Spring 2007 exam

Can anyone explain question 8? thanks in advance, the solution to it is extremely confusing.

[bjz99]

They do explain that really weird. I think it's because SOA, doesn't like to use a normal of a negative number. This is my explanation:
S=S(0) and K=S(0)e^(rt). This means that PV(K)=S.
Var[lnS(t)]=.4t, this implies that volatility=sqrt(.4)
Because PV(K)=S, d1=(.4/2)*10/(2)=1. Because sqrt(.4*10)=2. d2=-1
Black-Scholes holds true, so
Call = S(0)*N(d1)- S(0)*e^(rt)*e^(-rt)*N(d2)
Call= S(0)* [N(d1)-N(d2)]
Call= 100*[.8413-.1587]
Call=68.26

I hope that helps.

Originally Posted by bjz99

Var[lnS(t)]=.4t, this implies that volatility=sqrt(.4)
Because PV(K)=S, d1=(.4/2)*10/(2)=1. Because sqrt(.4*10)=2. d2=-1

bjz, thanks for the reply.

I had no idea that that equation implied the volatility. How did you solve for d1? i'm not sure I understand that either. do we just assume r = 0?

[bjz99]

Originally Posted by The Spocker

bjz, thanks for the reply.

I had no idea that that equation implied the volatility. How did you solve for d1? i'm not sure I understand that either. do we just assume r = 0?

I solved for d1 like this. Since S=S(0) and K=S(0)*e^(rt),
ln[S(0)/(S(0)*e^(rt)]+rt
=ln[S(0)/(S(0)*e^(rt)*e^(-rt)] = ln[S(0)*e^(rt)/(S(0)*e^(rt)]
=ln[S(0)/(S(0)]+rt-rt.

That's basically, four ways to write the beginning part of d1 and they all equal 0. We aren't assuming r=0, it's just that r gets cancelled, because PV(K)=S.

Since that equals 0, d1=[0+(.4/2)*10]/[sqrt(.4)*sqrt(10)]=1.

I hope that helps.

thank you very much bjz

for question 14, is it even necessary to mention that it is a straddle? i don't even know what it is...

[ReAct]

Originally Posted by The Spocker

thank you very much bjz

for question 14, is it even necessary to mention that it is a straddle? i don't even know what it is...

its a straddle, but they tell you what the payoffs are, so no, its not really necessary.

It would be if we were expected to know the typs of options and what they are comprised of, and they didn't tell the payoffs

[Actiger]

I don't expect the SoA to ask us to define what a straddle is. They'll provide a description of payoff.