Problem 8.1 Amber McClain mber 3lain the urreny speulator 4e met earlier in the haptersells haptersells eight &une futures ontrats for 500000 pesos at the losing prie 6uoted in #'hibit 8.1. a. What is the value of her her position at maturity if the ending 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?
Assumptions !umber of pesos per futures ontrat ontrat !umber of ontrats "uy or sell the peso futures?
#nding spot rate $/peso% &une futures settle prie from from #'h8.1 $/peso% (pot ) *utures +alue of total position at maturity ,($% +alue - ) !otional ' (pot ) *utures% ' 8
a. Values 500,000 8.00 Sell
b. Values 500,000 8.00 Sell
c. Values 500,000 8.00 Sell
$0.12000 $0.1077 $0.01227
$0.09800 $0.1077 !$ !$0.0097"
$0.11000 $0.1077 $0.00227
!$#9,080.00"
$8,920.00
!$9,080.00"
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.
Problem 8.2 Pele%&s Puts 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' months from no4. ;he option is for 12500000. What is Peleh0/$.
a" Values 12,500,000 180 $0.008000 $0.000080
b" Values 12,500,000 180 $0.008000 $0.000080
c" Values 12,500,000 180 $0.008000 $0.000080
'" Values 12,500,000 180 $0.008000 $0.000080
e" Values 12,500,000 180 $0.008000 $0.000080
(" Values 12,500,000 180 $0.008000 $0.000080
)" Values 12,500,000 180 $0.008000 $0.000080
110.00 $0.009091
115.00 $0.008*9*
120.00 $0.008
125.00 $0.008000
10.00 $0.007*92
15.00 $0.007#07
1#0.00 $0.0071#
7ross profit on option ess premium !et profit ,($/ ¥ ¥%
$0.000000 !$0.000080" !$0.000080"
$0.000000 !$0.000080" !$0.000080"
$0.000000 !$0.000080" !$0.000080"
$0.000000 !$0.000080" !$0.000080"
$0.00008 !$0.000080" $0.000228
$0.00059 !$0.000080" $0 $ 0.00051
$0.000857 !$0.000080" $0 $0.000777
!et profit total
!$1,000.00"
!$1,000.00"
!$1,000.00"
!$1,000.00"
$2,8#*.15
$*,#07.#1
$9,71#.29
Assumptions !otional prinipal ¥ ¥% aturity days% (trie prie ,($/ ¥ ¥% Premium ,($/ ¥ ¥%
#nding spot rate ¥ ¥/,($% in ,($/ ¥ ¥
Problem 8. Ventosa n+estments &amie DodrigueE a urreny trader for 3hiago)based +entosa nvestments uses the follo4ing futures 6uotes on the "ritish pound £% to speulate on the value of the pound. ritis% Poun' -utures, S$/poun' !CM" Maturit3 Marc% une
a. b. . d.
pen 1.>2> 1.>1>
4i)% 1.>28 1.>188
o6 1.>21> 1.>1>
Settle 1.>228 1.>12
C%an)e 0.00=2 0.00=0
f &aime buys 5 &une pound futures and the spot rate at maturity is $1.=980/ £ 4hat is the value of her position? 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? f &amie sells 12 &une pound futures and the spot rate at maturity is $1.=980/ £ 4hat is the value of her position?
Assumptions Pounds A% per futures ontrat aturity month !umber of ontrats Bid she buy or sell the futures?
a" Values *2,500 une 5 bu3s
b" Values *2,500 Marc% 12 sells
c" Values *2,500 Marc% bu3s
'" Values *2,500 une 12 sells
Contract *2,500 poun's pen 4i)% nterest 1.>@00 2505 1.>550 809
Problem 8. Ventosa n+estments &amie DodrigueE a urreny trader for 3hiago)based +entosa nvestments uses the follo4ing futures 6uotes on the "ritish pound £% to speulate on the value of the pound. ritis% Poun' -utures, S$/poun' !CM" Maturit3 Marc% une
a. b. . d.
pen 1.>2> 1.>1>
4i)% 1.>28 1.>188
o6 1.>21> 1.>1>
Settle 1.>228 1.>12
C%an)e 0.00=2 0.00=0
f &aime buys 5 &une pound futures and the spot rate at maturity is $1.=980/ £ 4hat is the value of her position? 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? f &amie sells 12 &une pound futures and the spot rate at maturity is $1.=980/ £ 4hat is the value of her position? a" Values *2,500 une 5 bu3s
b" Values *2,500 Marc% 12 sells
c" Values *2,500 Marc% bu3s
'" Values *2,500 une 12 sells
$1.980 $1.#1*2 !$0.0182"
$1.#5*0 $1.#228 $0.02
$1.#5*0 $1.#228 $0.02
$1.980 $1.#1*2 !$0.0182"
+alue of position at maturity $% !$5,*87.50" buysC !otional ' (pot ) *utures% ' ontrats sellsC !otional ' (pot ) *utures% ' ontrats
!$2#,900.00"
$*,225.00
$1,*50.00
Assumptions Pounds A% per futures ontrat aturity month !umber of ontrats Bid she buy or sell the futures?
#nding spot rate $/A% Pound futures ontrat settle prie $ (pot ) *utures
nterpretation
"uys a futureC &amie buys at the futures prie and s ells at the ending spot prie. (he therefore profits 4hen the futures prie is less 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.
Contract *2,500 poun's pen 4i)% nterest 1.>@00 2505 1.>550 809
Problem 8.# Sallie Sc%nu'el (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 urren t spot rate is $0.000/($. fter onsiderable study she has onluded that the (ingapore dollar 4ill appreiat e versus the ,.(. dollar in the oming 90 days probably to about $0.@000/($. (he has the follo4ing options on the (ingapore dollar to hoose fromC ption Put on (ing $ 3all on (ing $
Strie Price $0.500/($ $0.500/($
Premium $0.0000=/($ $0.000>/($
a. (hould (allie buy a put on (ingapore dollars or a all on (ingapore dollars? b. What is (allie
Call on S$ $0.*500 $0.000#*
Assumptions 3urrent spot rate ,($/(ingapore dollar% Bays to maturity #'peted spot rate in 90 days ,($/(ingapore dollar%
Put on S$ $0.*500 $0.0000
Values $0.*000 90 $0.7000
a. S%oul' Sallie bu3 a put on Sin)apore 'ollars or a call on Sin)apore 'ollars;
(ine (allie e'pets the (ingapore dollar to appreiate versus the ,( dollar she should buy a all on (ingapore dollars. ;his gives her the right to ",G (ingapore dollars at a future date at $0.5 eah and then immediately resell them in the open maret at $0.@0 eah for a profit. f her e'petation of the future spot rate proves orret.% b. <%at is Sallie&s breae+en price on t%e option purc%ase' in part a";
!ote this does not inlude a ny interest ost on the premium.
