Cameron-Martin-Girsanov theorem - working out gamma

[trog_8]

Hi all,

I have just been attempting Q5 from the ST6 April 2014 paper which requires the use of the CMG theorem.

I understand how to apply the CMG theorem but I am struggling to understand how I can easily identify what gamma should be?

In the answer to this question, the gamma chosen seems completely random to me and to work it out, I would have had to have used trial and error which would have taken up valuable time in the exam.

Please can someone help me to understand how to work out gamma quickly?

Thanks

 

[TryingHardToPass]

When I did it, the trick for that question seems to backsolve it based on the coefficients of t in the equation. We know that we want to remove \(\mu + r - \nu\). We also know that when we solve the SDE for a GBM, we end up with a \(-\frac{1}{2}\sigma^2\), so we want to make sure that we end up with a \(-\frac{1}{2}\sigma^2\) in the coefficients of t, so our gamma is now \(\mu + r - \nu + \frac{1}{2}\sigma^2\). Finally, since we are substituting \(W_t\) with \(\tilde{W_t}\), we need to take care of the additional \(\sigma\) by having it divided in the gamma.
Think this trick works for this question because it is a solved form of the GBM