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7/24/2019 MBF13e Chap08 Pbms_final
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Problem 8.1 Amber McClain
a. What is the value of her position at maturity if the ending spot rate is $0.12000/Ps?
b. What is the value of her position at maturity if the ending spot rate is $0.09800/Ps?
. What is the value of her position at maturity if the ending spot rate is $0.11000/Ps?
a. b. c.
Assumptions Values Values Values
!umber of pesos per futures ontrat 500,000 500,000 500,000
!umber of ontrats 8.00 8.00 8.00
"uy or sell the peso futures? Sell Sell Sell
#nding spot rate $/peso% $0.12000 $0.09800 $0.11000
&une futures settle prie from #'h8.1 $/peso% $0.1077 $0.1077 $0.1077
(pot ) *utures $0.01227 !$0.0097" $0.00227
+alue of total position at maturity ,($% !$#9,080.00" $8,920.00 !$9,080.00"
+alue - ) !otional ' (pot ) *utures% ' 8
nterpretation
mber buys at the spot prie and sells at the futures prie.
f the futures prie is greater than the ending spot prie she maes a profit.
mber 3lain the urreny speulator 4e met earlier in the haptersells eight &une futures ontrats for500000 pesos at the losing prie 6uoted in #'hibit 8.1.
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Problem 8.2 Pele%&s Puts
a" b" c" '" e" ("
Assumptions Values Values Values Values Values Values 12,500,000 12,500,000 12,500,000 12,500,000 12,500,000 12,500,000
aturity days% 180 180 180 180 180 180
$0.008000 $0.008000 $0.008000 $0.008000 $0.008000 $0.008000
$0.000080 $0.000080 $0.000080 $0.000080 $0.000080 $0.000080
110.00 115.00 120.00 125.00 10.00 15.00
$0.009091 $0.008*9* $0.008 $0.008000 $0.007*92 $0.007#07
7ross profit on option $0.000000 $0.000000 $0.000000 $0.000000 $0.00008 $0.00059
ess premium !$0.000080" !$0.000080" !$0.000080" !$0.000080" !$0.000080" !$0.000080"
!$0.000080" !$0.000080" !$0.000080" !$0.000080" $0.000228 $0.00051
!et profit total !$1,000.00" !$1,000.00" !$1,000.00" !$1,000.00" $2,8#*.15 $*,#07.#1
Peleh 4rites a put option on &apanese yen 4ith a strie prie of $0.008000/ 125.00/$% at a premium of 0.0080: per yen and 4ith an e'piration date si' month;he option is for 12500000. What is Peleh0/$.
!otional prinipal %
(trie prie ,($/%
Premium ,($/%
#nding spot rate /,($%
in ,($/
!et profit ,($/%
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Problem 8. Ventosa n+estments
ritis% Poun' -utures, S$/poun' !CM" Contract *2,500 poun'
pen
Maturit3 pen 4i)% o6 Settle C%an)e 4i)% nterest
Marc% 1.>2> 1.>28 1.>21> 1.>228 0.00=2 1.>@00 2505
une 1.>1> 1.>188 1.>1> 1.>12 0.00=0 1.>550 809
a" b" c" '"
Assumptions Values Values Values Values
Pounds A% per futures ontrat *2,500 *2,500 *2,500 *2,500
aturity month une Marc% Marc% une
!umber of ontrats 5 12 12
Bid she buy or sell the futures? bu3s sells bu3s sells
#nding spot rate $/A% $1.980 $1.#5*0 $1.#5*0 $1.980
Pound futures ontrat settle prie $ $1.#1*2 $1.#228 $1.#228 $1.#1*2
(pot ) *utures !$0.0182" $0.02 $0.02 !$0.0182"
+alue of position at maturity $% !$5,*87.50" !$2#,900.00" $*,225.00 $1,*50.00
buysC !otional ' (pot ) *utures% ' ontrats
sellsC !otional ' (pot ) *utures% ' ontrats
nterpretation
&amie DodrigueE a urreny trader for 3hiago)based +entosa nvestments uses the follo4ing futures 6uotes on the "ritish pound % to speulate on the value ofthe pound.
a. f &aime buys 5 &une pound futures and the spot rate at maturity is $1.=980/ 4hat is the value of her position?
b. f &amie sells 12 arh pound futures and the spot rate at maturity is $1.>50/ 4hat is the value of her position?