(trie prie Plus premium "reaeven
Per S$ $0.*5000 $0.000#* $0.*50#*
c. <%at is Sallie&s )ross pro(it an' net pro(it !inclu'in) premium" i( t%e en'in) spot rate is $0.70/S$;
(pot rate ess strie prie ess premium Profit
=ross pro(it !S$/S$" $0.70000 !$0.*5000" $0.05000
>et pro(it !S$/S$" $0.70000 !$0.*5000" !$0.000#*" $0.0#95#
'. <%at is Sallie&s )ross pro(it an' net pro(it !inclu'in) premium" i( t%e en'in) spot rate is $0.80/S$;
(pot rate ess strie prie ess premium Profit
=ross pro(it !S$/S$" $0.80000 !$0.*5000" $0.15000
>et pro(it !S$/S$" $0.80000 !$0.*5000" !$0.000#*" $0.1#95#
Problem 8.5 la'e Capital !A" 3hristoph Hoffeman trades urreny for "lade 3apital of 7eneva. 3hristoph has $10 million to begin 4ith and he must state all profits 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 $1.2800/I at the end of =0 days 4hat should he do?
Assumptions nitial investment funds available% 3urrent spot rate ,($/ €% =0)day for4ard rate ,($/ €% #'peted spot rate in =0 days ,($/ €%
a. Values $10,000,000 $1.58 $1.50 $1.*00
b. Values $10,000,000 $1.58 $1.50 $1.2800
Strate)3 (or Part a":
Jne of the more interesting dimensions of speulating in the for4ard maret is that if the speulator has aess to the for4ard maret ban lines or relationships 4hen 4oring on behalf of an established firm% many for4ard speulation strategies re6uire no atual ash flo4 position up front. n this ase 3hristoph believes the dollar 4ill be trading at $1.=/ € in the open maret at the end of =0 days but he has the ability to buy or sell dollars at a f or4ard rate of $1.==50/ €. He should therefore buy euros for4ard =0 days re6uires no atual ash flo4 up front% and at the end of =0 days tae delivery of those euros and sell in the spot maret at the higher dollar rate for profit. nitial in+estment principle 0 'a3 (or6ar' rate !S$/ €" uros bou)%t (or6ar' !n+estment / (or6ar' rate" Spot rate in open maret at en' o( 0 'a3s !S$/ €" S$ procee's !euros bou)%t (or6ar' e@c%an)e' to S$ spot" Pro(it in S$
$10,000,000.00 $1.50 ? 7,#90,**.70 $1.*00 $10,187,2*5.92 $187,2*5.92
Strate)3 (or Part b":
gain a profitable strategy an be e'euted 4ithout any atual ash flo4 hanging hands at the beginning of the period. (ine 3hristoph believes that the dollar 4ill str engthen to $1.28 in =0 days he s hould sell euros for4ard no4 at the higher dollar rate 4ait =0 days and buy the euros needed on the open maret at $1.28 and immediately then use those euros to fulfill his for4ard ontrat to sell euros for dollars at $1.==50. *or a profit. n+estment (un's nee'e' in 0 'a3s Spot rate in open maret at en' o( 0 'a3s uros bou)%t in open maret in 0 'a3s !n+estment / spot rate" Ste(an %a' sol' t%ese euros (or6ar' at t%e start o( t%e 0 'a3 perio'. 0 'a3 (or6ar' rate !S$/ €" S$ procee's !euros sol' (or6ar' into S$" Pro(it in S$
$10,000,000.00 $1.2800 ? 7,812,500.00
$1.50 $10,#29,*87.50 $#29,*87.50
Problem 8.* la'e Capital !" 3hristoph Hoffeman of "lade 3apital no4 believes the (4iss fran 4ill appreiate versus the ,.(. dollar in the oming three)month period. He has $100000 to i nvest. ;he urrent spot rate is $0.5820/(* the three)month for4ard rate is $0.5>0/(* and he e'pets the spot rates to reah $0.250/(* in three months. a. 3alulate 3hristoph
Assumptions nitial investment funds available% 3urrent spot rate ,($/(4iss fran% (i')month for4ard rate ,($/(4iss fran% #'peted spot rate in si' months ,($/(4iss fran% Strate)3 (or Part a: 1. ,se the $100000 today to buy (* at spot rate 2. Hold the (* indefinitely. =. t the end of si' months onvert (* at e'peted rate >. Gielding e'peted dollar revenues of 5. DealiEe profit revenues less $100000 initial invest% Strate)3 (or Part b: 1. "uy (* for4ard si' months no ash outlay re6uired% 2. *ulfill the si' months for4ard in si' months ost in ,($ =. 3onvert the (* into ,($ at e'peted spot rate >. DealiEe profit
a. Values $100,000 $0.5820 $0.5*#0 $0.*250
b. Values $100,000 $0.5820 $0.5*#0 $0.*250
S-r. 171,821.1 $0.*250 $107,88.2 $7,88.2
S-r. 177,0#.9* !$100,000.00" $110,815.*0 $10,815.*0
Problem 8.7 C%a+e S.A. 3haveE (.. a +eneEuelan ompany 4ishes to borro4 $8000000 for eight 4ees. 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 4hih soure should 3haveE borro4? Assumptions Prinipal borro4ing need aturity needed in 4ees Date of interest harged by potential lenders >e6 or interest rate practices nterest alulation usesC #'at number of days in period !umber of days in finanial year (o the interest harge on this prinipal is =reat ritain interest rate practices nterest alulation usesC #'at number of days in period !umber of days in finanial year (o the interest harge on this prinipal is S6iss interest rate practices nterest alulation usesC ssumed =0 days per month for t4o months !umber of days in finanial year (o the interest harge on this prinipal is
$
Values 8,000,000 8 *.250B
$
5* *0 77,777.78
$
5* *0 77,777.78
$
*0 *0 8,.
ndina should borro4 in 7reat "ritain beause it has the lo4est interest ost.
