CHAPTER 12: SWAPS
END-OF-CHAPTER QUESTIONS AND PROBLEMS 1.
(Introduction) Interest rate swas are !"re w#$e%& 'se$ tan 'rren& an$ e*'#t& swas+ ,ea'se near%& a%% ,'s#nesses ,'s#nesses ae ae s"!e "r! " #nterest rate r#s. Interest rate swas are te r#!ar& !eans " !ana/#n/ tat r#s. S"!e ,'s#nesse ,'s#nessess ae 'rren& 'rren& r#s an$ a ew ae ae e*'#t& r#s+ r#s+ ,'t tere #s 0#rt'a%%& n" ,'s#ness ,'s#ness tat $"es n"t ass'!e s"!e "r! " #nterest rate r#s.
.
(Structure of a Typical Currency Swap) N"t#"na% r#n#a% #s "ten e2an/e$ #n a 'rren& swa+ ,ea'se te a!"'nts are #n $#erent $#erent 'rren#es. Tese a!"'nts are e*'#0a%ent e*'#0a%ent at te start " te swa ,'t ,'t n"t %#e%& t" ,e e*'#0a%e e*'#0a%ent nt at te en$ " te swa. swa. In an #nterest rate "r e*'#t& swa+ te n"t#"na% n"t#"na% r#n#a% #s #n te sa!e 'rren&+ s" #t w"'%$ w"'%$ ser0e n" 'r"se t" e2an/e #t. It w"'%$ ,e an e2an/e " e*'a% a!"'nts at te ,e/#nn#n/ an$ en$ " te swa. swa.
3.
(Pricing and Valuation of Interet Rate Swap ) a. In an #nterest #nterest rate swa+ swa+ te art& a&#n/ a&#n/ #2e$ #2e$ an$ ree#0#n/ %"at#n/ as a "s#t#"n e*'#0a%ent t" #ss'#n/ a #2e$-rate ,"n$ (an$+ t's+ a&#n/ #nterest at a #2e$ rate) an$ 's#n/ te r"ee$s r"ee$s t" ,'& a %"at#n/-rate %"at#n/-rate ,"n$ (an$+ (an$+ t's+ ree#0#n/ #nterest at a %"at#n/ rate). A s#!#%ar ,'t ""s#te ar/'!ent+ an ,e 'se$ "r te "'nterart&. (Pricing and Valuation of Currency Rate Swap ) ,. In a 'rren& swa+ te art& art& !a#n/ a&!ents a&!ents #n 'rren& A an$ ree#0#n/ a&!ents #n 'rren& B as a "s#t#"n e*'#0a%ent t" #ss'#n/ a ,"n$ #n 'rren& A an$ 's#n/ te r"ee$s t" ,'& ,'& a ,"n$ ,"n$ #n 'rren& B. A s#!#%ar ,'t ""s#te ar/'!ent ar/'!ent an ,e 'se$ "r "r te "'nterart&.
3.
(Structure of a Typical Interet Rate Swap ) F%"at#n/ a&!ent4 567+777+777(7.78)(97:6;7) < 5=37+777 F#2e$ a&!ent4 567+777+777(7.78)(97:6;7) < 5==+777 Te net a&!ent #s tat te %"at#n/ a&er a&s 51=+777. 51=+777.
=.
(Structure of a Typical Currency Swap) D"%%ar a&!ent4 517+777+777(7.79 .79)(1>1:6;7) < 53=7+777 Sw#s Sw#sss ran ran a&!e a&!ent nt44 SF1= SF1=+7 +777 77+7 +777 77(7 (7.7 .7>) >)(1 (1>1 >1:6 :6;7 ;7)) < SF;76 SF;76+6 +666 66 Ea art& !aes te#r reset#0e reset#0e a&!ents. a&!ents. Tere #s n" nett#n/.
;.
(Structure of a Typical E!uity Swap ) F#2e$ a&!ent4 5177+777+777(.7==)(1>7:6;7) < 5+8=7+77 +777 E*' E*'#t& #t& a& a&!ent !ent44 5177+77 7+777+ 7+77 777( 7(((18=. 8=.> >9:1 9:11= 1=.= .= )? )? 1) 1)) < 53+9 53+9; ;;+= ;+=99 Te net a&!ent #s tat te art& a&#n/ e*'#t& a&s 5+1;+=99.
