 ~l!k ' nil ~ m ! .~,tiJil Ht ltil-f ~ i!iC'-~JJ.){. 'ti ' r.l1-. £ ~ !If1+ i't" ~ • • ;lfJ:.*'.~f£~*lt~S9.$~J:.*'~~~BS9.!kM~.~ t",*.o1~~.~~,a~ffiM • • .+t"~~.!k,JIt!lfltil~.£~!If .~lt~S9.$.~'~~~~~B.!kM~.$!-~m.£J:.*o&~, ~1¥{t~4f!l;tf1Jit.Htltil-f~ Student-t ~i!iC'-' )ltlt"lt~.A~~~~m1.£. J:. * ' ltil ~4f! l;t'tiJit.Htltil-fS9 ~i!iC'-){.~~JJ. r.l1-1m-*J f. £.~Jjlt~~..

(13) Journal of Financial Studies VoU7 No.1 March 2009. O· . $~~I~~.. 13. ~.~~.~WJ.$T~._~~nffl.!:~*D~~. ~~~.~~~'fLM~~~WJ.$T~·~nffl.!:~T~·~«~.. 1:£ ~100 ~ +~ JJIJ ~ Student-t ~jl,Ij(,..t::..,It~Jt T ' 1t ffl. £. ~ ~JJi T ~WJ1t1t5. Q. 1) ~ ~ 1:£ ~ + f~ ~ T. 1JlHiJ.il..Ht ~ + M $! Zj ;MJ Jlfl¥Hllll 'f !l£ ~ jl,Ij(,~ f'1T L 1 WJ~~4HiM1tA~ Li (2000)f'1T~til..t::.. JtIT~~;fI'J IiMilt ~Htt.(Gaussian copula)' ~/~g;iil&;;' *x...t::..1t~~ 5t~1~ffl Gaussian copula ~r ~ +-Gaussian copulaJ · f'1T.t~ WJ ~ Jt.1:£ ~ +,tj\~..t::.. T ' 1FHiJ.il..Ht ~ + M $! Zj jt)Jlfl¥t~lll 'f !l£ ~jl,Ij(,f'1T L 1-..t::..~~;fI'J IUHilt ~!.t:.t4 DMtl.WJ ' double-t copula f'1T.t~ WJ Jt.1:£ ~ + f~ ~..t::.. T ' 1FJ.. tt M ~ Zj jt) r:t ~ Student -t ~ 1Jie.f'1T L 1-..t::..~ ~;fI'J !UJ ,tilt ~. 2) . ,~t. I~. D. E.. ' ~A.4R ~ ~jl,Ije.~tt. ~. 1:£11*14~ljjtWJ1FJ..1iT. ,5. ' Hull and White (2004)~til ~;fti!t1~1•• ~,mAA distribution function) WJ 1i it: • 1/t -;ft 1i it: ;f'J ffl ill!! it: (Recursive Method) , ~ til ~ ~ ,f,!; T ~100 ~ WJ 'f L WJ ~ ~. $ fA ~,t.4A ~ ~. .1FJ... E'~1i*~.ffl~~WJ'fLWJ£~*~$!~4$~M'A~4$~OO~. ,T. , ,-t;. 'fttWJ,It1t5 • 1/t .::..;ft1i*11i~.$ f.J 4it:Jl'j(probability bucketing method) ,. ,Ht. ~1i*~~~1OO~WJ. ~ ~lj. ' Jt. -1OOtlJl Mt WJ;fj\~ D~ Jlt.*x..t:A.$ f.J 4iidN ~ ~ ~.~,~:.t4~~~ • • ~.~.~.~ • ..t::...~~E·~Ttt~~~~. 'f. ffl.$f.J4*~*~:.t4ft'f.~.~~ED. ~ ~ lie. ~ tt(loss. L.~~MWJ£~*~~~4$'A~~1~4$. ~oo ~ 'ftt..t::..1Jll11. M:. *J~ ~tfAA ~WJ~tl.te!tl ~Mt ~(K+ IHil!& r..,. 17;. 1JlLti1/t 0 1il4A~!& M WJ4A~~tl1r~{O,bo} , 1/t 1 1il4A~r&MWJ4A~~tl1r~{bo,bl} I ... • 1/t k 1OO4A~!& M WJ4A~~tl1r~{bk-j,bd ' JeAJlt.MJfl D~ bo~ 0 ' Jl'J 1/t 0 1il4A ~ r& M{O,bo} *- ;Fi9..~ 4A ~WJ,It~Jt • ~!& MWJ Jtli ~ .t:A*-,~«PfT~tJ:.*,j'I ..t::..4R ~ ~E.4li~~tt~·.r&MWJt.litl+~'.~~E~tt~~*'~tl • 4..t::..~~·~*'~r&M..t::..M.~8~tt~'~~.~ • • &M:.t4D~~ tt11t J;.-~.tJt1if'd•• :~.(single tranche CDO)~ , R 1;; ~~*4A ~~lie.~. ~. tttWJI-~~. WJ. -t. ..t::... Q. M(¥~.~~tl1r~~.~.3%-~)'~~~~.. ~~E1:£1;;~WJ~~..t::..!&MM • • 9'~~~1;;~WJ~~..t::..r&M~~~t.·. !:. ~~1:£.#.jt1FJ..ttT'~~.#..t::..M~~.jt'~~~*-~~4.. ~. L.

(14) 14. Journal of Financial Studies Vol.17 No.1 March 2009. •• ~ ••M. ~~~*~,~.#~~ ••• &.,*~ M~M~&M~ •••• &M~~.#.MM~*_·.ft •• ~.t rR-'j~~1:r1'1 W. ' llt.*tJt ~ 1t-~~ 1m &M{O,bo} (*,~Jt ~) ~+f.1+ ••• l·.~A~-M •• W.~~.*'M~~~&.±'~.#~~ •• ~ .~.~ ••• *,M~~ M8.~~~M~*~*,~&M(.ft.~k 1m ~ M{bk-I'~}) , ,ilt*At1~ W.1,*,"1+~~ •• ~ *+ ' ~!f~~f,r • • • ~ 0 MW.~A. °. M~M8.~~k1m&M'~*~M~k.~M~~.#.MM~Ak(i. .U~M~MM~*_.A);.¥.4~~1mW.~~~*~'~~~. ~~MW.~~.'~k.&M.~~.#.MM~~~~~.W.~~~. ..,. ~Jt~*_~~:ftl}t-S:.~A~'t:~Jt~&r. 1+~~. ,~}t, M*~l~~.W.~11f.. ••*+' ~~~?} •••• ~~ kM~Mf~.JIJ;t1mM~M u(k)'.lt. .t.M1~&M~fif.1+.M~Jt~Au(k); ~~}t, JiI11l.t.M~ k1m&M~1,*,"1+.M. M~At·~*M~.~• • • • 01m&M8.~~-1m~M'~ • • ~MW.~fif.1+~~. •• *+~~~?}~~ ••••. 0 M&Mf~.. AA.. ~-1m. &M~.t.MU~M~.#.MM~·*~.4.~1m·~m.·.~~N M;fl~W.~~~·Jt~, JiI1~~;£. a 1M. ft. O.5(bk_1+bk ). ,. k. ~JtA. •• ~j.li1,*,"1+~Jt~?}~(,~.~~.·. 1m ~ M(O;;;;k;;;;K) ~ 1,*," 1+. jiJl ~Jt ~ At ~ ~ ~ •• LGD ~ ~ j 1m W. ~ ~~ *_(1088 given default) , At j. ~. kM&r,,'~.1+.jiJl~Jt~,. u(k)~er.*1• • ~.~~~~Jt;k(Ak+LGDj). •• ~~'~~~M~&M~.#~~ •••• #.MM~ 1t .J.:ita r 91~ 1i.Jt ~Jl.. : ~&M·M* 1. (1). u(k»k: ~l!rW •• ±~~:ft, f•• ~~.Ii~~~~~A~(Ak+LGDj)~:i&. •. Mk~~~.~·~*~~~*~M&Mk.~Mu~~.#~~ •. ••• &Mu~~.#.MM~:itar: P/+I :;~J(l-HJ(tIM)) PJ;; :;P/rk) +~' Hi (t I M). (13). Ar :;A/ Af+1 :; u(kl. ~(k)A:(*l +.W[ Hi (I IM)x{Af +LGD)]. pJ+1. u(kl.

(15) Journal of Financial Studies Vo1.17 No.1 March 2009. t. (2)'f u(k)=k: 11' ~p j-.& ~t!ll!~~ft '. 15. 1i*jf.~~"~$,i~~ ~(Ak+LGDj)*;t!. ili~M~~~k~~~.~·~*.~~M~~k~.*B_.~~T:. ~. rt.. pJ+1 k. k. = pik. At =Af. o ~. (14). +[Hj(tIM}X(LGDJ]. J.t. tp pi (~(k»~1i*jf.~Ji. tp ~ j 1m .& ~t!ll!~ * ' J.t." ~;j~ ~tt.A~ k 1m (u(k));J~~ r..'~11f,1+#\£fs.' rrfJAI (A':(k))~~J.i~j1mj-'&fAl!~IR~>1.At,. ~. V-J. "~;j~~tt.A~ k 1m(u(k));J~~~ra'*' ~~~~~ra'fA1.f,1+jt,ij~~~~.'. ~. HltlM)~ 1itlit.(7)ffl Jt~ ~~ j. ~. tq. ~).#\ £fs.. 1m j-.& fA1.f,1+l!~~#\£fs. •. '\J -tit. JlIJ ~*.1i ~ttjf.jll~1.f,1+B_;j;1 ~ ft ' t; -t-#ff JI:!:Af,1+~~ ~. ~. ~Rft~*Mtl.~~~M~~~~,~*~.*jf.~~#.*.~~R. W. ~it(unconditionalloss. N. Student-t ~!jc.. '. distribution)· ,*-5(~'ttM 4 ~ JI:!:. t; ltl&it .~~ 1iit. ;lJt;ttt. ~~BIi.1ft~li1!'fN;~rJic.~ 0. m·+~~.~.* • • ~.~.tfi.. ~. .*jf.~.~fA~4Jttl'*~.~1i* • • ~~.fAaj-AA~~. 4k. ~fA.~*.tl&·. ~). • • ~~.~M~~R~N;'~~.ili~.M~~R. ~it~M~t'~~~~itA.i1!~.·A~. ~. ~.~~R~itfAM~. ~&.,Jt~ili.~.* • • fA.~.tfi.'.JI:!:.&~~~.~.~~ .a~.ff~~.~.~~.',*-5(.m.~.tfi.~T:. ~. (1). ~. w.... ~~~ ~~ &.{;1!~.~." ~~ ~l. a.. .~.~M~~-Mft*.'~~.*m;lJt."~~.fA.ft.~·. '*- 5( ~ Jl:1:A* m_ ~ ~~ ~ £fs. (expected. loss. percentage)~).. (leverage of expected loss) Ri;} ~~). jt,ij ~;j~ ~ ~ &~ fA .~. t ) 4. ",:;t f~ III Gauss-Hennite. ~ 4;1 ~;fA" ~~ ~l. •. *'. 1% it. ttiift st-;;? iHtll!#t "Ul Mi!rrft st-.;f.J. :. t:f(m)dm ~. e-m'[e"'l(m)]dm K. L w(m, )e"" l(m, ) bel. ~~KAtt.ft.ffl.IIl~MD~.tt·~~)A~*.tt·~A.~~M.·e~~).~ ~~·m~~IIl~~~J~A*~W.II!#t~ttM~ftst-·. l.