Problem 8.8 otan3 a3 Corporation "otany "ay 3orporation of ustralia sees to borro4 ,($=0000000 in the #urodollar maret. *unding is needed for t4o years. nvestigation leads to three possibilities. 3ompare the alternatives and mae a reommendation. L1. "otany "ay ould borro4 the ,($=0000000 for t4o years at a fi'ed 5K rate of interest L2. "otany "ay ould borro4 the ,($=0000000 at "JD M 1.5K. "JD is urrently =.5K and the rate 4ould be reset every si' months L=. "otany "ay ould borro4 the ,($=0000000 for one year only at >.5K. t the end of the first year "otany "ay 4ould have to negotiate for a ne4 one)year loan. Assumptions Prinipal borro4ing need aturity needed in years *i'ed rate 2 years *loating rate si')month "JD M spread 3urrent si')month "JD (pread *i'ed rate 1 year then re)fund
$
Values 0,000,000 2.00 5.000B .500B 1.500B #.500B -irst *Dmont%s
F1: -i@e' rate, 2 3ears nterest ost per year 3ertainty over aess to apital 3ertainty over ost of apital
Certain Certain
F2: -loatin) rate, si@Dmont% G H sprea' $ nterest ost per year 3ertainty over aess to apital 3ertainty over ost of apital
750,000 Certain Certain
F: -i@e' rate, 1 3ear, t%en reD(un' nterest ost per year 3ertainty over aess to apital 3ertainty over ost of apital
Certain Certain
Secon' *Dmont%s $
E%ir' *Dmont%s
1,500,000 Certain Certain
$
750,000 Certain ncertain
$
1,50,000 Certain Certain
-ourt% *Dmont%s $
1,500,000 Certain Certain
$
750,000 Certain ncertain
Certain Certain
$
750,000 Certain ncertain
;;; 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
;;; ncertain ncertain
Problem 8.9 Vatic Capital 3ahita Haynes 4ors as a urreny speulator for +ati 3apital of os ngeles. Her latest speulative position is to profit from her e'petation that the ,.(. dollar 4ill rise signifiantly against the &apanese yen. ;he urrent spot rate is 120.00/$. (he mu st hoose bet4een the follo4ing 90)day options on the &apanese yenC ption Put on yen 3all on yen
Strie Price 125/$ 125/$
Premium $0.0000=/($ $0.000>/($
a. (hould 3ahita buy a put on yen or a all on yen? b. What is 3ahita0/$? Assumptions 3urrent spot rate &apanese yen/,($% in ,($/yen aturity of option days% #'peted ending spot rate in 90 days yen/$% in ,($/yen
Values 120.00 $0.008 90 1#0.00 $0.0071# Call on 3en 125.00 $0.00800 $0.000#*
(trie prie yen/,($% in ,($/yen Premium ,($/yen%
Put on 3en 125.00 $0.00800 $0.0000
a. S%oul' s%e bu3 a call on 3en or a put on 3en; 3ahita should buy a put on yen to profit from the rise of the dollar the fall of the yen%. b. <%at is Cac%ita&s brea e+en price on %er option o( c%oice in part a"; 3ahita buys a put on yen. Pays premium today. n 90 days e'erises the put reeiving ,($.
(trie prie ess premium "reaeven
$0.00800 D$0.0000 $0.00797
in 3en/$ 125.00 125.#7
c. <%at is Cac%ita&s )ross pro(it an' net pro(it i( t%e en' spot rate is 1#0 3en/$;
(trie prie ess spot rate ess premium Profit
=ross pro(it !S$/3en" $0.00800 D$0.0071# $0.0008*
>et pro(it !S$/3en" $0.00800 D$0.0071# D$0.0000 $0.0008
Problem 8.10 Callin) All Pro(its ssume a all option on euros is 4ritten 4ith a strie prie of $1.2500/I at a premium of =.80: per euro $0.0=80/I% and 4ith an e'piration date three months from no4. ;he option is for I100000. 3alulate your profit or loss s hould you e'erise before maturity at a time 4hen the euro is traded spot at ..... !oteC the option premium is =.8 ents per euro not =8 ents per euro.
Assumptions !otional prinipal euros% aturity days% (trie prie ,($/euro% Premium ,($/euro% #nding spot rate ,($/euro%
7ross profit on option ess premium !et profit ,($/euro% !et profit total
a. Values ? 100,000.00 90 $1.2500 $0.080 $1.1000
b. Values ? 100,000.00 90 $1.2500 $0.080 $1.1500
c. Values ? 100,000.00 90 $1.2500 $0.080 $1.2000
'. Values ? 100,000.00 90 $1.2500 $0.080 $1.2500
e. Values ? 100,000.00 90 $1.2500 $0.080 $1.000
(. Values ? 100,000.00 90 $1.2500 $0.080 $1.500
). Values ? 100,000.00 90 $1.2500 $0.080 $1.#000
$0.0000 !$0.080" !$0.080"
$0.0000 !$0.080" !$0.080"
$0.0000 !$0.080" !$0.080"
$0.0000 !$0.080" !$0.080"
$0.0500 !$0.080" $0.0120
$0.1000 !$0.080" $0.0*20
$0.1500 !$0.080" $0.1120
!$,800.00"
!$,800.00"
!$,800.00"
!$,800.00"
$1,200.00
$*,200.00
$11,200.00
Problem 8.11 M3ster3 at aer Street
rthur Boyle is a urreny trader for "aer (treet a private investment house in ondon. "aer (treetQs lients are a olletion of 4ealthy private investors 4ho 4ith a minimum stae of N250000 eah 4ish to speulate on the movement of urrenies. ;he investors e'pet annual returns in e'ess of 25K. lthough offied in ondon all aounts and e'petations are based in ,.(. dollars. rthur is onvined that the "ritish pound 4ill slide signifiantly )) possibly to $1.=200/N )) in the oming =0 to 0 days. ;he urrent spot rate is $1.>20/N. rthur 4ishes to buy a put on pounds 4hih 4ill yield the 25K return e'peted by his investors. Whih of the follo4ing put options 4ould you reommend he purhase? Prove your hoie is the preferable ombination of strie prie maturity and up)front premium e'pense. Strie Price $1.=/N $1.=>/N $1.=2/N $1.=/N $1.=>/N $1.=2/N Assumptions 3urrent spot rate ,($/ £% #'peted endings spot rate in =0 to 0 days ,($/ £%