. f &amie buys = arh pound futures and the spot rate at maturity is $1.>50/ 4hat is the value of her position?
d. f &amie sells 12 &une pound futures and the spot rate at maturity is $1.=980/ 4hat is the value of her position?
"uys a futureC &amie buys at the futures prie and sells at the ending spot prie. (he therefore profits 4hen the futures prie isless than the ending spot prie.
(ells a futureC &amie buys at the ending spot prie and sells at the futures prie. (he therefore profits 4hen the futures prie is
greater than the ending spot prie.
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Problem 8.# Sallie Sc%nu'el
ption Strie Price Premium
Put on (ing $ $0.500/($ $0.0000=/($
3all on (ing $ $0.500/($ $0.000>/($
a. (hould (allie buy a put on (ingapore dollars or a all on (ingapore dollars?
b. What is (allieet pro(it
!S$/S$" !S$/S$"
(pot rate $0.80000 $0.80000
ess strie prie !$0.*5000" !$0.*5000"
ess premium !$0.000#*"
Profit $0.15000 $0.1#95#
(allie (hnudel trades urrenies for Feystone *unds in &aarta. (he fouses nearly all of her time and attention on the ,.(.dollar/(ingapore dollar $/($% ross)rate. ;he urrent spot rate is $0.000/($. fter onsiderable study she has onludedthat the (ingapore dollar 4ill appreiate versus the ,.(. dollar in the oming 90 days probably to about $0.@000/($. (hehas the follo4ing options on the (ingapore dollar to hoose fromC
. ,sing your ans4er from part a% 4hat is (allie
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Problem 8.5 la'e Capital !A"
a. b.
Assumptions Values Values
nitial investment funds available% $10,000,000 $10,000,000
$1.58 $1.58
$1.50 $1.50
$1.*00 $1.2800
Strate)3 (or Part a":
nitial in+estment principle $10,000,000.00
$1.50
uros bou)%t (or6ar' !n+estment / (or6ar' rate" ? 7,#90,**.70
$1.*00
S$ procee's !euros bou)%t (or6ar' e@c%an)e' to S$ spot" $10,187,2*5.92
Pro(it in S$ $187,2*5.92
Strate)3 (or Part b":
n+estment (un's nee'e' in 0 'a3s $10,000,000.00
Spot rate in open maret at en' o( 0 'a3s $1.2800
uros bou)%t in open maret in 0 'a3s !n+estment / spot rate" ? 7,812,500.00
Ste(an %a' sol' t%ese euros (or6ar' at t%e start o( t%e 0 'a3 perio'.
$1.50S$ procee's !euros sol' (or6ar' into S$" $10,#29,*87.50
Pro(it in S$ $#29,*87.50
3hristoph Hoffeman trades urreny for "lade 3apital of 7eneva. 3hristoph has $10 million to begin 4ith and he must state allprofits at the end of any speulation in ,.(. dollars. ;he spot rate on the euro is $1.==58/I 4hile the =0)day for4ard rate is$1.==50/I.
a. f 3hristoph believes the euro 4ill ontinue to rise in value against the ,.(. dollar so that he e'pets the spot rate to be$1.=00/I at the end of =0 days 4hat should he do?
b. f 3hristoph believes the euro 4ill depreiate in value against the ,.(. dollar so that he e'pets the spot rate to be $1.2800/Iat the end of =0 days 4hat should he do?
3urrent spot rate ,($/%
=0)day for4ard rate ,($/%
#'peted spot rate in =0 days ,($/%
Jne of the more interesting dimensions of speulating in the for4ard maret is that if the speulator has aess to the for4ardmaret ban lines or relationships 4hen 4oring on behalf of an established firm% many for4ard speulation strategies re6uireno atual ash flo4 position up front. n this ase 3hristoph believes the dollar 4ill be trading at $1.=/in the open maret atthe end of =0 days but he has the ability to buy or sell dollars at a for4ard rate of $1.==50/. He should therefore buy eurosfor4ard =0 days re6uires no atual ash flo4 up front% and at the end of =0 days tae delivery of those euros and sell in the spotmaret at the higher dollar rate for profit.
0 'a3 (or6ar' rate !S$/"
Spot rate in open maret at en' o( 0 'a3s !S$/"
gain a profitable strategy an be e'euted 4ithout any atual ash flo4 hanging hands at the beginning of the period. (ine3hristoph believes that the dollar 4ill strengthen to $1.28 in =0 days he should sell euros for4ard no4 at the higher dollar rate4ait =0 days and buy the euros needed on the open maret at $1.28 and immediately then use those euros to fulfill his for4ardontrat to sell euros for dollars at $1.==50. *or a profit.
