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#1
05-14-2007, 05:31 PM
 SirenSong Join Date: May 2007 Posts: 12
CAS Spring07 Exam 3 #35

In Dr. Broverman's solution,
1) where does the volatility term in the drift go after Ito's Lemma is applied?
2) how do we know that C=S?
#2
05-15-2007, 09:30 AM
 SirenSong Join Date: May 2007 Posts: 12

Here's the link to the CAS Exam:

Here's the link to Broverman's solutions:
http://www.sambroverman.com/07s-cas3sol.pdf
#3
05-15-2007, 10:07 AM
 sam_broverman Member Join Date: Feb 2005 Posts: 638

SirenSong,

Ito's Lemma applies to a function C to get an
expression for dC. C is a function of S and t.
In this probelm we are asked to find dS , so the
function C is simply S. Then dC/dS = 1 ,
d^2 C /dS^2 = 0 and dC/dt = 0.

Sam Broverman
2brove@rogers.com
#4
05-15-2007, 10:45 AM
 SirenSong Join Date: May 2007 Posts: 12

Thank you. I still am unsure how the sigma-squared term drops out when you go from S(t) to dS(t).
#5
05-15-2007, 03:30 PM
 jenclose Guest Posts: n/a

That is because d^2 C /dS^2 = 0, the sigma^2 term is multiplied by d^2 C /dS^2 in Ito's Lemma.
#6
05-15-2007, 03:56 PM
 SirenSong Join Date: May 2007 Posts: 12

Thanks, but why isn't there a sigma^2 term multiplied by dC/dS since there is one in S(t) that's multiplied by t?
#7
05-15-2007, 04:13 PM
 jenclose Guest Posts: n/a

It is example 20.1 in derivatives markets, on page 665. Maybe that will help?

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