Maturit3 =0 days =0 days =0 days 0 days 0 days 0 days
Premium $0.00081/N $0.00021/N $0.0000>/N $0.00===/N $0.00150/N $0.0000/N Values $1.#2*0 $1.200
Problem 8.11 M3ster3 at aer Street
rthur Boyle is a urreny trader for "aer (treet a private investment house in ondon. "aer (treetQs lients are a olletion of 4ealthy private investors 4ho 4ith a minimum stae of N250000 eah 4ish to speulate on the movement of urrenies. ;he investors e'pet annual returns in e'ess of 25K. lthough offied in ondon all aounts and e'petations are based in ,.(. dollars. rthur is onvined that the "ritish pound 4ill slide signifiantly )) possibly to $1.=200/N )) in the oming =0 to 0 days. ;he urrent spot rate is $1.>20/N. rthur 4ishes to buy a put on pounds 4hih 4ill yield the 25K return e'peted by his investors. Whih of the follo4ing put options 4ould you reommend he purhase? Prove your hoie is the preferable ombination of strie prie maturity and up)front premium e'pense. Strie Price $1.=/N $1.=>/N $1.=2/N $1.=/N $1.=>/N $1.=2/N
Maturit3 =0 days =0 days =0 days 0 days 0 days 0 days
Assumptions 3urrent spot rate ,($/ £% #'peted endings spot rate in =0 to 0 days ,($/ £% Potential investment prinipal per person £%
Premium $0.00081/N $0.00021/N $0.0000>/N $0.00===/N $0.00150/N $0.0000/N Values $1.#2*0 $1.200 250,000.00
Put options on poun's (trie prie ,($/ £% aturity days% Premium ,($/£%
Put F1 $1.* 0 $0.0008
Put F2 $1.# 0 $0.0002
Put F $1.2 0 $0.0000
Put options on poun's (trie prie ,($/ £% aturity days% Premium ,($/£%
Put F# $1.* *0 $0.00
Put F5 $1.# *0 $0.0015
Put F* $1.2 *0 $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
(trie prie ess e'peted spot rate ess premium Profit f (ydney invested an individual
Put F# >et pro(it $1.*000 !1.2000" !0.00" $0.0**7
Put F5 >et pro(it $1.#000 !1.2000" !0.00150" $0.01850
Put F* >et pro(it $1.2000 !1.2000" !0.000*0" !$0.000*0"
75,075,075.08
1**,***,***.*7
#1*,***,***.*7
$2,75,00.00 $5*,500.00 772B
$,08,. $5*,500.00 8*5B
D$250,000.00 $5*,500.00 D70B
Problem 8.12 Contrarious Calan'ra 3alandra Panagaos 4ors for 3"3 3urreny *unds in ;oronto. 3alandra is something of a ontrarian )) as opposed to most of the foreasts she believes the 3anadian dollar 3$% 4ill appreiate versus the ,.(. dollar over the oming 90 days. ;he urrent spot rate is $0.@50/3$. 3alandra may hoose bet4een the follo4ing options on the 3anadian dollarC ption 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
Values $0.*750 90
Jption hoies on the 3anadian dollarC (trie prie ,($/3anadian dollar% Premium ,($/3anadian dollar%
Call option $0.7000 $0.000#9
Put option $0.7000 $0.000
a" <%ic% option s%oul' Calan'ra bu3;
(ine 7iri e'pets the 3anadian dollar to appreiate versus the ,( dollar he should buy a all on 3anadian dollars. b" <%at is Calan'ra&s breae+en price on t%e option purc%ase' in part a";
(trie prie Plus premium "reaeven
$0.7000 0.000#9 $0.7005
c" <%at is Calan'ra&s )ross pro(it an' net pro(it !inclu'in) premium" i( t%e en'in) spot rate is $0.7*00/C$;
(pot rate ess strie prie ess premium Profit
=ross pro(it !S$/C$" $0.7*00 !0.7000" $0.0*00
>et pro(it !S$/C$" $0.7*00 !0.7000" !0.000#9" $0.05951
'" <%at is Calan'ra&s )ross pro(it an' net pro(it !inclu'in) premium" i( t%e en'in) spot rate is $0.8250/C$;
(pot rate ess strie prie ess premium Profit
=ross pro(it !S$/C$" $0.8250 !0.7000" $0.1250
>et pro(it !S$/C$" $0.8250 !0.7000" !0.000#9" $0.12#51
Problem 8.1 Gai' =auloises Daid 7auloises is a rapidly gro4ing *renh sporting goods and adventure raing outfitter. ;he ompany has deided to borro4 I20000000 via a euro) euro floating rate loan for four years. Daid must deide bet4een t4o ompeting loan offerings from t4o of its bans. "an6ue de Paris has offered the four)year debt at euro)"JD M 2.00K 4ith an up)front initiation fee of 1.8K. "an6ue de (orbonne ho4ever has offered euro)"JD M 2.5K a higher spread but 4ith no loan initiation fees up)front for the same term and prinipal. "oth bans reset the interest rate at the end of eah year. #uro)"JD is urrently >.00K. DaidQs eonomist foreasts that "JD 4ill rise by 0.5 perentage points eah year. "an6ue de (orbonne ho4ever offiially foreasts euro)"JD to begin trending up4ard at the rate of 0.25 perentage points per year. Daid 7auloisesQs ost of apital is 11K. Whih loan proposal do you reommend for Daid 7auloises?