(16) r. 16. Journal of Financial Studies Vol.17 No.1 March 2009. .~«._.~~~~~~.~*~~~~M~~~·a~~A~~ ~M~~~ • • ~~M~~~*a~~§~*~~~'~~~~M~~~. ~~*.f*it~'l ~A.~~JtJl ~;fA ~.f§1tm-1•• _.JtJl ~;fA ~.~1%it. '. *0. rPIT (15). (16). -it 'f E[L:;l ] .1iUi(.(3)PJT ~A~ ~~ j 1£ ti *,16 rtfJJtJl~;fA ~ , E[L,,] ~'l .1•• _~J1~Wl ~;fA ~ • ~~j~Wl~~~8~*itA~~~MtfJ~. •• ~m.~.'*~~~. M~~~M~*itAI5'~*U~~*I~~*PJT~.~a~A«._.. 1 ~~*PJT~•• ~tfJ. 151% •. (2) J-A~ftAJlJl;fA ~A£tt!~a~m.;f~.. • 1~*.i! '*" iii ill JtJl~;fA ~1t Y , ~* 7dA~·ttvtAr-1. r~;fA~*a· ~:5t;fl;fj: Gibson (2004)' ~A~~ ~ftAJlJl;fA ~(Unexpected Loss)A~ ~JlJl ~;fA ~JJoJ:.~~;fA ~ *atfJ-1m • ~ftAJlJl;fA~AtAJtJl ~J.1r~;fA ~ *a. •. ·.~~~~~~~~.it'~*~~*.r~~jtfJ~~*a. •• A. SD(J) : I,. (17). (18). 1t~~~ftAJtJl;fA ~~~:f.f*ite:it. -1ilf§. afittfJm.;fij:fl. ~~*~.m-«.~.l~~*PJT~.~.fit*it·. ' 1.\(.* 1t 4* 1.

(17) omoweD. elPO .~~i!4:"~\fatf4P;l{rWr;ffW~1t'tt:.!!J11 ..k' lllr~4:"~lfw¥Htl~HJ*~4:"'ljf~W~~-TWri'f. 0. ii~f#~lfw.r. W~W~f#.~.±' • • • • f#.~i!~*~X.~'f#~f#~i!.Y .N*~oii~4:"ll.W±~~ • • • • • f#*~~'lf~( • • • • ) Y.f#W~W~f# • • • • ,w.W~f#~~*W~_ • • ~.~'~~ .f# • • W~.~~'~Y.W~~.f#!*~~~ • • ~.r;ffW~ 1t*4:".~~~~\fi • • 1!fr.r;ffW~ y o. : ~W~nf ' ilft4:"WlFW.¥J • • f#. (. w¥r W~rf#~f4:"~(t~_ Os ~ if. !*~~fJ!a(dq{)~"IiY--tJ~. ~*T!aWw.W~.~ • • V~1l9.4:"w.W~f#.~fJ!*~. o 'ljf~W(v)'¥.~tf1(.1)7cl.1f!~~4:"*~t:.!!J ' 'ljf ~W(£)'¥.~tf1(.1)7cl.1f!4:"Y~*~'. • • • •4:". f*~"*"trr(.l)W.LW ~if. (1 z;). it~. ,. :.1f!~~~~4:"*~~~.1f!Y~~~4:"*~_ • • • • f# (l,nfleW-Ol-){lew).¥r• • 4:"it~'ljf~,¥. -t:*~"f#Y .'.fifit~),J. 0. W~'.1l9.4:"~lfY.W~¥&f#.~.~ • • ~fJit~'ljf~~. (9 119.4:"~lfY.W~f#.~fJit~W. o ¥~f.Vf~t4:"lJ~~f#._ !'7 ~ if. (s. (oz;).

(18) r. I. !. 18. Journal of Financial Studies Vol. 17 No.1 March 2009. ~.~~ffl~*.~ • • • • ~.~ • • ~ • • ~4~~.D~aA~ ~.. • Gamma °. Delta. ~Mt~*~~itffli!~5C..j~ilt'£~tlf~' ~.A1M~. ~~ • • • • ~.If • • &·~~ • • • M~.~nffl5C. • • .£~ttlf·. 5l iif~[!j~~(lH~~it fflilt. ~MJ~.(Average. Spread Movement),J.:k&.(2)-' -1~~~it ffl • .£If. ° 1f.(l)lt(2)T' iif ~J}lj ~Mt dl Sc2sind t).ltb1(jgleCDS * ft • • ~nffl.'£tt ~·~.A.~nffli!~5C. • • • • • ~~.~ %-J..:J..fiw A.~ fI! &*-:t ' ~ •• ~ •• Delta ~ ~. ' .iF.X ~.~ .fi w A. ' ;t t dlit ffl it!.!!] 5C..j~.f~ .*-.~ , ;ff- ~p X A i;'f-11(Buy Protection) , ~4ij:-1f.;t.t1titffl • .£1~~.~.* ~.j~.~ Delta ~MtitoT:. .0. ... 0. [Percentage Change in M'TMj)] [Percentage Change in the Index Value]. 01). °CDSind. =_[ o!J). 1. Cl~j) (1 bp)]/[. as. All). _. Slng!,CDS -. [. (23). 1. ClIndex _Value (1 Index NotIonal. as. bp)]. (. [Percentage Change in MTMW]. h 'In the CDS Value ]. Percentage C ange. (24). ::;:: _[ I. aMTM(j) (1 bp )]/[ I acDS PV (1 b )] P AIJ) aso CDS Notional aso. ~ • • ~• • • M(nfflit~5C..~.)~~~'.iF • • • M~MJ .'£slf.-.£.~'~ • • • ~.~~§*~W~~~.~ • • •M•. •. ~.~~§*~W~~~~.·~*.~. ••••••. Gamma(yW) • • iF 1i• • Mit ffl1Jt .£ ~;l:~ ~. - . £.fli B~ • •li' itoTAffliF °. ,. ~.j~. ~. Delta ~ ~. (25).

(19) J9. Journal of Financial Studies Vol.17 No.1 March 2009. Bt. -It' it {tJt *1t7}~Jf. ~{~ ~. ,. )... ,*, ~~. ,-ag. I) ,. ;f.. iP >fIJ m ~ *" ~p I'fT 1t' 1.(5 ag ~ ~"JJ! !k. fr ~c.. ~ it ag 'jj if-: ' -tE Gaussian copula $t double-t copula lifi3 ~:f: ~ IN -f-l! ~ $:g ~..~~ 1:! T ' tf1.1t !lX.1:! ffi 1* 1.:ffl i~ 1ft (Synthetic CDO) , .lt~.ttlifi3~1N -f-l! ~,~:g.T ~t·N. ,~:g* ~1t,fi m~ *"~fi tl'fT~A~fr • • ~.t~.'fr#~fr.~.~~.o • • ,;f..~~. :f:~IN-f-l!~M • • 1:!T~fr.~.~*"it$t.~!IX.;f..,.lt.*.~M* 0. ~fr#o. :3). -!to t.r f'ff lit ' ;f..lfi t ag Gaussian copula J~ ag kIN -f-l! ~ f~ ~ t .~ IN. M ~ Zj JSj JlIUft. ~ 'f ~ fr ~Uff ,{ 1.. ~it #J.ffi n~ -til! ~ #t. copula J~ ag k-tE IN -f-l! ~f~ ~ t ' M $t Z; JSj }Ul-t:t Student-t ~~ t~ JUj -til! ~ ,~:g~... 0. ~ ~~ ag. ,double-t. fr~c..I'fT'{ 1..~it. 0. 4). - ,. 1t!IX.1:!?~ 1*1.:ffl i~ 1ft ~ 1f-f.. (l) m .?o 1~H~. JSj. 1.. . t t• • ~~-1t!IX.~.~~:ffl~.m.?oI~MaA5.,.ag4. m loo.~mit#J~.I'fT.!IX.' • • ~mit#J~.ag~~;f..~A-W.A j(. , ;lIb!!:. ft :ffl4 #Ji ~ jl~ :flJ ~t ~ t3 ;f.. ~ A -11 A j(. ~o;ft I I'fT iF ' 1tut1t:ffl 4j.ll#~t1t T !l!1~:f: ~ -:t1t}'IJH.ll~fr. ' fr.*'+(tranche size);ft iF ~fr. 0. ~. *ff~a~.:ffl4.M~;f..~~~~'~~~fr.I'fT&~ffi~:ffl4.it#J. ~. ~jl. 5). !k. ~. *. tot 111. 0. ~. mPh 53i (credit enhancementHl?.;ft ~ fr • Fit'. **. ~ffi ~jl. !k.. t.r,~~.tt~~fr.~~~ffi~lg~!k.~~'IN~~.~~.tt~~fr. ~A~~.tt~fr.~ • • Mo~*,.ttfr.ag#~'jj~A.~.~# -::kag1t1t~.t.#(pay. in arrears). lRJf~lit~m.?o.tt. 1.:ffl4j.lltag .'{*1..it#J~':fflAfr • • ~.lgit#J~!k.~t.r~'~~fr.' • • ~ffi Igit~~~jl!k.~ 3%-6% ' ;:k1tfr.~.~{f~ffi I~it#.!~~jl!k.~ 6% 10% ' l~it#J~jl !k.~l& lO%ag~~frM m~1ffr.~. -M:!1iJ-t ' ~~fr .~1~mtf-*~A AANAaa I ;:k1tfr.~nm1f-*~1t'M- A $t BBB/Baa ~M ' :fflAfr.M:f:l!1ttfJ'f: 0. 0. 0. I.

