Hi, How did everyone find the exam? I felt the first 7 questions were reasonable to an extent, I cant remember what they were exactly now. But I distinctly remember 8,9,11. For 8 - the black scholes question, how did everyone solve it? Because it wasnt the normal type of call/put option. 9. Unless you knew how to differentiate phi d1 then you could solve it otherwise its not possible. Then differentiating the pde wrt sigma was ok, but the last bit when they say its gamma hedged, did you just let gamma = 0 and show that sigma dissapears? 11. The merton model, and calculation, there was a similar question in the past papers, but they gave us the expected return as 10%, but thats not r, so did we have to solve for r in the black scholes or solve it some other way? Besides those 3 which did make up the bulk of the paper I felt the rest was reasonable. Good Luck!
8. I used St*phi(d1)-St*phi(d1') (i.e. 1/2 of two black & scholes eqns) 9. phi(d1) = delta, so this part falls out easily (just switch the partial derivatives), in the notes it mentions K*e(-rt)*phi(d2) relates to Vega in some way (i didn't get this part) but i'm sure it wouldn't be too hard if you had some more time (as the second part just relates to the cash)? I thought this was a bit tough, proving properties of the b-s equation with second partial derivatives, i didn't mention my assumption that you can switch the order of partial derivatives as i don't really know under what conditions this would not be valid 11. this question annoyed me, the only way you could get r out was to solve iteratively until equity value (known) = equity value from b-s assumptions because r appears in the equation explicitly (i.e. from the discounted strike price) & inexplicitly (from d1 & d2) so if you made the right initial guess you do well but if not, you have to recalculate (how many times??), i guess it adds a bit of randomness to the exam results - how else are you going to distinguish candidates!