0 'a3 (or6ar' rate !S$/"
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Problem 8.* la'e Capital !"
a. 3alulate 3hristoph
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Problem 8.7 C%a+e S.A.
Assumptions Values
Prinipal borro4ing need $ 8,000,000
aturity needed in 4ees 8
Date of interest harged by potential lenders *.250B
>e6 or interest rate practices
nterest alulation usesC
#'at number of days in period 5*
!umber of days in finanial year *0
(o the interest harge on this prinipal is $ 77,777.78
=reat ritain interest rate practices
nterest alulation usesC
#'at number of days in period 5*
!umber of days in finanial year *0
(o the interest harge on this prinipal is $ 77,777.78
S6iss interest rate practices
nterest alulation usesC
ssumed =0 days per month for t4o months *0
!umber of days in finanial year *0
(o the interest harge on this prinipal is $ 8,.
ndina should borro4 in 7reat "ritain beause it has the lo4est interest ost.
3haveE (.. a +eneEuelan ompany 4ishes to borro4 $8000000 for eight4ees. rate of .250K per annum is 6uoted by potential lenders in !e4 Gor
7reat "ritain and (4itEerland using respetively international "ritish and the(4iss)#urobond definitions of interest day ount onventions%. *rom 4hihsoure should 3haveE borro4?
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Problem 8.8 otan3 a3 Corporation
L1. "otany "ay ould borro4 the ,($=0000000 for t4o years at a fi'ed 5K rate of interest
Assumptions Values
Prinipal borro4ing need $ 0,000,000
aturity needed in years 2.00
*i'ed rate 2 years 5.000B
*loating rate si')month "JD M spread
3urrent si')month "JD .500B
(pread 1.500B
*i'ed rate 1 year then re)fund #.500B
-irst *Dmont%s Secon' *Dmont%s E%ir' *Dmont%s -ourt% *Dmont%s
F1: -i@e' rate, 2 3ears
nterest ost per year $ 1,500,000 $ 1,500,000
3ertainty over aess to apital Certain Certain Certain Certain
3ertainty over ost of apital Certain Certain Certain Certain
F2: -loatin) rate, si@Dmont% G H sprea'
nterest ost per year $ 750,000 $ 750,000 $ 750,000 $ 750,000
3ertainty over aess to apital Certain Certain Certain Certain
3ertainty over ost of apital Certain ncertain ncertain ncertain
F: -i@e' rate, 1 3ear, t%en reD(un'
nterest ost per year $ 1,50,000 ;;; ;;;
3ertainty over aess to apital Certain Certain ncertain ncertain
3ertainty over ost of apital Certain Certain ncertain ncertain
Jnly alternative L1 has a ertain aess and ost of apital for the full 2 year period.
lternative L2 has ertain aess to apital for both years but the interest osts in the final = of > periods is unertain.
lternatvie L= possessing a lo4er interest ost in year 1 has no guaranteed aess to apital in the seond year.
Bepending on the ompany
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Problem 8.9 Vatic Capital
ption Strie Price Premium
Put on yen 125/$ $0.0000=/($
3all on yen 125/$ $0.000>/($
a. (hould 3ahita buy a put on yen or a all on yen?
b. What is 3ahita
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Problem 8.10 Callin) All Pro(its
!oteC the option premium is =.8 ents per euro not =8 ents per euro.
a. b. c. '. e. (.Assumptions Values Values Values Values Values Values
!otional prinipal euros% ? 100,000.00 ? 100,000.00 ? 100,000.00 ? 100,000.00 ? 100,000.00 ? 100,000.00
aturity days% 90 90 90 90 90 90
(trie prie ,($/euro% $1.2500 $1.2500 $1.2500 $1.2500 $1.2500 $1.2500
Premium ,($/euro% $0.080 $0.080 $0.080 $0.080 $0.080 $0.080
#nding spot rate ,($/euro% $1.1000 $1.1500 $1.2000 $1.2500 $1.000 $1.500
7ross profit on option $0.0000 $0.0000 $0.0000 $0.0000 $0.0500 $0.1000
ess premium !$0.080" !$0.080" !$0.080" !$0.080" !$0.080" !$0.080"
!et profit ,($/euro% !$0.080" !$0.080" !$0.080" !$0.080" $0.0120 $0.0*20
!et profit total !$,800.00" !$,800.00" !$,800.00" !$,800.00" $1,200.00 $*,200.00
ssume a all option on euros is 4ritten 4ith a strie prie of $1.2500/I at a premium of =.80: per euro $0.0=80/I% and 4ith an e'piration date three months frooption is for I100000. 3alulate your profit or loss should you e'erise before maturity at a time 4hen the euro is traded spot at .....