8.
(Pricing and Valuation of Interet Rate Swap ) Te $ea%er #s #n$#at#n/ tat #t w#%% enter #nt" a swa t" ,e te #2e$-rate a&er (an$ %"at#n/-rate %"at#n/-rate ree#0er) at a rate " 8.;7 @ 7.17 < 8.87 "r te #2e$-rate #2e$-rate ree#0er (an$ %"at#n/-rate a&er) at a rate " 8.;7 @ 7.1= < 8.8=
>.
(Pricing and Valuation of Interet Rate Swap ) Swas are s#!#%ar t" "rwar$ "rwar$ "ntrats #n tat te& #n0"%0e #n0"%0e te "!!#t!ent t" !ae a #2e$ #2e$ a&!ent a&!ent an$ ree#0e a %"at#n/ %"at#n/ a&!ent a&!ent at a 't're $ate. #%e a "rwar$ "rwar$ "ntra "ntratt #s a s#n/%e s#n/%e a&!ent+ a&!ent+ a swa swa #s a ser#es ser#es " a&!ents a&!ents.. T's+ T's+ a swa #s %#e a ser#es ser#es " "rw "rwar$ ar$ "ntrats. B"t swas an$ "rwar$ "rwar$ "ntrats re*'#re re*'#re n" ' r"nt a&!ents+ a&!ents+ an$ ,"t are s',et s',et t" $ea'%t $ea'%t r#s. Tere Tere are s"!e $#er $#erene enes+ s+ "we0er+ "we0er+ #n tat #n a swa ,"t s#$es s#$es " te #rst #rst a&!ent a&!ent are n"wn. n"wn. A%s"+ A%s"+ "r a swa+ swa+ a%% " te #2e$ #2e$ a&!ents a&!ents are te sa!e+ wereas wereas #n a ser#es " "rwar$ "rwar$ "ntrats "ntrats++ ea ea "ntrat w"'%$ ,e r#e$ searate%& an$ w"'%$ a0e $#erent #2e$ rates.
9.
(So"e #inal Word a$out Swap) Tere are se0era% se0era% wa&s t" ter!#nate ter!#nate a swa. A art& an /" ,a ,a t" te "'nterart& an$ as "r an "sett#n/ swa. Te art#es eet#0e%& reate te ""s#te swa. Te& ten "%$ ""s#te ""s#te "s#t#"ns t" ea ea "ter. Te& an ee ee te tw" swas #n %ae w#t ea !a#n/ te#r ser#es " a&!ents+ a&!ents+ ,'t tere w#%% ,e re$#t r#s. A%ternat#0e%&+ A%ternat#0e%&+ te art#es an ane% te tw" swas+ w#t te art& "w#n/ te /reater a!"'nt !a#n/ a as a&!ent a&!ent " te net a!"'nt "we$ "n te tw" swas swas t" te "ter
Chapter 12
90
End- of-Chapter Solutions
art&. I t#s !et"$ #s 'se$+ te art#es s#!%& a/ree t" aet aet wate0er wate0er ter!s e2#st #n te !aret at te t#!e te ""s#te swa swa #s 't #n %ae. An"ter !eans " ane%#n/ ane%#n/ te swa #s "r "r "ne art& t" a0e a0e a%rea$& entere$ #nt" e#ter a "rwar$ "rwar$ "ntrat "r an "t#"n "n a swa " te ""s#te ""s#te "s#t#"n. T#s arran/e!ent er!#ts esta,%#s!ent esta,%#s!ent " te ter!s " te "sett#n/ "sett#n/ swa swa ,e"re ,e"re tat swa #s nee$e$. nee$e$. 17.
