I have been looking at September 2015 Q3. Part (i) on CDS seems fine, however there seem to be some pretty big issues with the rest of the question in both the exam paper and the examiners' report. Namely, the formula seems to assume one can substitute the continuously compounded risk free rate with the real world drift in the Merton model analysis. If mu as written in the question is the risk-free rate the formula correctly gives the risk neutral default probability. However, one can't motivate simply replacing this with the real world drift to obtain a real world default probability, which is what the question (and solution) seems to implicitly assume. Also: Even if one could do this, the solution says mu is the 'expected annual return on the firm's assets', when in fact is is related to the log-return. The solution says that sigma is between 0 and 1, but there is no reason for an upper limit on sigma. The examiners' report refers to the core reading - did the core reading back in 2015 contain formulae and discussion for such a 'real world' option price analysis, or is this just a really bad question? Would you get marks for giving what appears to be the actual correct explanation?
I must admit, I dont cover CT8 and am probably not the best person to answer this one. Maybe another student with detailed CT8 / Black Scholes knowledge can shed light on this. It was a strange question - the core reading it refers to must, I assume, be CT8 because the core reading for SA5 has never included anything on this topic and has not changed since 2015. I also suspect, like most SA5 questions, the examiners report contains only a subset of the comments that could have scored marks. If you knew the meanings of the underlying terms in the formula, you would have scored marks whether you got the exact details right (lognormal returns rather than returns) or not. I hope this helps, and maybe someone else can shed light.