(20) 20. Journal of Financial Studies Vol.17 No.1 March 2009. i'- pj, ~ t! 1*1t;ijf 7t- ~;ij ,£ 1fll9:.. ~l. ;;:k-$. ))-.~1M. ;fl~~.. ;;:kfl~.f.. -fi-ff~jft. 3alt~it. 3alt~it. ~.:k+. 3%. 3%. 4%. 90%. ~m~5i. N/A. 3%. 6%. 10%. it m~f~. Unrated. BBB/Baa. A. AAAlAaa. ~. ;t-$~.. 9+lt~it. 11-1111 ~1.;ijf If 1Jl tp ~ it mi! #J X ~ ~ raJ f 'Ii.(homogeneolls) ,. .4~.#J.M~. lli!#J. ••• ,.~~.~.~itmi!#Jx~~itm.£&.. *ilii!~.4°.~itm~~x~~~M.~~~2M*:. itrr~:iji. la!4~7t. ,ill. a. 51f. 40%. l:§Hltfi 1~ mi. i!#J5§l4. 60bp. 0.01. ~*a~.~.a~~tfi~.~.M~m~.5%'~.~itmi!#Jx~M ~~1iI n~~.(pairwise. correlation). j~..li.a~.+ ~ ~~ •• .JOj. 30%. 0. .li:t... +tj\~. tp ~~#H!.Xi~~. 0. (2)tf•. .tt*. tPtAt ~ -*- iP ft $(5 t¥J :#l-t- ¥J 4- ik M' it 7t~ ~~ ~;f.!i r it a~~~. ••. ••aA•• *?IJ~~ 3 :. *. jf- ~Jl:t.. '~~*~~~Dr~~:t..M~a~'~.~#.~~ ~~#t¥Jm.**~nm.koa~.~~~t¥JW.~.

(21) Journal of Financial Studies Vol.l7 No.1 March 2009. ;f<. 3 tt1f( .*t *( JF.-fir. :. t~. BP). ~. Gaussian copula. double-t copula (eM=5, ez=5). ~li!1}~. 1487. 1706. ::.kff1}~'~. 474. 364. ::.kff1}~l..~. 203. 137. 7. 9. '---- 7t ff 1} ~. L .... 21. ~.~~A4~.B+ • • • ~~~AA'.B~~~~4~~~tl. ~#. ~t.~'tt"'A.1-~ ~~~~{A~~fJie.~tt·. 4 double-tcopula. ~1fll'tt~'. 1;. ~AA31:.!itHtB. J.i; Student-t ~1Jje., ~~,{.tM-'11.~1~f-A.~*4~~~~*1f ~~ • • ~~' • • f-A.~M~4~~~tlB~.*'~.A~.~nm ~A~~'~~~~.~B.BB*~~4~tl*~~~.~~wm~. A • 1; ~f ~ AAA1:.!itHtB+ J.i; Student-t ~Ilie.* ' 1~}H f- A.-'~~4~~ •• '" ~~'~.A~.~.~~Wm~A'~~~~.~. m~A"'~~'~. .*.~~ • • f-A.M4~~~tl~~~·.~*2~~.M*'*~.. tt.. JJtft~~ltA~.~1; '~f~AA:t1:.!itHtB+J.i;. Student-t ~fJie.~~f!A~~Mt. t1:.!itHt B + Student-t ~Ilie.~~ f! ' A ~.4 double-t copula 1flHt ~ J!ff.>tt 1~~11: m11 A ... :fi4 Gaussian-copula f~H~~ J!ff *ff~11: m fJ AA ; :ft~~ ff~.~ '~.#t.'I1.!it~B + J.i; Student-t ~Ilie.~~f!'" A~~f ~ AAA1:.!itHt B + J.i; Student-t ~fJie.~~ f!' B ~t~1:K ~.4 double-t copula f~Ht~ ~1t m 11 A ... :fi Gaussian-copula 1~1"tt ~ ~ ~ • .f.. ~ ~ 1m] ::.J\,. ~ ~ • J{1j 4 double-t copula ~ ~"ttfJ M * ~ IJ'~ Gaussian copula ~ ~ J!ffff~M * •. M ~. (3)A jH1:.$t~,I{~~lT 4*ir'f ,a1I"l:ft~~.l1!1tfit.~B+ ~ ~1fttt(factorloadings)~@]11 .(recovery rate)~$t%\,I{~tlT ' l:t.~.B +;f§ ~m'l1.$t.f~~~ ~ ,!it~ B. t. +.~~tt~@]4.~~~~.Wm.A~~f!·. ~. -. 4*~J!ff~"tt~.A.~~'.A~.~~~~.4~.-'B+~~. ~-!-. "0. ,t1:. ~t .~!it ~ Gaussian copula ~ double-t copula ~ ~ , B + ~ ~ ~ tt ~ @] ~l • • ~~.Wm~A~~ • • ~:.~.A~.~ ' • • 1 l~M*'. L.

(22) r 22. Journal of Financial Studies Yo!.l? No.1 March 2009. I I. •• I~~M.~A~M •• I&~M.:.~~~~ .~~' •• ~4~M*,~m~.A~~s •• I&~M.~A.~m ~ •••• I~~M.·&a~~~.'.~2a~3~a.~'4~~ m~~4M.~~,~~m. ~.~m •••• As•• ~.~~.. ~m~.A~~S. I JJt ~ -. ~ {/-JiJt l.. ·. (J.: t,!}- 1),4. factor loading Gaussian Copula. factor loading double-! Copula.

(23) Journal of Financial Studies Vol.I7 No.1 March 2009. 10'. 112. ::k1f0'-~f~1tffl1• .l.:t..~~&0'-#. it IN. f:Iij. ~¥. factor loading Gaussian Copula. factor loading douhle-t Copula. i. L. 23.

(24) I. I. 24. Journal of Financial Studies Vo1.17 No.1 March 2009. , (!_-'. recovery ratc " i. t. Gaussian Copula. douhk-t Copula. factor loading..

(25) Journal of Financial Studies Vol. 17 No.1 March 2009. 25. 114 7t1t1t~1tm1.&:~~"'J.t1tllT. {) 1. n::. factor loading. Gaussian Copula. tranche sprcad. :J (>. Q; (}?; t;,<). factor loading dnubh:H Copula. .~~~ •••• *A~*.~.~~*A'W.~~#~A~~.. •••• ~*,~.~a~§a~~~1t~~•• ~~~~o~~4. ~~. .(W .~~1...~ ~,:}t;l-Mt1.1t(residual value)1~~ *-111t~ a 1t1;t.)1l.'" -m-~c'*- 'f'CfJ1J~Frey. and McNeil (2003»fI-J.J~fcJ*A.i.!lJ.~JJt&.fcJfI-J~ .a1l.• • • ~~.~,~~~ • • ~.~fI-J •• ~~~~,A:}tW.~. ;l-Mt.{t• • ~.o~~~4.~~~.&.~~.~m_~~a~~u.

(26) 26. Journal of Financial Studies Vol.17 No.1 March 2009. 1.. given default)i~Y , :flUHlI..:t. :«ll~jt *'.I!l i1i1 ~1~ • ii jl ~ ~ I!l Jt.PlT71~!t.:t. ~m&~A.~ • • • ~~.~~.:t.&~'~Tm~*'..:t.~*~fi~~l Jt.&~~ • .:t.~.~~'I!l~A~.~m.~A&~H.;i1i1Jt.~*'.~~ .&••• ~jl~.ii~.:«ll~*'..:t.~y'~~~m.~I!li1i1~~ • •. ~:. fiJ. ~1. Im~~H.·~«~~.:t.&~~.~iijl~~~&'I!l~A~m.~~. ~~~ • •. • • • • I~~H~·i1i1~«~~1!l ~ • • &~~.~~~&~~~I~ffl.&'~ • • fi~Jt.~ffl.~.:t.. f!IJJt~-Ji~JJt*- •. ~. &~H.i1i1A&~I!l~. .. .. . ~~.*. *- -1- ip J-A ~ •. ~. ~. .:t.&~~#. ip PIT ~ A.:t. & ~. double-t copula.:t.it ~,~.1JlLttr. :tt 4 ?IJ J:l:l41!l ~:fX ~ -. {if". ~~:fl. '. ~ jJI14. Gaussian copula ' ~:f1f 4)..~~.:t.Jil~4:t ••. ~. Gaussian copula ~ double-t copula l$J ~ I!l ~it ~. M.r'4)..~~4~Ma*~*'..o~.~.·. ------. ;tft~.Jf..·. 1.~UHa. ,ffilt~.Jf... ;J:.ft~.Jf.. IF ~. ;J:.ft~~r...Jf... Gaussian copula. 2.9262. 1.5301. 0.6497. 0.3985. 0.3446. double-t copula. 2.9302. 1.7082. 05244. 0.2748. 0.4192. .~4)..~~~.ff.O~~~M'I!l~~*'..O~M~ • • *ffl*.. G. 4 A {~IJ ' 4 Gaussian copula.:t. r . ;.k 1:1 ~ a ~:JtJl~~jt*'..'3}t~jJllA 39.85 ~~it~. 11. .. 4).. ~ ~f!jJ 1t &~ ~ .k + .. t),.t<.. ~t.~~~1f?t~4.#]fIJ:JtJl. MM~. it'.~4Mfi.'3}t~~.~.k'.l$J~~~.ff.O?t~A4. a ~ ~ it~ 9 + ~ J;. it ' f!jJ ~ & ~. ;. M:fl~. , 4 double-t copula .:t.r ' ;.k« ~~t.~~~1:1?t~4:JtJl*~:JtJl~~jt*'.~'3}t~jJIJA 27.48 ~J;.it~ 41.92 ~ ~it,.~~«~~~.~~*'..~.~~t.~.k'~~*~4~~~~. ~. EI. G: G de. *-.{t i"~fJJt ' ~«~~~Jil~.;.k1:1~~t.~+~ ~ •. •. ~~~'.~~~~.~.*'.~~~~W~~«A-~.~~fflW. ce.