(Str Struct ucture ure of a Typical Typical Currenc Currency y Swap) In a 'rren& swa+ te tw" art#es a/ree t" !ae #nterest a&!ents a&!ents t" ea "ter #n $#erent $#erent 'rren#es. 'rren#es. I ,"t 'rren#es 'rren#es are te sa!e+ ten te 'rren& swa w"'%$ #n0"%0e ea art& !a#n/ #nterest a&!ents #n te sa!e 'rren&+ w# w"'%$ !ae #t an #nterest rate swa. Te ase " 'rren& 'rren& swas swas w#t ,"t a&!ents a&!ents at %"at#n/ rates "r ,"t a&!ents at #2e$ rates w"'%$ n"t n"t a%& ere. T#s ar/'!ent a%#es "n%& t" 'rren& 'rren& swas swas w#t "ne a&!ent a&!ent at a #2e$ rate an$ "ne at a %"at#n/ rate.
11.
(Pricing and Valuation of Currency Swap) A 'rren& swa t" Pa& SF %"at#n/ Ree#0e %"at#n/ P%'s a 'rren& swa t" Pa& %"at#n/ Ree#0e SF #2e$ #s e*'#0a%ent e*'#0a%ent t" a %a#n 0an#%%a #nterest rate swa t" Pa& SF %"at#n/ Ree#0e SF #2e$
1.
(Interet Rate Swap Strategie ) Te ,an ree#0es LIBOR %'s 677 ,as#s "#nts. It "'%$ enter #nt" a swa t" a& LIBOR LIBOR an$ ree#0e te #2e$ #2e$ rate " 8.= erent. Te LIBOR "!"nents "!"nents " tese tese a&!ents w"'%$ w"'%$ "set+ "set+ %ea0#n/ %ea0#n/ #t w#t a net ree#t " 8.= 8.= %'s 7.76 < 17.= #2e$. Te a&!ent a&!ent $ates an$ ter!s ($a&s:6;7+ ($a&s:6;7+ et.) "n te %"an an$ te swa w"'%$ nee$ t" ,e te sa!e.
16.
(Currency Currency Swap Strategie ) Te !ana/er w"'%$ "nt#n'e t" "%$ te e'r"-$en"!#nate$ ,"n$+ /enerat#n/ #nterest #n e'r"s+ an$ w"'%$ enter #nt" a 'rren& swa t" a& a& e'r"s an$ ree#0e ree#0e "'n$s. "'n$s. Te 'rren& swa swa w"'%$ a0e a0e n"t#"na% n"t#"na% r#n#a% " 3;.1= !#%%#"n an$ 67 !#%%#"n. Its #nterest a&!ent a&!ent $ates an$ an$ !at'r#t& $ate w"'%$ a0e t" !at t"se " te ,"n$. T's+ at te start te swa tere w"'%$ ,e a ree#t ree#t " 3;.1= !#%%#"n an$ a a&!ent " 67 !#%%#"n+ w# are e*'#0a%ent a!"'nts. S" tere #s n" net as #n%"w "r "'t%"w. Te e'r"-$en"!#nate$ ,"n$ w#%% "nt#n'e t" ree#0e #nterest at =. erent+ w#%e te swa w#%% res'%t #n a&!ent " #nterest #n # n e'r"s at =.8 erent an$ ree#t ree#t " #nterest #n "'n$s at 3.9 erent. erent. N"te tat te swa a&!ent #n e'r"s $"es n"t !at te ,"n$ #nterest a&!ent #n e'r"s+ ,'t t#s r",%e! ann"t ,e a0"#$e a0"#$e$. $. Te swa rate #s s#!%& s#!%& n"t te ,"n ,"n$ $ rate. Te swa swa w#%% res'%t #n a net "'t%" "'t%"w w " e'r"s+ e'r"s+ ,'t #nterest w#%% ,e ree#0e$ #n "'n$s. At te en$ " te swa+ tere w"'%$ ,e a a&!ent " 3;.1= !#%%#"n an$ ree#t " 67 !#%%#"n "n te swa+ w# w"'%$ n"t ,e e*'#0a%ent a!"'nts. Te net eet #s tat te "r#/#na% ,"n$ re!a#ns #n %ae+ ,'t te swa a&!ents w#%% ar"2#!ate te eet " se%%#n/ te e'r"-$en"!#nate$ ,"n$ an$ #n0est#n/ te r"ee$s #n te "'n$-$en"!#nate$ ,"n$.
