solutions for assignment 1.docx

solutions for assignment 1.docx

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solutionsforassignment1

Problem1.3.

Inthefirstcasethetraderisobligatedtobuytheassetfor$50.（Thetraderdoesnothavea

choice.）Inthesecondcasethetraderhasanoptiontobuytheassetfor$50.（Thetraderdoes

nothavetoexercisetheoption.）

Problem1.4.

Sellingacalloptioninvolvesgivingsomeoneelsetherighttobuyanassetfromyou.Itgives

youapayoffof

-max（ST-K,0）=min（K-ST,0）

Buyingaputoptioninvolvesbuyinganoptionfromsomeoneelse.Itgivesapayoffof

max（K-ST,0）

InbothcasesthepotentialpayoffisK-ST.Whenyouwriteacalloption,thepayoffis

negativeorzero.（Thisisbecausethecounterpartychooseswhethertoexercise.）Whenyou

buyaputoption,thepayoffiszeroorpositive.（Thisisbecauseyouchoosewhetherto

exercise.）

Problem1.5.

（a）Theinvestorisobligatedtosellpoundsfor1.5000whentheyareworth1.4900.Thegain

is（1.5000-1.4900）x100,000=$1,000.

（b）Theinvestorisobligatedtosellpoundsfor1.5000whentheyareworth1.5200.Theloss

is（1.5200-1.5000）x100,000

=$2,000.

Problem1.7.

Youhavesoldaputoption.Youhaveagreedtobuy100sharesfor$40pershareiftheparty

ontheothersideofthecontractchoosestoexercisetherighttosellforthisprice.Theoption

willbeexercisedonlywhenthepriceofstockisbelow$40.Suppose,forexample,thatthe

optionisexercisedwhenthepriceis$30.Youhavetobuyat$40sharesthatareworth$30;

youlose$10pershare,or$1,000intotal.Iftheoptionisexercisedwhenthepriceis$20,you

lose$20pershare,or$2,000intotal.Theworstthatcanhappenisthatthepriceofthestock

declinestoalmostzeroduringthethree-monthperiod.Thishighlyunlikelyeventwouldcost

you$4,000.Inreturnforthepossiblefuturelosses,youreceivethepriceoftheoptionfrom

thepurchaser.

Problem1.10.

Youcouldbuy5,000putoptions（or50contracts）withastrikepriceof$25andanexpiration

datein4months.Thisprovidesatypeofinsurance.Ifattheendof4monthsthestockprice

provestobelessthan$25youcanexercisetheoptionsandsellthesharesfor$25each.The

costofthisstrategyisthepriceyoupayfortheputoptions.

Problem1.22.

Solution:

Theterminalvalueofthelongforwardcontractis:

ST–F0

whereSTisthepriceoftheassetatmaturityandF0istheforwardpriceoftheassetatthetime

theportfolioissetup.（ThedeliverypriceintheforwardcontractisF0.）

Theterminalvalueoftheputoptionis:

max（F0-ST,0）

Theterminalvalueoftheportfolioistherefore

ST-F0+max（F0-ST,0）

=max（0,ST-F0]

ThisisthesameastheterminalvalueofaEuropeancalloptionwiththesamematurityasthe

forwardcontractandanexercisepriceequaltoF0.ThisresultisillustratedintheFigureS1.3.

Theprofitequalstheterminalvaluelesstheamountpaidfortheoption.

Problem1.23.

Supposethattheyenexchangerate（yenperdollar）atmaturityoftheICONisST.Thepayoff

fromtheICONis

1,000ifST>169

1,000–1,000（169/ST-1）if84.5≦ST≦169

0ifST<84.5

When84.5≦ST≦169thepayoffcanbewritten

2,000–169,000/ST

ThepayofffromanICONisthepayofffrom:

ThepayofffromanICONisthepayofffrom:

（a）Aregularbond

（b）Ashortpositionincalloptionstobuy169,000yenwithanexercisepriceof1/169

（c）Alongpositionincalloptionstobuy169,000yenwithanexercisepriceof1/84.5

Thisisdemonstratedbythefollowingtable:

Problem1.24

SupposethattheforwardpriceforthecontractenteredintoonJuly1,2005isF1andthatthe

forwardpriceforthecontractenteredintoonSeptember1,2005isF2withbothF1andF2

beingmeasuredasdollarsperyen.IfthevalueofoneJapaneseyen（measuredinU.S.dollars）

isSTonJanuary1,2006,thenthevalueofthefirstcontract（inmillionsofdollars）atthat

timeis

l0（ST-F1）

whilethevalueofthesecondcontract（peryensold）atthattimeis:

10（F2-ST）

Thetotalpayofffromthetwocontractsistherefore

10（ST–F1）+10（F2-ST）=10（F2-F1）

ThusiftheforwardpricefordeliveryonJanuary1,2006increasesbetweenJuly1,2005and

September1,2005thecompanywillmakeaprofit.

Problem1.27

Solution：

Problem1.29

Solution:

Problem4.3

Problem4.4

Solution:

Problem4.7.

Whenthetermstructureisupwardsloping,c>a>b.Whenitisdownwardsloping,b>a>c

Problem4.11

Solution:

Problem4.14.

Solution:

Theforwardrateswithcontinuouscompoundingareasfollows:

Year2:

4.0%

Year3:

5.1%

Year4:

5.7%

Year5:

5.7%

Problem4.16

Problem4.27

Solution：

Problem6.1.

Solution:

Thereare33calendardaysbetweenJuly7,2004andAugust9,2004.Thereare184calendar

daysbetweenJuly7,2004andJanuary7,2005.Theinterestearnedper$100ofprincipal

therefore3.5×33/184=$0.6277.Foracorporatebondweassume32daysbetweenJuly7

andAugust9,2004and80daysbetweenJuly7,2004andJanuary7,2005.Theinterest

earnedis3.5×32/180=$0.6222.

Problem6.2.

Problem6.9.

Solution:

ThenumberofdaysbetweenJanuary27,2005andMay5,2003is98.Thenumberofdays

betweenJanuary27,2005andJuly27,2005is181.Theaccruedinterestistherefore

6×98/181=3.2486

Thequotedpriceis110.5312.Thecashpriceistherefore

110.5312+3.2486=113.7798

or$113.78.