(27) Journal of Financial Studies Vol.17 No.1 March 2009. 27. ~.~. • • • ~.~.ta.'.~~.* • • &~ili • • • • • • ~.~M~. .1~T. 1t.fft~*+. .7f.-t. ~t.1;HHt..tt~~.~:f11l1t.~. 0. I!lJlt*3C.~fflIJr~4l~~~"$' ;f1fflM~4l~16*4t~ 0. -fl~. !:.~. .I!l ~~. * 5. ~ Gaussian copula. a~. double-t copula. (%). :.kfl'~!--. :.k1't~!--. ,~. l..:J... 51.00. 21.66. 9.96. 0.38. 56.94. 17.48. 6.87. 0.47. ft;fllfm. ;fl~~~. 2.93 2.93. ;t1't~!--. ,. '11. Gaussian copula r ' • 11 ~ •. * 5 lit i!~. M~41~~. ~ -it jf A.11. ~ #J. jlJ M~-t. ~ 51%~fll,ij*4t41~' ;.k1t~.f.~;.k1t~.l...~~IJ~ 21.66%~ 9.96%~M~41~~. ,. :fI1Itt~• • ~jll. 2.93%~1,ij~41~~. , IItJJtilitt1,f,1•. • • • ~.~.~~.fft~#tl°.~~1t~ • • ~~~I~~~~~n ffl1,f,llJt '1~~.11.~#JjIJI,ij a R~ 0.38%~I,ij~41~~' ~~.~Jit~.£ ~~~ • • ~.*.~Jit~'I!lJlt~1t~.~nffl.!:.tt • • ~.£ft~ 1t ffl1Jt 1:. + Q. 1. ~.. f~. .~. ~ 4. 11. double-t copula r ' .11~.~~1t~.~M~4l~~;jtf~~~ffl Gaussian copula 1f1..1tPIT-fljIJ~~*- ' ~~:.k1t~.~M~4l~4l ' JlI1+~ Gaussian copula 1¥1..1t r PIT -fl jlJ ~ l,ij ~ 4l ~ 4l ' JIt ~ *- lit -F I!l .:r;fl ~ 11. double-t copula l!~~~1fLtir ' .la.~.~~1t~.PlTIii1t~Jit~:f81t~ Gaussian copula 1f1..1ir ~* ' I!l JIt. double-t copula PIT .;jt-fl~.jt ~.~~ 1t ~ • ~ ~ 1£ 1t ffl1. 1:. 'JT- :f81ttt ~ ; ja] t1 ~ ~ tIT ~ ~ ;;y 9;a , 11. double-t copula 1f1..1tr ' ;.k 1t ~ • Iii 1t ~ Jit~ :f!i1ttt 1~ , I!lll:l:-. -t ~ tt 1~ ~ 1t ffl1. 1:.. '*. 0. ~tr. ~T~.M~a~~~~'*n • • ~.~M~.~~A£.';;Y.. ~. -ffi" .;jt-fl~.~~4A ~~.~t)\f¥.fg-tt(leverage) a11"] ffl1i.~.1f.~~ .~M~a~4lA.~'~.~.11.~~.r~M~.~4l:fl1l.~ • • ~ .M~a~4l~*tt'~A~-~.t~.~M:fI1I • • ~~a.oa~;jtf. ~~. 0. ~ja]~.1f.~~.~M~a~~#*tt~~*6Q. .11.

(28) r. Journal of Financial Studies Vol. t 7 No.1 March 2009. 28. $<;. 6 M iF;(± Gaussian copula r ' ,ffi 1l1t ~;(± ~ ~ .fIJ 'JI a tr.J #( t-,-tg.:it ~ l! 17.43 ' :.fQ~~Jt~1t~ 0.13 .fIJ 7.40 ~ itr.Jt1tt-,-tg.:it ' 1t.1tAlJJiw,ffi~ 1t~~.~tr.J#~o •• *~tr.J • • ·.~1t~tr.J#(#tg.:itI~.*r~ tr.J~~·$<;.iF,ffi~1t~;(±~~AA~tr.J~~~oo~tr.J.~~~~~~AA~. *;&.~.~.1t~tr.J#(#tg.:it~ •• *~ • • ~.*~*'$<;.iF~. 1t~;(±~~~~tr.J~.a~oo.tr.J.~:.fQ~~*o~~~.1t~;(±~~~ ~~tr.J#(#e:itI.~*&W'~~I~Jt •• ~ •• ~~#~D. ;(±. ~. r · ••*r.., •• ' ,ffi~1t~tr.Jt1t:f-'-tg.:itIlti~~ , 1t-~1t~tr.J#(#e:itjU ... lt~ , ~ Gaussian copula 1F1't.tr ffl.f.f.fIJ~.tt. ~-~. double-t copula. 0. mJl:!::.1if.~.fIJ,ffi~1t~~~1t1t~;(±. Gaussian copula rtr.J.~~ '1tJJa1~. double-t copula rtr.J.~~. 19.43 ~0.16. 0. ;(±~~~'JI ',ffi~1t~. tr.J:.fQ~.~~~'.~~~,ffi~m~~3%"ff~~~~",~m,ffi~1t~~. ~,.~~,.~1t~;(±~~~AA"'~~*.1ttr.J.~'~."ff~~~ ~~3&3%tr.J1l,ffi~j.ll*~*' ;:k1t1t~;;fr,J)~1l~4~~' ~JI:!::.;:k.;,t~A. ~~~~~~~AAtr.J~.~m~A~~tr.J.~o .1l,ffi~m~~A*±~~,.~1t~~~.~.~'~~$<;.6~,ffi. e.. ... JJi~4. ~(realized lossHt .f.f,ffi~1t~~~.~*±tr.J~4~~:.fQ~~Jt~1t~W.f.f • • o~~~. 1t~~~.1t~~~,m~,ffi~1t~~~~tr.J.~~~,.*~ •• ,,ffi ~1t~tr.J*~~4.~*±~.i.tJr~Y , 1;'f,ti"tr.JA+t.fii~' .i!~Jt~;,t~ ~ 1t~tr.J#(:f-'-tg.:it.*Mlt~tr.J~ ~ k~ ~. ~~*±.~tr.J~4~~.~,~~#(#tg.:it"'.*~~~I~~*tr.J~ ~D. $<;. 6 ~,;~~.* T 4t ~ A(11; m1;'f,1{ t. 7J)~1t~tr.JM!i~tfl,~. D:tt~,ffi1l. 1t~tr.J&~A~~'~~~~M!i~tr.J~A.~~~tr.J.~:~~tr.J~Atr.J ~~*±~~~.~',ffi~1t~tr.J*~A;(±~*~~~~tr.J~m.~~ .'*~~1if~ll~.~,«.tr.J~Atr.J~~~*±~~~~AA'~~. ~~*tr.J~m.~~~1if~~.,ffi~1t~;(±*~~tr.J.1t.~o~~.,ffi. ~;,t~&~A~~'~~~~M!i~tr.J~A~~~.AA~~~.~D~.1if. • • ~.;,t~tr.J&~A' ~o. ~~~M!itr.J.~~~~ •• ~tr.J. Atr.J~~..