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Problem 8.11 M3ster3 at aer Street
Strie Price Maturit3 Premium
$1.=/N =0 days $0.00081/N
$1.=>/N =0 days $0.00021/N
$1.=2/N =0 days $0.0000>/N
$1.=/N 0 days $0.00===/N
$1.=>/N 0 days $0.00150/N
$1.=2/N 0 days $0.0000/N
Assumptions Values
$1.#2*0
$1.200
250,000.00
Put options on poun's Put F1 Put F2 Put F
$1.* $1.# $1.2
aturity days% 0 0 0
$0.0008 $0.0002 $0.0000
Put options on poun's Put F# Put F5 Put F*
$1.* $1.# $1.2
aturity days% *0 *0 *0
$0.00 $0.0015 $0.000*
ssues (or S3'ne3 to consi'er:
1. "eause his e'petation is for O=0 to 0 daysO he should onfine his hoies to the 0 day options to be sure and apture
the timing of the e'hange rate hange. We have no e'pliit idea of 4hy he believes this speifi timing.%
2. ;he hoie of 4hih strie prie is an interesting debate.
;he lo4er the strie prie 1.=> or 1.=2% the heaper the option prie.
;he reason they are heaper is that statistially speaing they are inreasingly less liely to end up in the money.
;he hoie given that all the options are relatively OheapO is to pi the strie prie 4hih 4ill yield the re6uired return.
;he $1.=2 strie prie is too far
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Problem 8.12 Contrarious Calan'ra
the 3anadian dollarCption Strie Price Premium
Put on 3$ $0.@000 $0.0000=/($
3all on 3$ $0.@000 $0.000>9/($
a. (hould 3alandra buy a put on 3anadian dollars or a all on 3anadian dollars?
b. What is 3alandra
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Problem 8.1 Gai' =auloises
@pecte' C%)
Assumptions Values in G
Prinipal borro4ing need ? 20,000,000
aturity needed in years #.00
3urrent euro)"JD #.000B
"an6ue de Paris< spread R e'petation 2.000B 0.500B
"an6ue de Paris< initiation fee 1.800B
"an6ue de (orbonne
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Problem 8.1# Sc%i(ano Motors
Assumptions Values
Prinipal borro4ing need ? 5,000,000
aturity needed in years #.00
3urrent "JD #.000B*elini)year I5 million loan on a floating rate basis. t is no4 4orried ho4ever about rising interestosts. lthough it had initially believed interest rates in the #uro)Eone 4ould be trending do4n4ard 4hen taing out the loan reenteonomi indiators sho4 gro4ing inflationary pressures. nalysts are prediting that the #uropean 3entral "an 4ill slo4 monetarygro4th driving interest rates up.
(hifano is no4 onsidering 4hether to see some protetion against a rise in euro)"JD and is onsidering a *or4ard Dategreement *D% 4ith an insurane ompany. ording to the agreement (hifano 4ould pay to the insurane ompany at the end ofeah year the differene bet4een its initial interest ost at "JD M 2.50K .50K% and any fall in interest ost due to a fall in "JD.3onversely the insurane ompany 4ould pay to (hifano @0K of the differene bet4een (hifanoQs initial interest ost and any inrease ininterest osts aused by a rise in "JD.
Purhase of the floating Date greement 4ill ost I100000 paid at the time of the initial loan. What are (hifanoQs annual finaningosts no4 if "JD rises and if "JD falls.? (hifano uses 12K as its 4eighted average ost of apital. Bo you reommend that (hifano
purhase the *D?
;his rather unusual for4ard rate agreement is some4hat one)sided in the favor of the insurane ompany. When (hifano is orret(hifano pays the full differene in rates to the insurane ompany. "ut 4hen interest rates move against (hifano the insurane ompany
pays (hifano only @0K of the differene in rates. nd all of that is after (hifano paid I100000 up)front for the agreement regardless ofoutome. !ot a very good deal.
final note of signifiane is that sine (hifano reeives only @0K of the differene in rates its total ost of funds is not effetively
OappedOS they ould in fat rise 4ith no limit over the period as interest rates rose.