13.
(E!uity Swap Strategie ) F#rst r""sa%4 r""sa%4 Te e2e't#0e e2e't#0e enters #nt" a swa swa t" a& te $ea%er $ea%er te ret'rn "n = !#%%#"n sares+ w#%e te $ea%er a&s te e2e't#0e a #2e$ rate. Se"n$ Se"n$ r""sa%4 r""sa%4 Te e2e't#0e e2e't#0e enters #nt" a swa t" a& te $ea%er te ret'rn "n = !#%%#"n !#%% #"n sares+ w#%e te $ea%er a&s te e2e't#0e a %"at#n/ rate s' as LIBOR. T#r$ r""sa%4 Te e2e't#0e e2e't#0e enters #nt" a swa swa t" a& te $ea%er $ea%er te ret'rn "n = !#%%#"n sares+ w#%e te $ea%er a&s te e2e't#0e te ret'rn "n a $#0ers##e$ st" "rt"%#". In a%% ases+ te n"t#"na% r#n#a% #s = !#%%#"n 2 57 < 5177.
Chapter 12
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End- of-Chapter Solutions
1=.
(Pricing and Valuation of Interet Rate Swap) a. Te $#s"'nt ,"n$ r#es are as "%%"ws4 "%%"ws4 Ter! 97 $a&s 1>7 $a&s 87 $a&s 6;7 $a&s
Rate 8.77 8.= 8.3= 8.==
D#s"'nt B"n$ Pr#e B7(97) < 1:(1 @ 7.78(97:6;7)) < 7.9>> B7(1>7) < 1:(1 @ 7.78=(1>7:6;7)) < 7.9;=7 B7(87) < 1:(1 @ 7.783=(87:6;7)) < 7.9381 B7(6;7) < 1:(1 @ 7.78==(6;7:6;7)) < 7.99>
Te #2e$ rate #s 1 − 7.99> 6;7 = 7.7863 7.9>> + 7.9;=7 + 7.9381 + 7.99> 97
,.
Te #rst net a&!ent a&!ent #s ,ase$ "n "n a #2e$ rate " 8.63 erent erent an$ a %"at#n/ rate " 8 erent4 erent4 F#2e$ a a&!ent4 F%"at#n/ a&!ent4
56=+777+777(7.7863)(97:6;7) < 5; 5;3+=7 56=+777+777(7.78)(97:6;7) < 5;1+=77
Te net #s tat te art& a&#n/ #2e$ !aes a a&!ent " 59+8=7 .
Te Te ne new $#s #s"'nt ,"n$ r#e #es ar are as as " "%%"w %"ws4 Ter! ;7 $a&s 1=7 $a&s 37 $a&s 667 $a&s
Rate ;.> 8.7= 8.1= 8.7
D#s"'nt B"n$ Pr#e B67(97) < 1:(1 @ 7.7;>(;7:6;7)) < 7.9>>> B67(1>7) < 1:(1 @ 7.787=(1=7:6;7)) < 7.981= B67(87) < 1:(1 @ 7.781=(37:6;7)) < 7.9=3= B67(6;7) < 1:(1 @ 7.787(667:6;7)) < 7.96>1
F"r a 51 n"t#"na% r#n#a%+ te 0a%'e " te re!a#n#n/ #2e$ a&!ents a&!ents #s 7.7863(97:6;7)(7.9>>> 7.7863(97:6;7)(7.9>>> @ 7.981= @ 7.9=3= @ 7.96>1) @ 7.96>1 < 1.77>8>; (n"te4 "r a%% a%'%at#"ns+ a "!'ter was 'se$ t" ",ta#n te #/est re#s#"n). F"r a 51 n"t#"na% r#n#a%+ te 0a%'e " te re!a#n#n/ %"at#n/ a&!ents #s (1@ 7.78(97:6;7))(7.9>>>) 7.78(97:6;7))(7.9>>>) < 1.77;798; Te 0a%'e " te swa #s+ tere"re+ 56=+777+777(1.77;798; 56=+777+777(1.77;798; ? 1.77>8>;) < ?593+79; 1;.