(29) Journal of Financial Studies Vol. 17 No.1 March 2009. ~. ·it~. {#j! r",". ~Ji;. ~~7!-~. Gaussian. doublt t. 29. 6 'Jl :l{~ .klfJ~*.'f.-m-it ;xft7!-~'l'~. Gaussian. double-t. ;xft7!-~!.~. ;tft7!-~. Gaussian. double-t. Gaussian. double-t. M~. 31mJil. 30.93. 31.67. 1.85. 0.87. 0.32. 0.36. 0.004. 0.01. ;.k11t. 61mJil. 29.27. 30.01. 2.93. 1.37. 0.63. 0.60. 0.009. 0.04. ~M. 91mJil. 27.93. 28.95. 3.72. 1.73. 0.91. 0.13. 0.02. 0.06. 1.If. 26.78. 28.02. 4.33. 2.11. 1.16. 0.86. 0.02. 0.07. 1.lf-31mJil. 25.78. 27.37. 4.82. 2.39. 1.39. 0.95. 0.03. 0.08. 1~1!. 1.If-61m Jil. 24.88. 26.55. 5.23. 2.77. 1.60. 1.07. 004. 0.09. 1!:...~. 1.lf-91mJil. 24.07. 25.94. 5.51. 3.06. 1.80. 1.17. 0.04. 0.09. Fft~. 2.1f. 2332. 25.30. 5.86. 3.37. 1.98. 1.27. 0.05. 0.10. ;,t~. 2.lf-31m Jil. 22.64. 24.74. 6.11. 3.64. 2.15. 1.36. 0.06. 0.10. 2.1f-61mJil. 22.01. 24.13. 6.33. 3.93. 2.30. 1.46. 0.06. 0.11. 2.1f-91mJil. 21.42. 4.19. 2.45. 1.55. 0.G7. ~~. 23.60. 6.51. 0.12. 3.1f. 20.87. 6.68. 4.43. 2.58. 1.64. 0.08. ~;k.. 23.08. 0.12. 3.1f-31mJil. 20.35. 22.52. 6.82. 4.68. 2.71. 1.74. 0.08. 0.13. 3.1f-61mJil. 19.86. 22.06. 6.94. 4.89. 2.83. 1.83. 0.09. 0.13. 3.1f-91li1Jil. 19.40. 21.62. 7.05. 5.09. 2.94. 1.91. 0.10. 0.13. 4.1f. 18.97. 21.13. 7.14. 5.30. 3.04. 2.00. 0.11. 0.14. ;sH~. 4.1f-31li1Jil. 18.55. 20.73. 7.22. 5.46. 3.14. 2.08. 0.11. 0.14. ::k1f ,{#. 4.1f-61li1Jil. 18.16. 20.26. 7.29. 5.65. 3.23. 2.18. 0.12. 0.15. 4.1f-91li1Jil. 17.79. 19.85. 7.35. 5.81. 3.32. 2.26. 0.12. 0.15. $1-~. 5.1f. J7.43. 19.43. 7.40. 5.97. 3.41. 2.34. 0.13. 0.16. ~if<... .p{#. ¥J;;t!. ti~. (2) J-XJ}ffft ~t1H~.k~ 1i" ~JitFft{tjt {ijt;. !!.1!:... J}f fft M{~ .k ~p fft 'Jl ~.A 9/- 1!:..{~ .k ~~ , 1& 4t~ it 'f ~ til 'Jl :l {~ .k 1ft ~ , ~~.;k.~.k.OCrlfJ~.k~~· • • '.llfJ.1!a~·*~m.mlfJ J}ffftM{~.k~ A ~ r ~1i"~'Jl :l{~ .khrtJ:. -1m{~.k ~tA lfJ~l~£ J ' j[~.A~!:.. t..~. ~ :l.~ ;,t # ~ ;,t ~1!:..:fEl f.t Jit fit •. tlfJ. ft{#. £'1". KJJit. :Jt it!!. 'f Jt lfJ J}f fft 'JJ{~ .k lfJ 1(: A ' -kn ~;,t ~{~ .k lfJ JitFftli(Value-at-Risk, VaR) ji~ ~1;- m*-1(: A ;,t ~lfJ J}f fft 'Jl{~.k. ' I!I ~1f i! 1m 1~J.:r-.p , ~11 ~;,t ~. A::k1f;,t~'~~~~~~.klfJ • • ~;k.II!I~*~~~.k~~t;~£~. £~*-~.#fftM~.k·~7~til.{#~MA~;,t~~.~~M8*lfJ# fft'JJ{~.k ~~. :.

(30) 30. Journal of Financial Studies Vol.17 No.1 March 2009. ------. f.~UH.ll.. ,*~~.f.. =x. ft ~.f. if' .f.. =x.1t 71" ~ z:.. .f.. ;t1t~.f.. Gaussian copula. 7.1252. 2.7616. 1.7910. 1.4963. 2.2130. double-t copula. 7.5615. 2.813. 1.5478. 1.2031. 3.3477. .#B• • ~~~A~~' • • • • ~#BM.~A~ • • ~m.~ -*-.1fBifJJ;fjl ~.t:.At~ , iJJ.l!p .1fBifJJ;fjl ~~ ~1f lB ~;/1:. ~.3--~ -*-~ .1fB 0. M.~.~M~.~.~~'.*. •• ~-*-~~~* •• '~~A1f.~. ~.£.~.~~'#B • • ~~~ • • m~. •. .3--~-*-. jtJil~~A+. $J.A.t:~.jt.~. 0. *". •. •• ~-*-~lB • • ~oA~. ' *3(~ tJ-M.1fBM;fjl ~.~"'.f.A.J;~AfBifJJ;fjl ~ 8 A • • • • ~.3--~-*-~~it.JfIJ. a .t:..1fBifJJ;fjl. ~$:. •*" 8 .t:..*t. 92.05. 59.70. 37.41. 2.46. 93.77. 51.60. 30.08. 3.72. Gaussian copula.t:. ~ , .1f B.;fjl ~M oft. j1 ~ -*-il-t iii It 92.05%~ *.;fjl ~ , .rTJ ~.::x 1f ~-*-~7tf.t ~-*-iJJ.M~ }JIJ il-t 59.7%' 37.41%~ 2.46%~*.;fjl~ ~7tt.rPIT1t"'.t:.ifJJ~;fjl~$ , ::3:, f.t~-*-~7tf.t~-*-.~$~~~~4 • • j1~-*-AA'~~.#BM.~ *~~M**' • • ~-*-.~~.t:.t.r~il~~~A~~.~'.rTJ~.~~ .~f.t~.~.h,~*.j1~-*-.*.~.t:..~ • • *.~.~f.t~. ~ ~ ~o , ~. 0. • •. ;fo7t1f~.7f<.lj;fjl~.t:.#t$A~' ~~3!'=".~.~.1fBifJJ;fjl~*~*' .~.l.L~~~~J~-.~~~.~o. *' *3(*JJi' ••. • ~-Tl!~~.i!.t;f* double-t copula ~-*-~7t1f~ -*- ~ .1f B.;fjl ~ $ laJ:fl.tl Gaussian copula PIT 1~ flJ .t:..*t ~ A A ' .rTJ::3:, f.t ~ • ~.1fBM;fjl~$JI'J.+ ' Jtl::.j-6 ~~;flJ mM ~;fjl ~$."1t ~lel1t JiLM-~PIT q.f£fJ.~*-ft. 0. J:.

(31) Journal of Financial Studies Vol. 17 No.1 March 2009. ~ tA ~*J,5f.ll;lf ~.Il:t.Af 1fi ltJU~!k:f'. ~ £,bJ! ,. ~. fil1t ~f1fi hH~. ~~. t~!k. 31. IN iif *-1f~1t ~1f 1fi It.,ij. a!k~.~ • • ·a~~.ll;lfM.~*J,5~*1fiMa!k:f'.~.ft'~. ~ 1t ~ qf 1fi It.,ij 4~ !k :f'. :flil tt:l.it-1t II ;If M1f 1fi It.,ij 4~ !k :f'. ~ . . . ' I!p iif *- lli ~ 9 ~.~*. .. tlHf~. 9 ' .qf1filt.,ij4~ !k-ft-1.. ~,tij-~)(. r ' llJ! 1t~~lAt' • •.fi;t. .~mM~a!k:f'.M*1f~.~ • • ~~,~~ • • *~~.a~~*r fit, ~1OO=-k1f1t4-~;t.1l1t~~tAt' • • JI'1.fiiE.'t·tij-~)(.r ~~ , ~tl.~ *~~.a~*~*o M~~Ma*'m1OO1t~~#1fiM~!k8~ • • 1t>J'J~ 12.92' 8.38' 5.25 ~ 0.35 ' ~1t~rB'~:flilifJ.itfft.l.J(.i"~'l' , ~7F .*1fiM~!k-ft-1..*'~~k*-«4ft.fi.;t.~1t4-$iif • • ~tA~~ !k o • double-t copula ~ r '. 1tij4~. ~. i" .i..JJilllt 1t4-~1f1filt.,ij4~ !k:fJt'~:f'... ~*~.a.~,~~1t4-.~*~.~~~~o~~~*1fiM~!k~a. fft;flf" ~ £,bJ! , double-t copula r ~ lllt 1t ~~ ;t.1l1t 4-aI'ir1~:fIiI if.fi Gaussian copula ~ r ~A ' £.:I.it-=-k1f1t4-~afftJl'l:fliltt.fi+. ~. .~.~+~.~. ... 0. ar'lllt1t4-~:flilttafft,.~*~.a~. ~&./~' ~~~iifM"~4f1filt.,ij4A!k~-ft-1..xtm.A"~ r e. .... JJiJ 4~!k' ~~lllt1t4-~#~_1t*.,tt~~!k-ft-1..~~4~~~1f.fi~;£.:I.it ;k1f1t~. , JI'l ~ ~llJ!1t~'?&~t4A!k~~h ~/l' , 1't1f;k«~~if~4~!k. ~~4~~A • • ~'~~.M~.M~:fIiI.J.itI'ir.fi~o. • • ~~~*,. r.l1t. *~-ft-~~~~1t4-:fIiI~'llJ!~~.~*1fiMa!k~-ft-1...fi~.6'~. 11.:. Jl:l:.;flil Jt Ji1..fft J\t ntl ~ • Jt.fi ~ ~ ~ 4-+. , =-k '~!k ~1lf ;r~ ~,. • • j.A~M~ ,. 'fl!~ .1!f:-~t1... 0. '. 1tll;lf~.Il~e.""JJi4~ !k(realized loss). .~~1t~~:flilttafft~~~.Jt~.~oe.""~~!k.~ttllJ!1t~xt m.~~,~~~*fIt~llllt1t4--ft-1..a!k~~4~~·&..~1l1t4-'. 'f e. .... JJi4A !k 1f,,*~ =-k/llft 1'l'!.1t m1lf- tl;f (subordination level)* ' i" ~ ntl ~4A !k-ft-1..~.:f'.':flilttafft~~.~'A~e.""~~!kM~-ft-1..~~«1t~ *,~«1t4-*i"~-ft-1..~!k~~4~~fIt~'.1..:fIiI.al'irrflt~~m·. ;r~. ~9~7F''f*1fiM~!k-ft-1..*'.lt1t4-~.~.''.fi;t..~mM~~ !k:f'.M*-1f~.~ • • ~'~A~ • • ~*M~.a~*rflt'~1OO~«. fPIT. 1t~~;t.1f1t4-~lA~ • •M.fiiE. 't'tij-i)(.r ~. t1t. ~*. a. £.M~~J'Jlt.,ij. a* '. ,. ~tl.~*M ~j~l&~itJf. m1OO1t4-~qf1filt.,ij4A!klA*,f$-.1t>J'1~. 12.92'.