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Problem 8.15 C%r3sler C
a. f the floating)rate interest three months from no4 is .00K 4hat did 3hrysler gain or lose?
b. f the floating)rate interest three months from no4 is 8.00K 4hat did 3hrysler gain or lose?
Assumptions Values
nterest rate futures losing prie 9.07
#ffetive yield on interest rate futures *.90B
E%ree Mont%s -rom >o6
-loatin) Gate is -loatin) Gate is
C%r3sler&s interest rate pa3ments 6it% (utures *.000B 8.000B
nterest payment due in three months *.000B 8.000B
(ell a future tae a short position% D*.90B D*.90B
7ain or loss on position D0.90B 1.070B
oss =ain
3hrysler 3 the no4 privately held ompany sold)off by Baimler3hrysler must pay floating rate interestthree months from no4. t 4ants to lo in these interest payments by buying an interest rate futures ontrat.nterest rate futures for three months from no4 settled at 9=.0@ for a yield of .9=K per annum.
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Problem 8.1* C Solutions
Assumptions Values
!otional prinipal $ 5,000,000
"JD per annum #.000B
(pread paid over "JD per annum 2.000B
(4ap rate to pay fi'ed per annum 7.000B
-irst Secon' E%ir' -ourt%
nterest J S6ap Pa3ments *Dmont%s *Dmont%s *Dmont%s *Dmont%s
a. G increases 50 basis pts/* mont%s 0.500B
#'peted "JD #.500B 5.000B 5.500B *.000B
Current loan a)reement:
#'peted "JD for months% D2.250B D2.500B D2.750B D.000B
(pread for months% D1.000B D1.000B D1.000B D1.000B
#'peted interest payment D.250B D.500B D.750B D#.000B
S6ap A)reement:
Pay fi'ed for )months% D.500B D.500B D.500B D.500B
Deeive floating "JD for months% 2.250B 2.500B 2.750B .000B
>et interest !loan H s6ap" D#.500B D#.500B D#.500B D#.500B
S6ap sa+in)s;
!et interest after s4ap $ !225,000" $ !225,000" $ !225,000" $ !225,000"
oan agreement interest !1*2,500" !175,000" !187,500" !200,000"
S6ap sa+in)s !s6ap cost" $ !*2,500" $ !50,000" $ !7,500" $ !25,000"
b. G 'ecreases 25 basis pts/* mont%s D0.250B
#'peted "JD .750B .500B .250B .000B
Current loan a)reement:
#'peted "JD for months% D1.875B D1.750B D1.*25B D1.500B
(pread for months% D1.000B D1.000B D1.000B D1.000B
#'peted interest payment D2.875B D2.750B D2.*25B D2.500B
S6ap A)reement:
Pay fi'ed for )months% D.500B D.500B D.500B D.500B
Deeive floating "JD for months% 1.875B 1.750B 1.*25B 1.500B
>et interest !loan H s6ap" D#.500B D#.500B D#.500B D#.500B
S6ap sa+in)s;
!et interest after s4ap $ !225,000" $ !225,000" $ !225,000" $ !225,000"
oan agreement interest !1#,750" !17,500" !11,250" !125,000"
S6ap sa+in)s !s6ap cost" $ !81,250" $ !87,500" $ !9,750" $ !100,000"
n bot% cases C Solutions is su((erin) %i)%er total interest costs as a result o( t%e s6ap.
