I am studying for an exam in financial mathematics, and have been going through past exam papers. Here is one of the questions I've come across, and I'm struggling with it:
The first part I have done, by direct susbtitution. After factoring out , and messing around a little bit, I got something very similar to the Black-Scholes equation except the coefficient of the term is slighly different. My PDE seemed reasonable.
So I proceed to part ii), where I struggle. I tried changing the variable of differentiation by using but my calculations don't work out, I think my differentiation has messed up somewhere along the way.
Could anyone please help me with this? I need to make sure I understand and can do this question, in case something similar comes up in the exam!