Assumptions Prinipal borro4ing need aturity needed in years 3urrent euro)"JD "an6ue de Paris< spread R e'petation "an6ue de Paris< initiation fee "an6ue de (orbonne
Values ? 20,000,000 #.00 #.000B 2.000B 1.800B 2.500B 0.000B
@pecte' C%) in G
0.500B 0.250B
Daid 7auloises must evaluate both loan proposals under both po tential interest rate senarios. anIue 'e Paris oan Proposal #'peted interest rates R paymentsC #'peted euro)"JD "an spread nterest rate
*unds raised net of fees #'peted interest osts Depayment of prinipal ;otal ash flo4s ll)in)ost of funds ifC euro)"JD rises 0.500K per year euro)"JD rises 0.250K per year anIue 'e Sorbonne oan Proposal #'peted interest rates R paymentsC #'peted euro)"JD "an spread nterest rate
*unds raised net of fees #'peted interest osts Depayment of prinipal ;otal ash flo4s ll)in)ost of funds ifC euro)"JD rises 0.500K per year euro)"JD rises 0.250K per year
ear 0
ear 1
ear 2
ear
ear #
#.000B 2.000B *.000B
#.500B 2.000B *.500B
5.000B 2.000B 7.000B
5.500B 2.000B 7.500B
*.000B 2.000B 8.000B
D? 1,00,000
D? 1,#00,000
D? 1,500,000
D? 1,00,000
D? 1,#00,000
D? 1,500,000
D? 1,*00,000 D? 20,000,000 D? 21,*00,000
? 19,*#0,000
? 19,*#0,000
7.7#8B 7.1*5B
*ound by plugging in .250K in e'petations above.
ear 0
ear 1
ear 2
ear
ear #
#.000B 2.500B *.500B
#.250B 2.500B *.750B
#.500B 2.500B 7.000B
#.750B 2.500B 7.250B
5.000B 2.500B 7.500B
D? 1,50,000
D? 1,#00,000
D? 1,#50,000
D? 1,50,000
D? 1,#00,000
D? 1,#50,000
D? 1,500,000 D? 20,000,000 D? 21,500,000
? 20,000,000
? 20,000,000
7.070B 7.10*B
*ound by plugging in .500K in e'petations above.
;he "an6ue de (orbonne loan proposal is atually lo4er all)in)ost under either interest rate senario.
Problem 8.1# Sc%i(ano Motors (hifano otors of taly reently too out a >)year I5 million loan on a floating rate basis. t is no4 4o rried ho4ever about rising interest osts. lthough it had initially believed interest rates in the #uro)Eone 4ould be trending do4n4ard 4hen taing out the loan reent eonomi indiators sho4 gro4ing inflationary pressures. nalysts are prediting that the #uropean 3entral "an 4ill slo4 monetary gro4th driving interest rates up. (hifano is no4 onsidering 4hether to see some protetion against a rise in euro)"JD and is onsidering a *or4ard Date greement *D% 4ith an insurane ompany. ording to the agreement (hifano 4ould pay to the insurane ompany at the end of eah 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 in interest 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 finaning osts 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? Assumptions Prinipal borro4ing need aturity needed in years 3urrent "JD *elini
Values ? 5,000,000 #.00 #.000B 2.500B 70B ? 100,000 ear 0
ear 2
ear
ear #
.500B 2.500B *.000B
.000B 2.500B 5.500B
2.500B 2.500B 5.000B
2.000B 2.500B #.500B
D? 100,000
D? 00,000 D? 25,000
D? 275,000 D? 50,000
D? 250,000 D? 75,000
? #,900,000
D? 25,000
D? 25,000
D? 25,000
D? 225,000 D? 100,000 D? 5,000,000 D? 5,25,000
ear 1
ear 2
ear
ear #
#.500B 2.500B 7.000B
5.000B 2.500B 7.500B
5.500B 2.500B 8.000B
*.000B 2.500B 8.500B
D? 100,000
D? 50,000 ? 17,500
D? 75,000 ? 5,000
D? #00,000 ? 52,500
? #,900,000
D? 2,500
D? #0,000
D? #7,500
D? #25,000 ? 70,000 D? 5,000,000 D? 5,55,000
#'peted annual hange in "JD
"JD "an spread nterest rate
*unds raised net of fees #'peted interest interest rate ' prinipal% -or6ar' Gate A)reement Depayment of prinipal ;otal ash flo4s ll)in)ost of funds DD%
( G Gises 50 asis Pts Per ear
D0.500B #.000B 2.500B *.500B ? 5,000,000
7.092B
ear 0
#'peted annual hange in "JD
"JD "an spread nterest rate
*unds raised net of fees #'peted interest interest rate ' prinipal% -or6ar' Gate A)reement Depayment of prinipal ;otal ash flo4s ll)in)ost of funds DD%
ear 1
0.500B #.000B 2.500B *.500B ? 5,000,000
7.#58B
;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 of outome. !ot a very good deal. final note of signifiane is that sine (hifano reeives only @0K of the differene in rates its t otal ost of funds is not effetively OappedOS they ould in fat rise 4ith no limit over the period as interest rates rose.
Problem 8.15 C%r3sler C
3hrysler 3 the no4 privately held ompany sold)off by Baimler3hrysler must pay floating rate interest three months from no4. t 4ants to lo in t hese 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. 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 nterest rate futures losing prie #ffetive yield on interest rate futures
C%r3sler&s interest rate pa3ments 6it% (utures
nterest payment due in three months (ell a future tae a short positi on% 7ain or loss on position
Values 9.07 *.90B E%ree Mont%s -rom >o6 -loatin) Gate is -loatin) Gate is *.000B 8.000B *.000B D*.90B D0.90B oss
8.000B D*.90B 1.070B =ain
Problem 8.1* C Solutions Heather J.00K per annum. Heather has Tust made an interest payment today so the ne't payment is due si' months from today.