Heather J
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Problem 8.17 lu+ia an' Para)uas
Assumptions Ka+ier Lulu
3redit rating AAA
Prefers to borro4 -loatin) -i@e'
*i'ed)rate ost of borro4ing 8.000B 12.000B
*loating)rate ost of borro4ingC
"JD value is unimportant% 5.000B 5.000B
(pread 1.000B 2.000B
;otal floating)rate *.000B 7.000B
Comparati+e A'+anta)e in orro6in) Values
luvia
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Problem 8.18 Eri'ent&s Cross Currenc3 S6ap: S(r (or S$
Assumptions Values S6ap Gates D 3ear bi' D3ear as !otional prinipal $ 10,000,000 JriginalC ,( dollar 5.5*B 5.59B
Jriginal spot e'hange rate (*r./$ 1.5000 JriginalC (4iss fran 1.9B 2.01B
!e4 1)year later% spot e'hange rate (*r./$ 1.55*0
!e4 fi'ed ,( dollar interest 5.20B
!e4 fi'ed (4iss fran interest 2.20B
a. nterest J S6ap Pa3ments ear 0 ear 1 ear 2 ear
Deeive fi'ed rate dollars at this rateC 5.5*B 5.5*B 5.5*B
Jn a notional prinipal ofC $ 10,000,000
;rident 4ill reeive ash flo4sC FFF FFF FFF
U
1.5000
V
;rident 4ill pay ash flo4sC S-r. 01,500 S-r. 01,500 S-r. 15,01,500Jn a notional prinipal ofC S-r. 15,000,000
Pay fi'ed rate (4iss frans at this rateC 2.01B 2.01B 2.01B
b. n6in'in) t%e s6ap a(ter oneD3ear ear 1 ear 2 ear
Demaining dollar ash inflo4s $ 55*,000 $ 10,55*,000
P+ fator at no4 urrent fi'ed $ interest 5.20B 0.950* 0.90*
P+ of remaining dollar ash inflo4s $ 528,517 $ 9,58,22
3umulative P+ of dollar ash inflo4s $ 10,0**,750
Demaining (4iss fran ash outflo4s S-r. 01,500 S-r. 15,01,500
P+ fator at no4 urrent fi'ed (* interest 2.20B 0.9785 0.957#
P+ of remaining (* ash outflo4s S-r. 295,010 S-r. 1#,*#9,818
3umulative P+ of (* ash outflo4s S-r. 1#,9##,827
!e4 urrent spot rate (*r./$ 1.55*0
3umulative P* of (* ash outflo4s in $ $ 9,*0#,*#5
Settlement:
3ash inflo4 $ 10,0**,750
3ash outflo4 !9,*0#,*#5"
!et ash settlement of un4inding $ #*2,105 ;his is a ash reeipt by ;rident from the s4ap dealer.
;rident 3orporation entered into a three)year ross urreny interest rate s4ap to reeive ,.(. dollars and pay (4iss frans. ;rident ho4ever deidedto un4ind the s4ap after one year thereby having t4o years left on the settlement osts of un4inding the s4ap after one year. Depeat thealulations for un4inding but assume that the follo4ing rates no4 applyC
#'hange rate time of s4ap (*r./$)
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Problem 8.19 Eri'ent&s Cross Currenc3 S6ap: en (or uros
a. 3alulate all prinipal and interest payments in both euros and (4iss frans for the life of the s4ap agreement.
Assumptions Values S6ap Gates D 3ear bi' D3ear as
!otional prinipal ? 5,000,000 .2#B .28B
(pot e'hange rate Gen/euro 10#.00 &apanese yen 0.5*B 0.59B
a" nterest J S6ap Pa3ments ear 0 ear 1 ear 2 ear
Deeive fi'ed rate euros at this rateC .2#B .2#B .2#B
Jn a notional prinipal ofC ? 5,000,000
;rident 4ill reeive ash flo4sC FFF FFF FFFU
10#.00
V
;rident 4ill pay ash flo4sC ,0*8,000 ,0*8,000 52,0*8,000
Jn a notional prinipal of yen%C 520,000,000
Pay fi'ed rate &apanese yen at this rateC 0.59B 0.59B 0.59B
b" n6in'in) t%e s6ap a(ter oneD3ear ear 1 ear 2 ear
Demaining euro ash inflo4s ? 1*2,000 ? 5,1*2,000
.*0B 0.9*5 0.917
? 15*,71 ? #,809,#8#
? #,9*5,855
S-r. ,0*8,000 S-r. 52,0*8,000
0.80B 0.9921 0.98#2
S-r. ,0#,*51 S-r. 51#,798,280
517,8#1,91
11#.00
? #,5#2,#7
Settlement:
3ash inflo4 ? #,9*5,855
3ash outflo4 !#,5#2,#7"
!et ash settlement of un4inding ? #2,82 ;his is a ash reeipt by ;rident from the s4ap dealer.
,sing the table of s4ap rates in the hapter #'hibit 8.1=% and assume ;rident enters into a s4ap agreement to reeive euros and pay &apanese yenon a notional prinipal of I5000000. ;he spot e'hange rate at the time of the s4ap is 10>/I.
b. ssume that one year into the s4ap agreement ;rident deides it 4ishes to un4ind the s4ap agreement and settle it in euros. ssuming that at4o)year fi'ed rate of interest on the &apanese yen is no4 0.80K and a t4o)year fi'ed rate of interest on the euro is no4 =.0K and the spot rate ofe'hange is no4 11>/I 4hat is the net present value of the s4ap agreement? Who pays 4hom 4hat?
