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

Originally Posted by redwoody86

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

for future knowledge, is that what a straddle is? something that pays the absolute value?

[Jo.M.]

Originally Posted by The Spocker

for future knowledge, is that what a straddle is? something that pays the absolute value?

A purchased straddle is made of a purchased call and a purchased put, both with the same strike. It is a bet on volatility; it pays off if the stock price moves far from the strike. (it is V shaped)

alright, I'm not sure if anyone wants to help me out on this. I'm basically asking you to play teacher.

I am looking at #13. I completely understand the solution. However, I am looking through the ASM model and see that Mr. Weishaus has his own solutions. He did #13 a different way.

In the first line after the "Then solving for r*", I don't understand where he gets the .9321 e^(r-.05)... from.

I know where the .9321 comes from. Why do they use that? And what makes it equal to "A"? and why r-.05?

Thanks in advance to anyone who understands this. I know I can always use the other solution, but I'm curious as to this.

[blahbla]

Originally Posted by The Spocker

alright, I'm not sure if anyone wants to help me out on this. I'm basically asking you to play teacher.

I am looking at #13. I completely understand the solution. However, I am looking through the ASM model and see that Mr. Weishaus has his own solutions. He did #13 a different way.

In the first line after the "Then solving for r*", I don't understand where he gets the .9321 e^(r-.05)... from.

I know where the .9321 comes from. Why do they use that? And what makes it equal to "A"? and why r-.05?

Thanks in advance to anyone who understands this. I know I can always use the other solution, but I'm curious as to this.

Dude, its given in the problem

Let P(r,t,T) denote the price at time t of $1 to be paid with certainty at time T, t≤T, if the
short rate at time t is equal to r.
For a Vasicek model you are given:

P(0.04, 0, 2)= 0.9445
P(0.05,1, 3)= 0.9321
P(r*, 2, 4)= 0.8960

Calculate r*

the price using vasicek has the form P(r,t,T) = A(t,T)*e^-B(t,T)*r