(Pricing a. Te $"%%ar $"%%ar n"t#"n n"t#"na% a% r#n# r#n#a% a% #s 56= 56=+777+ +777+777. 777. Pricing and Valuati Valuation on of Currenc Currency y Swap Swap) a. e*'#0a%ent e*'#0a%ent #n "'n$s #s 56=+777+777:51.;7 < 1+>8=+777. ,.
Te
Te $#s"'nt $#s"'nt ,"n$ r#es are "'n$ as as "%%"ws4 "%%"ws4 In $"%%ars4 Ter! 1>7 $a&s 6;7 $a&s =37 $a&s 87 $a&s
Rate 8.77 8.= 8.3= 8.==
D#s"'nt B"n$ Pr#e B7(1>7) < 1:(1 @ 7.78(1>7:6;7)) < 7.9;; B7(6;7) < 1:(1 @ 7.78=(6;7:6;7)) < 7.963 B7(=37) < 1:(1 @ 7.783=(=37:6;7)) < 7.>99= B7(87) < 1:(1 @ 7.78==(87:6;7)) < 7.>;>>
Te #2e$ rate #s Chapter 12
92
End- of-Chapter Solutions
1 − 7.>;>> 6;7 = 7.781; 7.9;; + 7.963 + 7.>99= + 7.>;>> 1>7
In "'n$s4 Ter! 1>7 $a&s 6;7 $a&s =37 $a&s 87 $a&s
Rate ;.=7 8.17 8.=7 >.77
D#s"'nt B"n$ Pr#e B7(97) < 1:(1 @ 7.7;=(1>7:6;7)) < 7.9;>= B7(1>7) < 1:(1 @ 7.7817(6;7:6;7)) < 7.9668 B7(87) < 1:(1 @ 7.78=(=37:6;7)) < 7.>9>9 B7(6;7) < 1:(1 @ 7.7>(87:6;7)) < 7.>;1
Te #2e$ rate #s 1 − 7.>;1 6;7 = 7.78=6 7.9;>= + 7.9668 + 7.>9>9 + 7.>;1 1>7
.
F#r F#rst $e $eter! ter!#n #nee te te #2 #2e$ e$ an$ an$ %"a %"at# t#n/ n/ rat rates es #n #n ea ea 'r 'rre ren n&. &. D"%%ars4 F%"at#n/4 F#2e$4
56=+777+777(7.78)(1>7:6; :6;7) < 51+=+777 56=+777+777(7.781;)(1>7:6;7) < 51+=6+777
F%"at#n/4 F#2e$4
1+>8=+777(7.7;=)(1>7:6;7) < 81 817+96> 1+>8=+777(7.78=6)(1>7:6;7) < > >6+=93
P"'n$s4
#. ##.. ###. #0.
$.
D"%%ar #2e$ a&!ent4 P"'n$ #2e #2e$ a&!ent4 D"%%ar #2e$ a&!ent4 P"'n$ P"'n$ %"a %"at#n/ t#n/ a&! a&!ent ent44 D"%%ar %"at#n/ a&!ent4 P"'n$ P"'n$ %"a %"at#n/ t#n/ a&! a&!ent ent44 D"%%ar %"at#n/ a&!ent4 P"'n$ #2e #2e$ a&!ent4
51+=6+777 >6+=9 6+=93 3 51+=6+777 817+ 817+96> 96> 51+=+777 817+ 817+96> 96> 51+=+777 >6+=9 6+=93 3
e #rst #rst #n$ #n$ te te new $#s $#s"'nt ,"n$ r# r#es4 In $"%%ars4 Ter! Rate D#s"'nt B"n$ Pr#e ;7 $a&s ;.>7 B17(1>7) < 1:(1 @ 7.7;>(;7:6;7)) < 7.9>>> 37 $a&s 8.7= B17(6;7) < 1:(1 @ 7.787=(37:6;7)) < 7.9==1 37 $a&s 8.1= B17(=37) < 1:(1 @ 7.781=(37:6;7)) < 7.967 ;77 $a&s 8.7 B17(87) < 1:(1 @ 7.78(;77:6;7)) < 7.>99 In "'n$s4 Ter! ;7 $a&s 37 $a&s 37 $a&s ;77 $a&s