#uros )) I
#'hange rate time of s4ap /I)
P+ fator at no4 urrent fi'ed Iinterest
P+ of remaining Iash inflo4s
3umulative P+ of Iash infllo4s
Demaining ash outflo4s
P+ fator at no4 urrent fi'ed interest
P+ of remaining ash outflo4s
3umulative P+ of ash outflo4s
!e4 urrent spot rate /I
3umulative P+ of ash outflo4s inI
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Problem 8.20 -alcor
a. 3alulate all prinipal and interest payments in both urrenies for the life of the s4ap.
Assumptions Values S6ap Gates 7D 3ear bi' 7D3ear as
!otional prinipal $ 50,000,000 ,( dollar 5.8*B 5.89B
1.1* #uros #.01B #.05B
a. nterest J S6ap Pa3ments ear 0 ear 1 ear 2 ear ear #
Deeive fi'ed rate dollars at rateC 5.8*B
!otional prinipal ofC $ 50,000,000
Deeive ash inflo4s ofC $ 2,90,000 $ 2,90,000 $ 2,90,000 $ 2,90,000U
1.1*
V
Pay ash outflo4s ofC ? 1,7#5,*90 ? 1,7#5,*90 ? 1,7#5,*90 ? 1,7#5,*90
!otional prinipal ofC ? #,10,##8
Pay fi'ed rate euros at rateC #.05B
b. n6in'in)t%e S6ap ear 0 ear 1 ear 2 ear ear #
f the s4ap is un4ound three years later there are four years of ash flo4s remainingC
Demaining dollar ash inflo4s $ 2,90,000
P+ fator at no4 urrent fi'ed $ interest #.#0B 0.9579
P+ of remaining dollar ash inflo4s $ 2,80*,51
3umulative P+ of $ ash infllo4s $ 52,*25,0
Demaining euro ash outflo4s ? 1,7#5,*90
5.5B 0.9#92
P+ of remaining euro ash outflo4s ? 1,*57,08
? #1,12,5#2
1.02
3umulative P+ of I ash outflo4s $ $ #1,955,19
Settlement:
3ash inflo4 $ 52,*25,0
3ash outflo4 !#1,955,19"
!et ash settlement of un4inding $ 10,**9,8#0 ;his is a net ash payment to *alor from the s4ap dealer.
*alor is the ,.(.)based automotive parts supplier 4hih 4as spun)off from 7eneral otors in 2000. With annual sales of over $2far beyond the traditional automobile manufaturers in the pursuit of a more diversified sales base. s part of the general diversifithe urreny of denomination of its debt portfolio as 4ell. ssume *alor enters into a $50 million @)year ross urreny interest radollars. ,sing the data in #'hibit 8.1= solve the follo4ingC
b. ssume that three years later *alor deides to un4ind the s4ap agreement. f >)year fi'ed rates of interest in euros have no4 rifallen to >.>0K and the urrent spot e'hange rate of $1.02/I 4hat is the net present value of the s4ap agreement? Who pays 4ho
(pot e'hange rate $/I
(pot e'hange rate $/I
P+ fator at no4 urrent fi'ed Iinterest
3umulative P+ of Icash outflows
(pot e'hange rate at un4inding $/I)
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Problem 8.21 .S. 'ollar/uro
Pricin) Currenc3 ptions on t%e uro
A U.S.-based firm wishing to buy A European firm wishing to buy
or sell euros (the foreign currency) or sel l dollars (the foreign currency)
Variable Value Variable Value
Spot rate !'omestic/(orei)n" $1.2#80 ? 0.801
Strie rate !'omestic/(orei)n" K $1.2500 K ? 0.8000
Nomestic interest rate !B p.a." 1.#5B 2.187B
-orei)n interest rate !B p.a." 2.187B 1.#5B
Eime !3ears, *5 'a3s" E 1.000 E 1.000
Na3s eIui+alent *5.00 *5.00
Volatilit3 !B p.a." s 12.000B s 12.000B
Call option premium !per unit (c" c $0.05# c ? 0.0#12
Put option premium !per unit (c" p $0.0*# p ? 0.0#2
!uropean pricin)"
Call option premium !B" c #.28B c 5.15B
Put option premium !B" p 5.15B p #.27B
S0
S0
r'
r'
r(
r(
When the volatility is inreased to 12.000K from 10.500K the premium on the all option on euros rises to $0.0>12/ or 5.15K.
