CAS Spring07 Exam 3 #35

[SirenSong]

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?

[SirenSong]

Here's the link to the CAS Exam:
http://www.casact.org/admissions/stu...am3/sp07-3.pdf

Here's the link to Broverman's solutions:
http://www.sambroverman.com/07s-cas3sol.pdf

[sam_broverman]

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

[SirenSong]

Thank you. I still am unsure how the sigma-squared term drops out when you go from S(t) to dS(t).

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.

[SirenSong]

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?

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