Rate ;.37 ;.97 8.67 8.3=
D#s"'nt B"n$ Pr#e B17(1>7) < 1:(1 @ 7.7;3(;7:6;7)) < 7.9>93 B17(6;7) < 1:(1 @ 7.7;9(37:6;7)) < 7.9=;7 B17(=37) < 1:(1 @ 7.786(37:6;7)) < 7.91= B17(87) < 1:(1 @ 7.783=(;77:6;7)) < 7.>>9=
F#n$ te 0a%'e " te re!a#n#n/ a&!ents a&!ents er n"t#"na% r#n#a% " 51 "r 1. D"%%ars4 F#2e$4 7.781;(1>7:6;7)(7.9>>> 7.781;(1>7:6;7)(7.9>>> @ 7.9==1 @ 7.967 @ 7.>99) @ 7.>99 < 1.783=;8>; F%"at#n/4 (1 @ 7.78(1>7:6;7))(7.9>> 7.78(1>7:6;7))(7.9>>>) >) < 1.763713= P"'n$s4 F#2e$4 7.78=6(1>7:6;7)(7.9>93 7.78=6(1>7:6;7)(7.9>93 @ 7.9=;7 @ 7.91= @ 7.>>9=) @ 7.>>9= < 1.7679>16 Chapter 12
93
End- of-Chapter Solutions
F%"at#n/4 (1 @ 7.7;=(1>7:6;7))(7.9 7.7;=(1>7:6;7))(7.9>93) >93) < 1.71;79 Ten te 0a%'e " te a&!ents are as "%%"ws4 D"%%ars4 F#2e$4 F#2e$4 56=+777+ 56=+777+777( 777(1.78 1.783=;8 3=;8>;) >;) < 56=+9;7+ 56=+9;7+9>> 9>> F%"at#n/4 56=+777+777(1.763713=) 56=+777+777(1.763713=) < 56=+>19+7=1 P"'n$s4 F#2e$4 1+>8=+777(1.7679>16) 1+>8=+777(1.7679>16) < +==+81; +==+81; F%"at#n/4 1+>8=+777(1.71;79) 1+>8=+777(1.71;79) < +638+=;6 +638+=;6 Ten we "n0ert te "'n$s t" $"%%ars4 F#2e$4 +==+81;(51.3) +==+81;(51.3) < 56+73+>=8 56+73+>=8 F%"at#n/4 +638+=;6(51.3) +638+=;6(51.3) < 561+866+=37 561+866+=37 Ten+ te 0a%'es " te swas t" ree#0e "'n$s an$ a& $"%%ars are as "%%"ws4 #. ##. ###. #0. 18.
P"'n P"'n$s $s #2e #2e$+ $+ $"%% $"%%ar arss #2 #2e$ e$44 56+ 56+7 73+ 3+>= >=8 8 ? 56=+ 56=+9; 9;7+ 7+9> 9>> > < ?56+ ?56+96 96;+ ;+16 167 7 P"'n P"'n$s $s #2e #2e$+ $+ $"%% $"%%ar arss %" %"at at#n #n/4 /4 56+ 56+7 73+ 3+>= >=8 8 ? 56=+ 56=+>1 >19+ 9+7= 7=1 1 < ?56+ ?56+89 893+ 3+19 196 6 P"'n$ P"'n$ss %"a %"at#n t#n/+ /+ $"%%a $"%%ars rs %"a %"at#n t#n/4 /4 561+8 561+866+ 66+=37 =37 ? 56=+> 56=+>19+ 19+7=1 7=1 < ?53+7 ?53+7>=+ >=+=11 =11 P"'n$ P"'n$ss %"a %"at#n t#n/+ /+ $"%%a $"%%ars rs #2e$ #2e$44 561+8 561+866+ 66+=37 =37 ? 56=+9 56=+9;7+ ;7+9>> 9>> < ?53 ?53+ +8+3 8+338 38
(Pricing and Valuation of E!uity Swap) a.