(32) 32. Journal of Financial Studies Vol. I? No.1 March 2009. 8.38, 5.25 ~ 0.35 • ~1i- -*-lB 1t Ji\.F,lt{#J.!. lHffi -1- • :fl7fq'fAffjOtH~ #df-1. at . ~~~~«~~_.~{#J1i--*-~~. {#Jil A/f. •• ~.*{#J.~o. ~'~~~.~ •••• 1i--*-~.F,lt1i-#. .ji. ~~. .~~~.~ • • • • 1i--*-.F,ltat·1i--*-#~A~*.m* • • {#JJi\.. •• ~.~{#Jftm~~~.a.~~.-.4~ftm~~~ .(single-name credit default swap)*,i!,ft.F,lt ° *tJ.1~ m~~ ~.~~. 'f1'¥ .~L~'m* •• {#Jk.B«~~._~.{#J.4~m • .!.~ata~{#J Ji\.~;~rt.-.L~m~~~.~.~L~at·~* •• {#Jk~~.{#J nm • .!.~.~A~~{#JJi\.F,lt'~a~~{#J.~LA~.~{#J~*~rt* ~ ~ 4~* {#J .!. .J4 tJ. r ~~ ~ Gaussian copula $!. double-t copula ~ a 1El-f ~~ ~ F,lt.~'._. J:/J. ~(. .1:1 at·. .N. I!lA. 0. M.r·~.~1i--*-{#J.F,lt • • ~1i-#.F,lt~*·A~_~~.F,lt.4m. rt* °. 41. {#J. .1lt1f-*-• • ~ III JR.* ~.~1b{#J1~ m~~ ~4~~~.~ iii"co • -kG DJ CDX NA;fa DJ iTraxx Europe ~ , 'f~~~.1*1t.i~1i~~1l{#J.{#Jki!~~. m. ~~~.a.at'a.A~ • • ~mUa.i!ff.~'A • • J.D{#J. ~~.F,lt • • {#J~A'~.~~~.~ • • • • ~1i--*-~.~~~Ornoc~. Delta). 0. *-9. qf fMtlJ 4jt ~ {#J tA ;f.'f~ •. .,. ,jt1}. 31illl 61illl 91ilJl 11f.. I1f..31ilJl 11f..61ilJl 11f..91ilJl 21f.. 21f..31ilJl 21f..61ilJl 21f..91ilJl 31f.. 31f..31ilJl 31f..61ilJl 31f..91ilJl 41f.. 41f..31ilJl 41f..61ilJl 41f..91illl 51f... 27.45 24.98 23.26 21.91 20.80 19.85 19.02 18.28 17.62 17.01 16.46 15.95 15.48 15.04 14.63 14.25 ]3.89 13.55 13.23 12.92. doubltt 26.19 21.42 19.62 18.52 17.91 17.24 16.78 16.33 15.93 15.52 15.16 14.81 14.44 14.13 13.84 13.52 13.26 12.94 12.68 12.40. Gaussian 6.92 7.72 8.11 835 8.50 8.60 8.66 8.69 8.71 8.72 8.71 8.69 8.67 8.64 8.60 8.56 8.52 8,48 8.43 8.38. double-t 5.59 5.26 5.18 5.24 5.33 5.48 5.61 5.75 5.88 6.01 6.13 6.24 6.35 6,43 6.51 6.59 6.65 6.72 6.77 6.82. c..~. Gaussian 2.78 3.38 3.74 4.00 4.20 4.36 4.50 4.61 4.71 4.80 4.87 4.94 4.99 5.05 5.09 5.13 5.17 5.20 5.23 5.25. double-t 3.56 3.47 3.36 3.32 3.31 334 3.37 3.41 3.45 3.50 3.55 3.60 3.65 3.70 3.74 3.79 3.84 3.89 3.93 3.98. 1}~. Gaussian 0.09 0.12 0.15 0.17 0.19 0.20 0.22 0.23 0.24 0.25 0.27 0.28 0.29 0.30 0.30 0031 0.32 0.33 0.34 0.35. double-t 0.16 0.36 0.42 0.45 0.46 0.47 0.47 0.47 0.48 0.48 0.48 0.48 0,48 0.48 0,48 0.49 0,49 0,49 0,49 0.49. ~;f.

(33) 33. Journal of Financial Studies VoU7 No.1 March 2009. t~,. 't~._.M~{fJ~~nffl.~~~-.£D~'~~ • • ~._.. {fJrfl.tf1.{t(mark-to-market value)" L!l ~ A~~~oa~~ffl~ •••• _.{fJ~. ~ {fJ ~fIJ. '. Jl~~.~fIJ{fJ tiJ.t. •• {t~fIJ.*~.~~.~.. ~~~'~*~*10ffl~°'t • • _.{fJ~~nffl.~~~-.£D~'. t {fJ lit. X ~ 't11= ~~!J. .~{fJ. Al{fJ ,~* .Jf~.. .~PlT. .+ '. .A~.ffl~~{fJ.~.*'~~k~~~.'~~«~.M~~{fJ.~ ~ rfl.tf1t{t~1t.+ilt-l.f..+~ • • _.*h {fJrfl.tf1. {t ~1t.+iJ.t. -t±. Gaussian copula r '. .A~.''/HJ}{fJ. 0. '1\*$-t-Jt~!!. Delta 11;-15.5547. • • • _.t.{fJ.Lnffl.~~fIJ{fJlit~'a.A~~IA~.{fJ~ ~ ,r ttl:: J ~ 't~.A ~.*~ 15.5547 -H}~tJi {fJ. {fJ1t ffll!#J x~• .tlii tt 0. .~4*~.~~~.~~~M~~~.M~#{fJnffl.~'~~M~# OO~{fJnffl.~*,.~*~~.q_~tt~.£~~M • • ~ • • • ~tE1 ~M!!~. x. 0. * 10 .Fft$.tt -~. DELTA. (~fIJ-.£D). CDX {fJ~. mche. ;i/U.4t.§.. 9 9 9. Delta. Gaussian. double-t. Gaussian. double-t. Gaussian. double-t. -0.0200. -0.0235. -0.6667. -0.7833. -15.5547. -18.5014. .§.. -0.0118. -0.0117. -0.3933. -0.39. -9.1456. -9.1920. -0.0087. -0.0066. -0.2175. -0.165. -5.0803. -3.9118. 7I:.1.4t~. -0.0006. -0.0093. -00107. -0.0103. -0.2503. -0.2430. tUIJ. A..m%. -0.0428. -0.0424. -0.0428. -0.0424. N/A. N/A. ~T ~.Delta. 8 8 9. 4t~. (%). ;k ft 4t .§. z:. .§.. ;kft4t~.". !6 12 15 16 17 17 17 18 18 18 18 :8. 1t11~thJfl.. ifrJj1l1t~th (a~it.). '1t ffl. $'r- '. *30i!-~;jt.~.{fJ. _.. -. Gamma'. ~*. 11. ffl~. 0. ~. .{fJ Gamma ~.l • • • _~Jl{fJ~~1t ffl1.~~fIJ-.£D~'~~.Delta ~fIJ{fJalt' f~Hr.:ft~.Fft*~~ 'Gamma {tkvt•• Fft~li-~~-t-{fJ $.~.t~.. 0. * 11. ~.. .Fft$.tt. Gamma. ftffl1l.l~th. ftlll1Ut~th. 1 bp 4t ~ Delta. 10 bp 4t.§. Delta. 4t~. Gamma. Gaussian. double-t. Gaussian. double-t. Gaussian. :i/iji4t~. -15.55. -18.50. -14.83. -1733. 0.08. double-t 0.13. ::kft4t~.,,~. -9.15. -9.19. -9.07. -9.33. 0.0089. -0.0155. ;kft4t~z:.~. -5.08. -3.91. -5.18. -4.12. -0.0111. -0.0233. 7I:.ft4t.§.. -0.25. -0.24. -0.27. -0.26. -0.0022. -0.0022.