Heather finds that she an s4ap her urrent floating rate payments for fi'ed payments of @.00K per annum. 3" (olutions
$
Values 5,000,000 #.000B 2.000B 7.000B -irst *Dmont%s
Secon' *Dmont%s
E%ir' *Dmont%s
-ourt% *Dmont%s
0.500B #.500B
5.000B
5.500B
*.000B
Current loan a)reement: #'peted "JD for months% (pread for months% #'peted interest payment
D2.250B D1.000B D.250B
D2.500B D1.000B D.500B
D2.750B D1.000B D.750B
D.000B D1.000B D#.000B
S6ap A)reement: Pay fi'ed for )months% Deeive floating "JD for months%
D.500B 2.250B
D.500B 2.500B
D.500B 2.750B
D.500B .000B
>et interest !loan H s6ap"
D#.500B
D#.500B
D#.500B
D#.500B
nterest J S6ap Pa3ments a. G increases 50 basis pts/* mont%s #'peted "JD
S6ap sa+in)s; !et interest after s4ap oan agreement interest S6ap sa+in)s !s6ap cost"
$ $
!225,000" !1*2,500" !*2,500"
$ $
!225,000" !175,000" !50,000"
$ $
!225,000" !187,500" !7,500"
$ $
!225,000" !200,000" !25,000"
b. G 'ecreases 25 basis pts/* mont%s #'peted "JD
D0.250B .750B
.500B
.250B
.000B
Current loan a)reement: #'peted "JD for months% (pread for months% #'peted interest payment
D1.875B D1.000B D2.875B
D1.750B D1.000B D2.750B
D1.*25B D1.000B D2.*25B
D1.500B D1.000B D2.500B
S6ap A)reement: Pay fi'ed for )months% Deeive floating "JD for months%
D.500B 1.875B
D.500B 1.750B
D.500B 1.*25B
D.500B 1.500B
>et interest !loan H s6ap"
D#.500B
D#.500B
D#.500B
D#.500B
S6ap sa+in)s; !et interest after s4ap oan agreement interest S6ap sa+in)s !s6ap cost"
$ $
!225,000" !1#,750" !81,250"
$ $
!225,000" !17,500" !87,500"
$ $
n bot% cases C Solutions is su((erin) %i)%er total interest costs as a result o( t%e s6ap.
!225,000" !11,250" !9,750"
$ $
!225,000" !125,000" !100,000"
Problem 8.17 lu+ia an' Para)uas luvia anufaturing and Paraguas Produts both see funding at the lo4est possible ost. luvia 4ould prefer the fle'ibility of floating rate borro4ing 4hile Paraguas 4ants the seurity of fi'ed rate borro4ing. luvia is the more redit)4orthy ompany. ;hey fae the follo4ing rate struture. luvia 4ith the better redit rating has lo4er borro4ing osts in both types of borro4ing. luvia 4ants floating rate debt so it ould borro4 at "JDM1K. Ho4ever it ould borro4 fi'ed at 8K and s4ap for floating rate debt. Paraguas 4ants fi'ed rate so i t ould borro4 fi'ed at 12K. Ho4ever it ould borro4 floating at "JDM2K and s4ap for fi'ed rate debt. What should they do?
Assumptions 3redit rating Prefers to borro4 *i'ed)rate ost of borro4ing *loating)rate ost of borro4ingC "JD value is unimportant% (pread ;otal floating)rate Comparati+e A'+anta)e in orro6in) luvia
f Paraguas borro4s fi'ed f Paraguas borro4s floating R s4aps 4ith luvia
Ka+ier AAA -loatin) 8.000B
Lulu -i@e' 12.000B
5.000B 1.000B *.000B
5.000B 2.000B 7.000B
Values #.000B 1.000B .000B Ka+ier D8.000B DDD D5.000B 8.500B D#.500B
Lulu DDD D7.000B 5.000B D8.500B D10.500B
*.000B #.500B 1.500B 12.000B 10.500B 1.500B
;he =.0K omparative advantage enToyed by luvia represents the opportunity set for improvement for both parties. ;his ould be a 1.5K savings for eah as in the e'ample sho4n% or any other ombination 4hih distributes the =.0K bet4een the t4o parties.
Problem 8.18 Eri'ent&s Cross Currenc3 S6ap: S(r (or S$ ;rident 3orporation entered into a three)year ross urreny interest rate s4ap to reeive ,.(. dollars and pay (4iss frans. ;rident ho4ever deided to un4ind the s4ap after one year thereby having t4o years left on the settlement osts of un4inding the s4ap after one year. Depeat the alulations for un4inding but assume that the follo4ing rates no4 applyC Assumptions !otional prinipal Jriginal spot e'hange rate (*r./$ !e4 1)year later% spot e'hange rate (*r./$ !e4 fi'ed ,( dollar interest !e4 fi'ed (4iss fran interest
$
a. nterest J S6ap Pa3ments
Values 10,000,000 1.5000 1.55*0 5.20B 2.20B ear 0
Deeive fi'ed rate dollars at this rateC Jn a notional prinipal ofC ;rident 4ill reeive ash flo4sC
$
D3ear as 5.59B 2.01B
ear 1
ear 2
ear
5.5*B
5.5*B
5.5*B
10,000,000
;rident 4ill pay ash flo4sC Jn a notional prinipal ofC Pay fi'ed rate (4iss frans at this rateC
FFF
FFF
FFF
S-r. 01,500
S-r. 01,500
S-r. 15,01,500
S-r. 15,000,000
b. n6in'in) t%e s6ap a(ter oneD3ear
Demaining dollar ash inflo4s P+ fator at no4 urrent fi'ed $ interest P+ of remaining dollar ash inflo4s 3umulative P+ of dollar ash inflo4s
Settlement: 3ash inflo4 3ash outflo4 !et ash settlement of un4inding
D 3ear bi' 5.5*B 1.9B
U 1.5000 V
#'hange rate time of s4ap (*r./$)
Demaining (4iss fran ash outflo4s P+ fator at no4 urrent fi'ed ( * interest P+ of remaining (* ash outflo4s 3umulative P+ of (* ash outflo4s !e4 urrent spot rate (*r./$ 3umulative P* of (* ash outflo4s in $
S6ap Gates JriginalC ,( dollar JriginalC (4iss fran
2.01B
2.01B
2.01B
ear 1
ear 2
ear
$ 5.20B $ $
$ $
S-r. 01,500 0.9785 S-r. 295,010
S-r. 1#,9##,827 1.55*0 $ 9,*0#,*#5
$ $
10,55*,000 0.90* 9,58,22
10,0**,750
2.20B
55*,000 0.950* 528,517
10,0**,750 !9,*0#,*#5" #*2,105
;his is a ash reeipt by ;rident from the s4ap dealer.
S-r. 15,01,500 0.957# S-r. 1#,*#9,818
Problem 8.19 Eri'ent&s Cross Currenc3 S6ap: en (or uros ,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 yen on a notional prinipal of I5000000. ;he spot e'hange rate at the time of the s 4ap is 10>/I. a. 3alulate all prinipal and interest payments in both euros and (4iss frans for the life of the s4ap agreement. 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 a t4o)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 of e'hange is no4 11>/I 4hat is the net present value of the s4 ap agreement? Who pays 4hom 4hat?