1 − 7.9=3 6;7 = 7.79>8 7.98>7 + 7.9=3 97 ,.
Swa 1 (a& (a& #2e$ rate+ ree#0e ree#0e e*'#t& ret'rn) F#2e$ a&!ent4 a&!ent4 5;7+777+777(7.79>8)(97 5;7+777+777(7.79>8)(97:6;7) :6;7) < 51+3>7+=77 E*'#t& a&!ent4 a&!ent4 5;7+777+777((=;79.>1:==1 5;7+777+777((=;79.>1:==13.;8) 3.;8) ? 1) < 51+76=+167 Net a&!ent4 a&!ent4 51+76=+167 ? 51+3>7+=77 51+3>7+=77 < ?533=+687 Swa (a& %"at#n/ rate+ ree#0e e*'#t& ret'rn) F%"at#n/ a&!ent4 a&!ent4 5;7+777+777(.79)(1>7:6; 5;7+777+777(.79)(1>7:6;7) 7) < 51+6=7+777 E*'#t& a&!ent4 51+76=+167 (see a,"0e) Net a&!ent4 a&!ent4 51+76=+167 ? 51+6=7+777 51+6=7+777 < ?5613+>87 Swa 6 (a& "ne e*'#t& ret'rn+ ree#0e "ter e*'#t& ret'rnG reer t" tese as e*'#t& 1 an$ e*'#t& ) E*'#t& a&!ent4 a&!ent4 5;7+777+777((161.93:11 5;7+777+777((161.93:11.9>) .9>) ? 1) < ?5968+>=; E*'#t& 1 a&!ent4 51+76=+167 (see a,"0e) Net a&!ent4 a&!ent4 51+76=+167 ? 5968+>=; 5968+>=; < 598+83
.
Te Te 0a%' 0a%'ees " " te te re! re!a# a#n# n#n/ n/ a&! a&!en ents ts er er 51 n"t n"t#" #"na na%% r#n r#n# #a a%% are are as as "% "%%" %"ws ws44 F%"at#n/4 F#2e$4 E*'#t& 14 E*'#t& 4
(1 @ 7.79(97:6;7))7.9>>> < 1.711731=9 7.79>8(97:6; :6;7)(7.9>>> @ 7.98 .981=) @ 7.981= < 1.719>6;7; (=399.;:==13.;8) < 7.9988791; (171.3=:11.9>) < 7.9973933>=
Te 0a%'es " te swas are as "%%"ws4 Ree#0e e*'#t& 1+ a& a& #2e$ 4 5;7+777+777(7.9988791; 5;7+777+777( 7.9988791; ? 1.719>6;7;) 1.719>6;7; ) < ?51+6=6+871 ?51+6=6+87 1 Ree#0e e*'#t& 1+ a& %"at#n/4 5;7+777+777(7.9988791; 5;7+777+77 7(7.9988791; ? 1.711731=9) < ?5>;+68 Ree#0e e*'#t& 1+ a& a& e*'#t& 4 5;7+777+777(7.9988791 5;7+777+777 (7.9988791; ; ? 7.9973933>=) < 537;+=>; 1>.
(Interet Rate Swap Strategie )
Chapter 12
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End- of-Chapter Solutions
"'r %#a,#%#t& "n te ens#"n 'n$ "'r ret'rn r"! te %"at#n/-rate n"te "'r a&!ent t" te swa $ea%er "'r a&!ent ree#0e$ r"! te swa $ea%er T"ta%
?> @ LIBOR @ ? LIBOR @; @
Te a&!ent s"'%$ ,e ar"2#!ate%& "ne a% " t#s s#ne #t #s se!#-ann'a% a&. O "'rse+ $#erent $#erent a&!ent ter!s w"'%$ a%ter a% ter tese res'%ts s%#/t%&. 19.