(34) 34. Journal of Financial Studies Vol. 17 No.1 March 2009. * 11 MiF ' ..(£ WJ It I!l.:r.it iHt *4r ' .11 ~ 4t1f iE. fI-J Gamma fi ' * iF 't ~ mitt£, til *- fI-J fi li ~ *- ' ~ 4t fI-J Delta ~ f.t fi f" ~ + ' ~ f)' M-ff: ~ ~ 4t~.~fI-J.~~~ • • *~.~fI-J • • ~~'MSfI-J.~_~I!l~~ j;' • ;.k1t~4t~4t~;tit~4tfI-J Gamma fi~ ~ , 1~* 't1t mil :£tIl*-fl-J+i li@*-'~4tfl-JD~a~f.tfif".~~*-'~.~~~4t9~.~fI-J • • ~ /;0 ' I!l Jl:I::.M S fI-J. fiH~1l'l. ~ *- • ;.kit ~ 4t , 4t..(£ WJ It#f; ~ r fI-J Gamma fi iE.- ~ 'Mi!:.I!l~WJlt~~~~t$-~~4tfI-JlitFit~la~1fM;Y;:M ,..(£ Gaussian copula r;.k it ~ 4t, 4tfI-J litHt.t.t double-t copula r *- ' I!ll~l::...(£ Gaussian copula r;.kit ~ 4t , 4t f" ¥.. Jji m~~ ~.1,1 ~ 4t fI-J lit Fit 4t W Gamma ~ iE. fi· 't• • • • fI-J~m4~~.~.#..(£$-.~*'~4tfI-J*1fA~rt • • ~~.~ff~~fI-J.Fit'~~~m~m4~~.~.~ff.Fiti!:.-.# .'.fI-J.Ht.4,rtrM~#~m~m4~~.~ • •HtfI-J.*.MS 1t. .. fI-J RX. *" • -ft,1l"1 M Gaussian copula I!l.:r.~ *4r fI-J • Fit #$ * ~IJ $-* 12 ' double-t copula 1!l.:r.tt*4rfI-J.HtMi*~ll:&?-* 13 'f, *'ffI-J~":::"~ll~~~ 4t fI-J jtl} :fJ] ~ 111 *" ~ ~ fit ' ~.::.. ~!1 ~ ~~ 4t fI-J 1t m11:£ ' ~~ 4t fI-J Delta fi ~Ij :&?- ~ 1!!1 ~'l ' ~ .E..~ll fI-J PVOI fi1~* it• • • 'f 'I A.~-tU]1t m11:£ ~tIJ-100 !-..J5 * ~ ~ 4t I .1t*" ~ fI-J 11fi ~ tIJ • it;t-ft,1" M~ ~ 4t fI-J Delta fi ~U). ~ ~ 4tfI-Jjtl}~~I1I*"~'t~.m~~4tMSfI-J.Fit_~~fIt~*'f~*~M iF)·~T.ff.HtfI-J.*,-ft,1l"1..(£ • • • • fI-J-tU]~m1l:£~tIJ-.!-.D fl-J1f1"t~r. • • ~~~1l'l. fI-J • j~1lfi ~ 11::. ' ~IJ:&?- * 'f fI-J ~ -t: ' ~ A ~Il ' Jt. 'f ' M ~ 4t ttA:fJ] ~~1l'l. * J.::J. ~4t~ PVOlfi~1"'f'J ~4tfI-J.~1lfi~1t.f:; M.Ht~~~*J:..1t • • •fI-J PVOlfi~ *~.~~~{l'l.fI-J.j~1lfi~1t. :l-ft, -ft,1l"1~f~~4tfI-Jl/tA.(l!p~ ~4tfI-J~m1l:£*J:..~~4tfI-J~I1I*"~~~#.FitfI-JRX.~~ • • fI-J~m '. ~j)IUt.~~4t~ .j~1Ifi(mark-to-market)fI-J~11::.'. 0. .:£.J:..~~4tfI-J.Fit_~)'*.m*'f~~~fI-J~4t~I/tA.':l.-ft,1l"1 M~4t~I/tA.~rtU~4tjtl}~fI-J~I1I'lA.,~~~~~4tfI-J • • • ~f l~l::.. 111/ • J.::J. t!. .J'!; fI-J 7i t(. ,. * iF $-* 'f fI-J :l-ft-. ~IJ. 0. '-ft,1l"1 u..(£ 1§1j -st Gaussian copula. r ' .1,1~4tfI-J Delta ~-15.55' 1~*;6--t-~~:m.3 alJt*"~fl-J4~~JitFit, ~~Ji:&?-I A.~4t*, t m ~ 46.66 a 1Jt .1tfI-J1t m 4~ ~ • .t~. ~f.1,1~4t ~ PVOI *J:...j;i~4t~'A:fJ]~~1l'l.' ~1"'f'j.1,1~4tl!ll~fI-J'l A.1t m. ~ tlJPJfli.RX.~ .~1Ifii!t ~-20,OOO ' ~ .~~~1l'l.1!l1t m11:£ ~tlJMli.RX. fl-J11 fii!t~~+20,OOO ' .Fit_{l'l.1IfifI-J~/;u·t**~~ll1,1~4t .~1Ifii~.t~ fI-J 0. ~~. fI-J fI-J fI-J ~.

(35) Journal ofFinancial Studies Vol.1? No.1 March 2009. 1.'* ~ i.a; 7t IJl:I::.i~ ;.aH~. ~ if'-:l1t. ii lssian lsslan i.a;.iE. .fJ.:1! 1m~f. ·PlT1t 12 ' ~7t. ii?'j -1m ~7i. ?ljPIT Is..l'.; .g~1rc.. *fJ. mtr-J !!r~ ~Jfl. ~1r'l ~1r'l. pula Fit' ~;f.. ~~. r!J1. ~tr-J. 35. ~7t' I~HtA~P.~,l!!fFit~l:.M Delta .it.fTl!!fFit"TfJ..i!jIJJt~l!i!Fittr-J~* l£l!!fFit tr-JT£*"J:.' -tll.17t;f.tr-J*"~4i}-1f-"TfJ.~tjljI487bp tr-J~Jfl1.£' m:rl!!fFit.g~1rc. 0. tr-J*"~4i}-1f-1t~#OO~tr-J~Jfl~£'M7t;f.~A~~l!i!FitT£*".'l!!fFit. tr-J-tll.17t;f.*"*4i}-1f- "T J.'J.~jlj 553.7 bp tr-J1$ Jfl1W £ ' l!!fFit T£*":fEl of$-4i}-1f 933.3 bp , aHl:. "T Je.. DeIta l!i! Fit it -1m T£ *":fEl of ~ tr-J l!!f Fit 1ft ar3 0. 1£ double-t copula T . *$- Jf A7i-;f.* t tI:l ¥J 55.5 1i;¥; j(.tr-J~tr-J1$ Jfl it ¥J 5t ~.t~ tt ' jllj "T 7t 1:- #i l!!f ~ tr-J 1$ Jflit ¥J 5t {i.t~ tt1$ Jfl1. £ ~ fIJ ..i!: Jit Fit 1£ double-t copula tr-J 1~l~ T ' -tll.17t;f.4i}-1f- "T J.J. ~ jlj 1706 bp tr-J ~ Jfl1. 0. £'m:rl!i!Fit~~.~#4i}-1f-oo~tr-JnJfl~£'7t;f.~A~~l!!fFitT£*".'. -tll.17i- ;f.4i}-1f- "T ~t~ 595.9 bp tr-J n m1. £ ' :fEl of $-4i}-1f- 111 0.1 bp , ~ Gaussian copula :fEl ~l:. ' li l.17i-;f.1£ double-t copula ..i!: T tr-J l!!fFit T£*".fX ~ 0. 1£ Gaussian copula T ' ;;k1t7i-;f.,. ~l£M:.1J]tr-J Delta ¥Ji.a;(-9.15) • i\* *.f.Jt~#il!!f 3 1i ;¥;*"~tr-J1$ Jfl JitFit' ~Ji t tI:l ¥J 27,441i;¥; j(...i!:~tr-Jn Jflit ¥J 5t ~.t~ tt l!i!Fit T£*"l§ ~ 17) ~ Jt.;t'J Jfl1$ Jfl.t~ tt-i:t" Delta l!i!Fittr-J:Ift:k r", ~'*12M~'~~~~7t;f."~#il!!fl.-tl • • nJfl1W£~flJtr-JJitFit, l§~tr-Jl!!fFitT£*"~M • • 7i-;f.tr-J~~Ai.a;.iiol!!fFit.~~7i-;f.";f.4i}-1f 1t ~ 1t 74.7 bp tr-J1$ m{. £ • :fEl of$-4i}-1f- 548.7 bp tr-Jl!!fFit T£*" 0. 0. * 13 M~ , 1£ double-t copula T ' ;;k ~ 7t;f. ,. ~4i}-1f- "T ~tjlj tr-J 1$ Jfl1. £.R 1f 364 bp' 1]!l!i!FitT£*"4i}-1f-?1r~.i! 551.5 bp , 1~~l!i!Ht1t;;k1t7t~";f. tr-J ~iJf- ~ A i.a;. ' 4i}-1f-1t ~ 1t 187.5 bp tr-J Jfl1W £ Jt.1t!!. 7t ;f...i!: 7i-:fIT ;;7 t\. iJJ' :fEl ~ , 1£ Jl:l:. ~ .jlj. .. 1t 0. 0. *. ~ ~ J:.1t ..i!:.#i * ' t tI:l ~ tr-J n Jflit t;~ 5t .f!t.t~ tt .it..fT Delta l!!f Fit. ~ "T ~.i!~7t~l!i!Ht,~l§~tr-Jl!!fHtT£*"M~~.7i-~~~.7t~l£l!!fHt.tr-J ~ A i.a;. ' jt ~ it -1m -lef tr-J l!i! Ht 1ft ar3- ' .R 1f 1t-tll.1 7t ~1ij: Delta l!i! Fitit ' l!i!Ht.tr-Ja • • ~~&._.iEtr-J~~AoA1r'l~.7t;f.tr-J_1fAttl:l. .4nmlt¥J5t.f!t'~#il!i!~~~tr-J~m~£~flJtr-JJitHt°~$-.-.4 nJfllt¥J~.f!t..i!:l!!fFit.tttr-J~.'~."T.l§.if'-~4*M'~.~~~ Jfl.¥J~.f!tnJfl~£~fIJ.$-7t~ • • ~ii..i!: • • ,jt~.~~Jfli!¥J~. *. .f!t*"~..i!: • • ~ii~fIJ':Ift • • l§~**"~..i!:~.~ii~fIJ.&~tI:ll!i!Ht ~l:.M Delta ii -~m:r ,7t;f.1t~.-1$ m i!¥J ~#~·..i!:1. £ ~fIJ~~&-t ~ 1~ 1$ Jfl1. £ *" ~ i.a; + ' IN Jl:l:. Delta itit '*" +$- l' tt.:lt $-;;k 1t 7t ;f.~ ~ 1t 0.

(36) 36. Journal of Financial Studies Vol. 17 No.1 March 2009. ~~~aWA~~·~m. **-ilJ'J -. ~~.~~i*. -W.nm4~~M.~~~f.~~.~4 0. .J.1))-4f.. ~k it ))- 4f. ,. ~k it ))-4f. l... 7t:.it.ft4f.. Wl:;J}~~1$/. (a ~;it.). 3. 3. 4. 90. 1t!fl1J.t. (bp). 1487. 474. 202. 7. '(Tranche Delta). -15.5547. -9.1456. -5.0803. -0.2503. PVOI. 0,006667. 0.003933. 0.002175. 0.000107. ll!iNr~~1$/. (a ~;it.). 46.6641. 27.4368. 20.}212. 22.527. ftii.lfth (n bp). -20,000. -1l800. -8700. -9630. ll!il'itftii.lfth (il bp). 20000. 11800. 8700. 9630. ))-4f.M11Jii.. 166115.4. -22420.8. -41127.2. -72162. 553,718. -74.736. -102.818. -8.018. 933.282. 548.736. 304.818. 15.018. ll!iNrIt.1~1. .ft4f.i~~tA. (bp). ll!i1'it~A... Wl;fJ}~~{$l. (a ~;it.). .J.1))-4f.. ~k it.ft4f.'. "k fl.ft4f.l... 7t:.it.ft4f.. 3. 3. 4. 90. 1t!fl1J.t. (bp). 1706. 364. 137. 9. i!l!Nr ~1:.1~J (Tranche Delta). -18.5014. -9.192. -3.9118. -0.243. PV01. 0.007833. 0.0039. 0.00165. 0.000093. i!l!Nr~~1$/. (a~;it.). 55,5042. 27.576. 15.6472. 21.87. ftii.lfth (p bp). -20,000. -11800. -8700. -9630. i!l!Nrftii.lfth 01 bp). 20000. 11800. 8700. 9630. ))-Mtflii.. 178774.8. -56256. -39083.2. -50220. 595,916. -187.52. -97.708. -5.58. 1110.084. 551.52. 234.708. 14.58. ))-4f.*~tA. (bp). i!l!1'it~*-. .l. 7.. I ,.