Assumptions !otional prinipal (pot e'hange rate Gen/euro
Values ? 5,000,000 10#.00
a" nterest J S6ap Pa3ments
S6ap Gates #uros )) I &apanese yen
ear 0
Deeive fi'ed rate euros at this rateC Jn a notional prinipal ofC ;rident 4ill reeive ash flo4sC
D 3ear bi' .2#B 0.5*B
D3ear as .28B 0.59B
ear 1
ear 2
ear
.2#B
.2#B
.2#B
? 5,000,000
FFF
FFF
FFF
U #'hange rate time of s4ap / I)
10#.00
V ;rident 4ill pay ash flo4sC Jn a notional prinipal of yen%C Pay fi'ed rate &apanese yen at this r ateC
b" n6in'in) t%e s6ap a(ter oneD3ear
Demaining euro ash inflo4s P+ fator at no4 urrent fi'ed I interest P+ of remaining I ash inflo4s 3umulative P+ of I ash 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 in I Settlement: 3ash inflo4 3ash outflo4 !et ash settlement of un4inding
,0*8,000
,0*8,000
52,0*8,000
520,000,000
.*0B
0.59B
0.59B
0.59B
ear 1
ear 2
ear
? 1*2,000 0.9*5 ? 15*,71
? 5,1*2,000 0.917 ? #,809,#8#
S-r. ,0*8,000 0.9921 S-r. ,0#,*51
S-r. 52,0*8,000 0.98#2 S-r. 51#,798,280
? #,9*5,855
0.80B
517,8#1,91 11#.00 ? #,5#2,#7
? #,9*5,855 !#,5#2,#7" ? #2,82
;his is a ash reeipt by ;rident from the s4ap dealer.
Problem 8.20 -alcor *alor is the ,.(.)based automotive parts supplier 4hih 4as spun)off from 7eneral otors in 2000. With annual sales of over $2 billion the ompany has e'panded its marets far beyond the traditional automobile manufaturers in the pursuit of a more diversified sales base. s part of the general diversifiation effort the ompany 4ishes to diversify the urreny of denomination of its debt portfolio as 4ell. ssume *alor enters into a $50 million @)year ross urreny interest rate s4ap to do Tust that pay euro and reeive dollars. ,sing the data in #'hibit 8.1= solve the follo4ingC a. 3alulate all prinipal and interest payments in both urrenies for the life of the s4ap. b. ssume that three years later *alor deides to un4ind the s4ap agreement. f >)year fi'ed rates of interest in euros have no4 risen to 5.=5K and >)year fi'ed rate dollars have fallen to >.>0K and the urrent spot e'hange rate of $1.02/I 4hat is the net present value of the s4 ap agreement? Who pays 4ho m4hat?
Assumptions !otional prinipal (pot e'hange rate $/I
$
Values 50,000,000 1.1*
a. nterest J S6ap Pa3ments
S6ap Gates ,( dollar #uros
ear 0
Deeive fi'ed rate dollars at rateC !otional prinipal ofC Deeive ash inflo4s ofC
$
ear 1
7D 3ear bi' 5.8*B #.01B
7D3ear as 5.89B #.05B
ear 2
ear
ear #
ear 5
ear *
ear 7
5.8*B 50,000,000 $ 2,90,000 $ 2,90,000
$ 2,90,000 $ 2,90,000 $ 2,90,000 $ 2,90,000 $ 52,90,000
U (pot e'hange rate $/I
1.1*
V Pay ash outflo4s ofC !otional prinipal ofC Pay fi'ed rate euros at rateC
? 1,7#5,*90
? 1,7#5,*90
? 1,7#5,*90
? 1,7#5,*90
? 1,7#5,*90
? 1,7#5,*90
? ##,8#9,18
ear 1
ear 2
ear
ear #
ear 5
ear *
ear 7
? #,10,##8 #.05B
b. n6in'in)t%e S6ap
ear 0
f the s4ap is un4ound three years later there are four years of ash flo4s remainingC Demaining dollar ash inflo4s P+ fator at no4 urrent fi'ed $ interest P+ of remaining dollar ash inflo4s 3umulative P+ of $ ash infllo4s
$ 2,90,000 $ 2,90,000 0.9579 0.9175 $ 2,80*,51 $ 2,*88,21
#.#0B $
$ 2,90,000 $ 52,90,000 0.8788 0.8#18 $ 2,57#,9# $ ##,555,5#
52,*25,0
Demaining euro ash outflo4s P+ fator at no4 urrent fi'ed I interest P+ of remaining euro ash outflo4s 3umulative P+ of I cash outflows (pot e'hange rate at un4inding $/I ) 3umulative P+ of I ash outflo4s $
? #1,12,5#2 1.02 $ #1,955,19
Settlement: 3ash inflo4 3ash outflo4 !et ash settlement of un4inding
$ 52,*25,0 !#1,955,19" $ 10,**9,8#0
? 1,7#5,*90 0.9#92 ? 1,*57,08
5.5B
? 1,7#5,*90 0.9010 ? 1,572,889
? 1,7#5,*90 0.855 ? 1,#9,012
? ##,8#9,18 0.8118 ? *,#09,*0
;his is a net ash payment to *alor from the s4ap dealer.
Problem 8.21 .S. 'ollar/uro
Pricin) Currenc3 ptions on t%e uro
Spot rate !'omestic/(orei)n" Strie rate !'omestic/(orei)n" Nomestic interest rate !B p.a." -orei)n interest rate !B p.a." Eime !3ears, *5 'a3s" Na3s eIui+alent Volatilit3 !B p.a." Call option premium !per unit (c" Put option premium !per unit (c" !uropean pricin)" C ll
ti
i
!B"
A U.S.-based firm wishing to buy
A European firm wishing to buy
or se ll euros (t he forei gn currenc y)
or sel l dol lars (t he forei gn curre ncy )
Variable S0 K r' r(
Value $1.2#80 $1.2500 1.#5B
Variable S0 K r'
Value ? 0.801 ? 0.8000 2.187B
s
2.187B 1.000 *5.00 12.000B
r(
s
1.#5B 1.000 *5.00 12.000B
c p
$0.05# $0.0*#
c p
? 0.0#12 ? 0.0#2
E
# 28B
E
5 15B
Problem 8.21 .S. 'ollar/uro
Pricin) Currenc3 ptions on t%e uro
Spot rate !'omestic/(orei)n" Strie rate !'omestic/(orei)n" Nomestic interest rate !B p.a."