(E!uity Swap Strategie and Currency Swap Strategie ) Its 'rrent "s#t#"n #s @ #2e$ ? %"at#n/ F#rst+ enter #nt" a 'rren& swa t" a& $"%%ars #2e$ an$ ree#0e e'r"s %"at#n/4 @ %"at#n/ ? 5 #2e$ Te "!,#nat#"n " tese tw" swas #s e*'#0a%ent t" @ #2e$ ? 5 #2e$ N"w enter enter #nt" an e*'#t& swa swa t" a& te SJP =77 ret'rn an$ ree#0e ree#0e $"%%ars $"%%ars #2e$4 ? SJP=77 @ 5 #2e$ Lea0#n/ an "0era%% "s#t#"n " @ #2e$ ? SJP=77 N"te tat #t as tree swas #n %ae+ %ae+ ,'t te as %"ws %"ws net net "'t t" te attern #t wants.
7.
(E!uity Swap Strategie ) Te #r! w"'%$ %#e t" eet#0e%& se%% 5677+777+777(7.17) < 567+777+777 " st" an$ ,'& an e*'#0a%ent e*'#0a%ent a!"'nt " ,"n$s. ,"n$s. It an $" t#s 's#n/ a swa #n w# #t a&s te ret'rn ret'rn "n te st" an$ ree#0es te ret'rn "n a ,"n$ #n$e2 tat #t "ns#$ers reresentat#0e reresentat#0e " te ret'rn "n te ,"n$s #t w"'%$ "terw# "terw#se se ,'&. ,'&. Te st" st" a&!ent a&!entss w"'%$ w"'%$ #n a%% %#e%#"" %#e%#""$ $ ,e e//e$ e//e$ t" an #n$e2 tat tat w"'%$ ,e reresentat#0e " te st" #t w"'%$ "terw#se se%%. T's+ te #r! w"'%$ enter #nt" a swa "n 567+777+777 n"t#"na% r#n#a%+ r"!#s#n/ t" !ae a&!ents " te t"ta% ret'rn "n st" #n$e2 an$ ree#0e te t"ta% ret'rn "n a ,"n$ #n$e2. #n$e2. Te t"ta% ret'rn #n%'$es $#0#$en$s $#0#$en$s an$ a#ta% /a#ns "n te st" st" an$ "'"n "'"n #nterest an$ a#ta% /a#ns "n te ,"n$s. ,"n$s.
1.
(Pricing and Valuation of Currency Swap) F#rst $eter!#ne te a&!ents a&!ents "n te swa4 Pa&4 Pa&4 517+ 517+77 777+ 7+77 777( 7(7. 7.73 73)) < 5377 5377+7 +777 77 Ree#0e4 Ree#0e4 ;+=7+777(7.76=) ;+=7+777(7.76=) < 1>+8=7 Tere Tere are tw" a&!ents a&!ents.. On ea+ ea+ te A!er#an a&s a&s 5377+777 5377+777 an$ ree#0 ree#0es es 1>+8= 1>+8=7. 7. T's+ T's+ ea a&!ent an ,e 0#ewe$ 0#ewe$ as a "rwar$ "rwar$ "ntrat "ntrat "n te "'n$+ $en"!#nate$ #n $"%%ars+ w#t a rate " 5377+777 537 7+777:1 :1>+8=7 >+8=7 < 51.>>;. 51.>>;. F"r e2a!%e+ e2a!%e+ te A!er#an A!er#an an 0#ew ea ea a&!ent a&!ent as a %"n/ "rwar$ "rwar$ "ntrat #n w# e w#%% a& 5377+777 an$ ree#0e 1>+8=7. 1>+8=7. Bea'se te swa #s "rret%& r#e$+ te s'! " te 0a%'es " te tw" "ntrats as t" ,e Ker". One "ntrat+ "we0er+ "we0er+ as "s#t#0e 0a%'e+ 0a%'e+ an$ "ne as ne/at#0e 0a%'e. 0a%'e. #t"'t !"re #n"r!at#"n+ #n"r!at#"n+ we ann"t at'a%%& $eter!#ne te 0a%'e " ea "ntrat+ "ntrat+ ,'t we n"w tat "ne #s "s#t#0e an$ te "ter ne/at#0e. ne/at#0e. Oterw#se+ Oterw#se+ an ar,#tra/e ""rt'n#t& w"'%$ ,e a0a#%a,%e.
Chapter 12
95
End- of-Chapter Solutions