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Problem 8.22 .S. Nollar/apanese en
Pricin) Currenc3 ptions on t%e apanese 3en
A Japanese firm wishing to buy A U.S.-based firm wishing to buyor sell dollars (the foreign currency) or sell yen (the foreign currency)
Variable Value Variable Value
Spot rate !'omestic/(orei)n" P 105.*# $0.0095
Strie rate !'omestic/(orei)n" K P 100.00 K $0.0100
Nomestic interest rate !B p.a." 0.089B 1.#5B
-orei)n interest rate !B p.a." 1.#5B 0.089B
Eime !3ears, *5 'a3s" E 1.000 E 1.000
Na3s eIui+alent *5.00 *5.00
Volatilit3 !B p.a." s 12.000B s 12.000B
Call option premium !per unit (c" c P 7.27 c $0.000
Put option premium !per unit (c" p P .0* p $0.0007
!uropean pricin)"
Call option premium !B" c *.88B c .0*B
Put option premium !B" p 2.90B p 7.27B
A apanese (irm 6is%in) to sell .S. 'ollars 6oul' nee' to purc%ase a put on 'ollars. E%e put option premium liste' abo+e is P.0*/$.
Put option premium !P/S$" P .0*
>otional principal !S$" $750,000
Eotal cost !P" P 2,297,2#
S0
S0
r'
r'
r(
r(
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Problem 8.2 uro/apanese en
Pricin) Currenc3 ptions on t%e uro/en Crossrate
A Japanese firm wishing to buy A European firm wishing to buyor sell euros (the foreign currency) or sell yen (the foreign currency)
Variable Value Variable Value
Spot rate !'omestic/(orei)n" P 1.89 ? 0.0072
Strie rate !'omestic/(orei)n" K P 1*.00 K ? 0.007#
Nomestic interest rate !B p.a." 0.088B 2.187B
-orei)n interest rate !B p.a." 2.187B 0.088B
Eime !3ears, *5 'a3s" E 0.2#7 E 0.2#7
Na3s eIui+alent 90.00 90.00
Volatilit3 !B p.a." s 10.000B s 10.000B
Call option premium !per unit (c" c P 1.50 c ? 0.0001
Put option premium !per unit (c" p P #.0 p ? 0.0002
!uropean pricin)"
Call option premium !B" c 1.12B c 1.0B
Put option premium !B" p .21B p 2.90B
Put option premium !euro/P" ? 0.0002
>otional principal !P" P 10,#00,000
Eotal cost !euro" ? 2,1*7.90
S0
S0
r'
r'
r(
r(
#uropean)based firm lie egrand *rane% 4ould need to purhase a put option on the &apanese yen. ;he ompany 4ishes a strie rate of 0.00@2 eurofor eah yen sold the strie rate% and a 90)day maturity. !ote that the O;imeO must be entered as the fration of a =5 day year in this ase 90/=5 - 0.2>@.
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Problem 8.25 uro/ritis% Poun'
Pricin) Currenc3 ptions on t%e ritis% poun'/uro Crossrate
A European firm wishing to buy A British firm wishing to buy
or sel l pounds (the foreign currency) or sell euros (the foreign currency)
Variable Value Variable Value
Spot rate !'omestic/(orei)n" ? 1.#70 0.*789
Strie rate !'omestic/(orei)n" K ? 1.5000 K 0.***7
Nomestic interest rate !B p.a." #.000B #.1*0B
-orei)n interest rate !B p.a." #.1*0B #.000B
Eime !3ears, *5 'a3s" E 0.2#7 E 0.2#7
Na3s eIui+alent 90.00 90.00
Volatilit3 !B p.a." s 11.#00B s 11.#00B
Call option premium !per unit (c" c ? 0.021 c 0.0220
Put option premium !per unit (c" p ? 0.0#87 p 0.0097
!uropean pricin)"
Call option premium !B" c 1.#5B c .2#B
Put option premium !B" p .0B p 1.#2B
When the euro.000K the all option premium on "ritish pounds risesC
Call option on poun's 6%en euro interest is #.000B ? 0.021
Call option on poun's 6%en euro interest is 2.072B ? 0.0189
C%an)e, an increase in t%e premium ? 0.021
S0
S0
r'
r'
r(
r(