约克金融工程课程.pdfVIP

SolutionGuidelinesforTFEExerciseSet2(10%)Spring2014

1.Supposethatthestockreturnfollowsthelog-normaldistribution,

namely

2:

r=ln(P=P)N;

t+1t+1t

Supposethat=12%and=30%.Withprobability95%thereturn

willsatisfy

rt+1q0:05

andthefutureprice,Pt+1willsatisfy

St+1S0:05:

Findoutthe5%le,q0:05andS0:05.Giventhattherisk-rate

is8%,ndoutthe5%leVaRforPt+1.Repeatthierciseat

the1%le.

(Sol):Withprobability95%thereturnwillsatisfy

rt+1q0:05=+x0:05=121:64530=37:35%

Hence,withprobability95%,thefutureprice,Pt+1willsatisfy

PP=Pe+x0:05=100e0:373568:83

t+10:05t

assumingthatP=100.Giventhattherisk-rateis8%,

t

r+x0:050:080:3735

VaR=PePe=100e100e39:5

0:05tt

Next,withprobability99%thereturnwillsatisfy

rt+1q0:01=+x0:01=122:326230=57:79%

Hence,withprobability99%,thefutureprice,Pt+1willsatisfy

PP=Pe+x0:01=100e0:577956:1

t+10:01t

Then,

VaR0:01=100e0:08100e0:577952:22

2.ConsiderthedailyIBMlogdailyreturns(Tsay)overJuly1962-Sep-

tember1997withatotalof9190observations.Weusetwovolatility

modelstocalculateVaRof1-dayhorizonatt=9190foralongposi-

tionof$10m.

[1]

(a)Case1:Assumethatisstan