(37) Journal of Financial Studies Vol.17 No.1 March 2009. rttJfX.. .1-1:. "r.zz-. ... ~,t.. ,--0. *,51:. it;t,tH~1t-~JJJi.{f.Jir.H~T '. ~).. 37. ~A. "1IlJ. Hull and White (2004)PJT.flttl::~;#'\2fi. ~4*M~.+JfX.~.~ •• ~ ••• ~.~~~~~,·~*~~·n. ffl1l :£ ~..f)\l:fJT t(semi-analytic)lt11 ~~ ~. 0. ;fu 'f ~ ~ ~(, IE +. lfn ~,~. T {f.J. W1lM*~~·*,~~*~'#l~tl.~IE+.«;#'\2fi~~~.4_ • • ~~~~~~~~'M~ •• ~.nffl1l:£T~~;t«~.nffl1l£~. f!-'. J\.~*M{J;{m-JfA..rIlH!lnM't1pt/JtJ; #;Jf~~It1.~IE+JlIl1:t. Student-t. ~~~'M~ •• ~.nffl1l:£~f!-~;t«~.~nffl.:£T~'~*M. 1J;{m-Jf A.. r"'.t!l nM'tiFt1~ of ~ ~a;Jf ~ ~ IE + ~ JlIl«4_•• (f.J Student-t ~i!i(,B~' ftm-•• ~.~1; , ;Jf~~lti.~IE+ftm-~.~-f.}f!.t!lftAm 0. l~tl.~IE+'IE~W1IM*.~J\.nffl1l:£1E~/JtJA;;t«~.~~ ~tl.~IE+~-f.}f!~ •• A'~W1lM*.~J\.nffl.:£IE~TFto~ lJ=.1"~.fHt1l.1JiHt~tti~.~£i1!~. Gaussian copula IE +~~ , ~ ~1r1."t~ IE + ~ l\t ~tt ~ -'-- 'f• ~ , Gaussian copula ~ lt1l .~t * 11.11. i" ;ff • • ~ • • ;t«~ •• :£•• ~.1I.'~~«~.1I:£ •• ~.1I~{f.J*m·*, 5I:.*Jji*~ffl double-t copula 1E+i!~.~.*.;ft+JfX.~.i*1t.i~.~ W.'i"~.~*.tI::{f.J ••••A•• ~PJT •• ~{f.J •• ~.~· *,5I:..~.flt*A.tl.6&~:fJT'~.~.IE+i!~M • • t . Gaussian copula. double-t copula ~ T ' .~ IE + ~ l\t ~tt(factor loadings) A@1{12fi(recovery rate)~m-~.1t fflil:£ {f.JJjf! bJf~.~ **Jji' ~tt.~ • • ;t«~.4~.-'-IE+i!~M.~T'.~IE+~l\t~.A@1.2fi.m ~.nffl.£~-f.}f!M~:.m- •• ~.~1;'nffl • • ~~@1.2fiI ~~~~~A.~IE+~l\t~tt~.I&~~~;.m-;t«~.~ ,n ffl.:£A~~@1.2fiI&~~~~ •• ~IE+~l\t~.I~~~~·&. ~«~.'4~MIE+i!~M.~T'J\.nffl.:£~.~IE+~l\t~ •• 0. @1.2fi~.~-f.}'MI~~-a{f.J~ao. J\.~*,5I:.*.~~:fJT~M{f.J~ • • ~.t~.obJf~M*.~I~. ~~~~~~&~i"~~.***±~~~.~T~'~~.{f.J~~~~ .M~~~~i"~~.~~~~{f.J.~~f!-ou •• ~.~~,.m-J\.2fi.

(38) 38. . Journal of Financial Studies Vo!.1? No.1 March 2009. ~*.~m~~~. •••••~.~.~'~~~.~~*M~.~a~. ·~'~~·~.*~~-~.~~*~'~~~.***~.~~~4. ••. ~~~.'~.~ •• ;~~.A~ •• ~~~~~.~~~~~.'~ .A~.~*M.~.~~~.~.'~~~ ~.~~~&~~~,. 1. ~~~~~.~a~.~.*M.~~~*~#'.~~*.~M~d~ .~*'&~*.~A_~.~~~m~~.·~~~.~&~~.~* MA**~kA&W'~.*~.a~ ~~.~·. ••. ~~'*~~M~~~~M~~~~T~ff~.~~~.~*.~~ ~~~·~~*m+4~.~. ~~WA~~'A~.*'*.~~~ tili • • ~m~~.~~ma.*~~'.~~~~~~m« W.~& ~'~~.~~~4*~~'~~~~.~~«~.~~WA~.~*~. A'. '. ~Jt.Jt~f-11i1~ff~.~~~· *~~1l ' .jiWA~.A~.* ~ :f1 mt ili Jf..- • ,i.1~ m~~ ~.ji~ff~~ Jtl!.tf Delta 1i.~~Jf..-1~ m. ,. •• ••. ~~~.~A.~~A~*.~~~~§~·~A~~~ A~ ~ ~~m« W.~.6.4'.~~m.-~m~~~.*.~A.*~. •. ~~~ •••• ~m«AW.~&~'.~4*~ ••• 'A~.~4 .tf.~ • • 64.~~~m.~~.~A~~~A'ffl~&A.~~~~. ~rt*·. ..

(39) Journal of Financial Studies Yol.17 No.1 March 2009. 39. 1;.=txltJ:.. :..JitFit l~hi .. , -(f. t fij. 1. . ,. default and recovery rate: theory, empirical evidence and implications,". ~lt~ > Jt:.. ~#)~. Journal ofBusiness 78, 2203-2228.. I. 2. Andersen, L., J. Sidenius, and S. Basu, 2003, "All your hedges in one basket," Risk Magazine, November 2003.. ~$tl! ~ I:I:AJlj. Altman, E.1., B. Brady, A. Resti and A. Sironi, 2005, "The link between. 3. . Andersen, L. and J. Sidenius, 2004, Extensions to the Gaussian copula:. I~Jit. random recovery and random factor loadings (working paper, Bank of. ,~I/t. America).. '''1" ·~m. 4. . Black, F. and J. C. Cox, 1976, "Valuing corporate securities: some effects of bond indenture provisions," Journal ofFinance 31, 351-367.. 5. . Bluhm,. 6. . Burtschell, x., J.-P. Laurent. and J. Gregory, 2005, A comparative analysis. ·1t~. i"i:: '£. hi!! ~l!. c.,. L. Overbeck and C. Wagner, 2002, An introduction to credit risk modeling (Chapman and Hall).. of CDO pricing models (working paper, BNP-Paribas). 7. . Cifuentes, A. and G. O'Connor, 1996, "The binomial expectation method applied to CBO/CLO analysis," Moody's Special Report, Dec 13 th •. 8. . Duffie, D. and K. Singleton, 1999, "Modeling term structures of defaultable bonds," Review ofFinancial Studies 12, 687-720.. 9. . Frey, R. and McNeil, A. 1., 2003, "Dependent defaults in models of portfolio credit risk," Journal ofRisk 6( 1), 59-92. 10. Gibson, M., 2004, "Understanding the risk of synthetic CDOs", FEDS. Discussion Papers, no. 2004-36, Board of Governors of the Federal Reserve System. 11. Greenberg, A., D. O'Kane and L. Schloegl, 2004, "LH+: a fast analytical model for CDO hedging and risk. management;~. Lehman Brothers.

(40) 40. Journal of Financial Studies Vol.17 No.1 March 2009. Quantitative Credit Research Quarterly Report.. 12. Hellqvist, M., 2005, Comparison of approximation methods for combinations of differently distributed random variables (Mat-2.108 Independent research project in applied mathematics, Helsinki University of Technology).. I. 13. Hull, J. and A. White, 2004, "Valuation of a CDO and an n-th to default CDS without Monte Carlo simulation," Journal ofDerivatives 12(2),8-48. 14. Hull, J. and A. White, 2005, The perfect copula (working paper, Joseph L. Rotman School of Management, University of Toronto). 15. Jarrow, R., D. Lando, and S. Turnbull, 1997, "A Markov model for the term structure of credit spread," Review ofFinancial Studies 10,481- 523. 16. Jarrow, R. and S. Turnbull, 1995, "Pricing derivatives on financial securities subject to credit risk," Journal ofFinance 50, 53- 85. 17. J arrow, R. and F. Yu, 2001, "Counterparty risk and the pricing of defaultable securities," Journal ofFinance 56, 1765- 1799. 18. Laurent, J.P. and J. Gregory, 2003, Basket default swaps, CDO' s and factor copulas (working paper, ISFA Actuarial School, University of Lyon). 19. Laurent, J.P. and J. Gregory, 2004, "In the core of correlation," Risk magazine, October, 87-91.. crol. mel con mal the. 20. Li, D. X., 2000, On default correlation: A copula function approach (working paper, The RiskMetrics Group), 99-07. . fact. and. var. 21. Merton, R., 1974, "On the pricing of corporate debt: The risk structure of interest rates," Journal ofFinance 29, 449-470.. Ke:. 22. Peretyatkin, v., 2006, HPM+: a fast analytical model to pricing synthetic CDOs (working paper, Imperial College and Rabobank International).. , A,. U. o i.

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