Actuarial Outpost > MFE Spring 2007 exam
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

#1
04-30-2008, 02:07 AM
 The Spocker Guest Posts: n/a
Spring 2007 exam

Can anyone explain question 8? thanks in advance, the solution to it is extremely confusing.
#2
04-30-2008, 08:59 AM
 bjz99 Member Join Date: Apr 2007 Location: Earth? Studying for zombie survival Favorite beer: one with drinkability Posts: 951

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.
#3
05-01-2008, 09:52 AM
 The Spocker Guest Posts: n/a

Quote:
 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

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?
#4
05-01-2008, 10:30 AM
 bjz99 Member Join Date: Apr 2007 Location: Earth? Studying for zombie survival Favorite beer: one with drinkability Posts: 951

Quote:
 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.
#5
05-02-2008, 03:05 PM
 The Spocker Guest Posts: n/a

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...
#6
05-02-2008, 03:43 PM
 ReAct Member SOA AAA Join Date: May 2006 Favorite beer: Fat Tire Posts: 734

Quote:
 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
#7
05-02-2008, 03:52 PM
 The Spocker Guest Posts: n/a

Quote:
 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?
#8
05-02-2008, 04:06 PM
 Jo.M. Member Join Date: Oct 2007 Posts: 288

Quote:
 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)
#9
05-14-2008, 05:13 PM
 The Spocker Guest Posts: n/a

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.
#10
05-14-2008, 05:22 PM
 blahbla Member Join Date: May 2008 Posts: 1,408

Quote:
 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

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 11:35 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top