A U.S.-based firm wishing to buy
A European firm wishing to buy
or se ll euros (t he forei gn currenc y)
or sel l dol lars (t he forei gn curre ncy )
Variable S0 K r'
$1.2#80 $1.2500 1.#5B
Variable S0 K r'
Value ? 0.801 ? 0.8000 2.187B
s
2.187B 1.000 *5.00 12.000B
r(
s
1.#5B 1.000 *5.00 12.000B
Call option premium !per unit (c" Put option premium !per unit (c" !uropean pricin)"
c p
$0.05# $0.0*#
c p
? 0.0#12 ? 0.0#2
Call option premium !B" Put option premium !B"
c p
#.28B 5.15B
c p
5.15B #.27B
-orei)n interest rate !B p.a." Eime !3ears, *5 'a3s" Na3s eIui+alent Volatilit3 !B p.a."
r(
Value
E
E
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.
Problem 8.22 .S. Nollar/apanese en
Pricin) Currenc3 ptions on t%e apanese 3en
Spot rate !'omestic/(orei)n" Strie rate !'omestic/(orei)n" Nomestic interest rate !B p.a." -orei)n interest rate !B p.a." Eime !3ears, *5 'a3s" Na3s eIui+alent Volatilit3 !B p.a."
A Japanese firm wishing to buy
A U.S.-based firm wishing to buy
or sell dollars (the foreign currency)
or sell yen (the foreign currency)
Variable S0 K r' r( E s
Call option premium !per unit (c" Put option premium !per unit (c" !uropean pricin)"
c p
Call option premium !B" Put option premium !B"
c p
Value P 105.*# P 100.00 0.089B 1.#5B 1.000 *5.00 12.000B P 7.27 P .0*
*.88B 2.90B
Variable S0 K r' r(
Value $0.0095 $0.0100 1.#5B
s
0.089B 1.000 *5.00 12.000B
c p
$0.000 $0.0007
c p
.0*B 7.27B
E
A apanese (irm 6is%in) to s ell .S. 'ollars 6oul' nee' to purc%ase a put on 'ollars. E%e put option premium liste' abo+e is P.0*/$. Put option premium !P/S$" >otional principal !S$" Eotal cost !P"
P .0* $750,000 P 2,297,2#
Problem 8.2 uro/apanese en
Pricin) Currenc3 ptions on t%e uro/en Crossrate
Spot rate !'omestic/(orei)n" Strie rate !'omestic/(orei)n" Nomestic interest rate !B p.a." -orei)n interest rate !B p.a." Eime !3ears, *5 'a3s" Na3s eIui+alent Volatilit3 !B p.a."
A Japanese firm wishing to buy
A European firm wishing to buy
or sell euros (the foreign currency)
or sell yen (the foreign currency)
Variable S0 K r' r(
Value P 1.89 P 1*.00 0.088B
s
2.187B 0.2#7 90.00 10.000B
Call option premium !per unit (c" Put option premium !per unit (c" !uropean pricin)"
c p
Call option premium !B" Put option premium !B"
c p
E
Variable S0 K r' r(
Value ? 0.0072 ? 0.007# 2.187B
s
0.088B 0.2#7 90.00 10.000B
P 1.50 P #.0
c p
? 0.0001 ? 0.0002
1.12B .21B
c p
1.0B 2.90B
E
#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 euro for eah yen sold the strie rate% and a 90)day maturity. !ote that the O;imeO must be entered as t he fration of a =5 day year in this ase 90/=5 - 0.2>@. Put option premium !euro/P" >otional principal !P" Eotal cost !euro"
? 0.0002 P 10,#00,000 ? 2,1*7.90
Problem 8.2# .S. Nollar/ritis% Poun'
Pricin) Currenc3 ptions on t%e ritis% poun'
Spot rate !'omestic/(orei)n" Strie rate !'omestic/(orei)n" Nomestic interest rate !B p.a." -orei)n interest rate !B p.a." Eime !3ears, *5 'a3s" Na3s eIui+alent Volatilit3 !B p.a."
A U.S.-based firm wishing to buy
A British firm wishing to buy
or sel l pounds (the forei gn currenc y)
or sel l dollars (t he foreign curre ncy)
Variable S0 K r' r(
Value $1.8*7# $1.8000 1.#5B
s
#.525B 0.#9 180.00 9.#00B
Call option premium !per unit (c" Put option premium !per unit (c" !uropean pricin)"
c p
Call option premium !B" Put option premium !B"
c p
E
$0.0*9* $0.0**9 $0.0027
;he maturity doubled 4hile the option premium rose only about >K.
K r' r(
Value 0.555 0.555* #.525B
s
1.#5B 0.#9 180.00 9.#00B
$0.0*9* $0.00*
c p
0.0091 0.0207
.7B 1.*#B
c p
1.70B .87B
3all option premiums for a ,.(.)based firm buying all options on the "ritish poundC 180D'a3 maturit3 !$/poun'" 90D'a3 maturit3 !$/poun'" Ni((erence !$/poun'"
Variable S0
E
Problem 8.25 uro/ritis% Poun'
Pricin) Currenc3 ptions on t%e ritis% poun'/uro Crossrate
Spot rate !'omestic/(orei)n" Strie rate !'omestic/(orei)n"
A European firm wishing to buy
A British firm wishing to buy
or sel l pounds (the fore ign currency)
or sell euros (the forei gn currency)
Variable S0
Nomestic interest rate !B p.a." -orei)n interest rate !B p.a." Eime !3ears, *5 'a3s" Na3s eIui+alent Volatilit3 !B p.a."
K r' r(
Value ? 1.#70 ? 1.5000 #.000B
s
#.1*0B 0.2#7 90.00 11.#00B
Call option premium !per unit (c" Put option premium !per unit (c" !uropean pricin)"
c p
Call option premium !B" Put option premium !B"
c p
E
K r' r(
Value 0.*789 0.***7 #.1*0B
s
#.000B 0.2#7 90.00 11.#00B
? 0.021 ? 0.0#87
c p
0.0220 0.0097
1.#5B .0B
c p
.2#B 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 Call option on poun's 6%en euro interest is 2.072B C%an)e, an increase in t%e premium
Variable S0
? 0.021 ? 0.0189 ? 0.021
E
