April 2007_Q3(i)

I don't understand why the Examiner's report says the derivative pays off after two down moves, since it is possible for S2 < S0 after an up move and a down move.
e.g

let S0 =1

u = 1.25, d = 0.6

After an up move and a down move, S2 = 0.75 < S0???

Am I missing something?....Thanks.

 

This was an interesting exam question!

I agree with you - I don't think the reasoning given in the Examiners' Report is valid. The final answer is correct though. The way I did it was to equate the definition of the SPD to the values given in the question as follows:

A1(up) = exp(-r) * q/p = 0.7610
A1(down) = exp(-r) * (1-q)/(1-p) = 1.5220

Solving these two simultaneous equations gives p=0.75 and q =0.6

So that's part (i) solved without the need to worry about the relative sizes of u and d.

The value of a derivative that pays out at t=2 only after two down moves is then:
exp(-2r) * (1-q)^2 = 0.1448

This is the same as the value given in the question of a derivative that pays out if S2<S0. So the two derivatives must be the same.

Therefore we must conclude that (for this tree) S2 can't be less than S0 after an up and a down move, ie ud>=1.

This rules out the example you give for u and d.

So the question is doable, but not quite as straightforward as the examiners intended. I imagine they were assuming the usual convention that d is set so that d=1/u, but since they didn't specify this, it's wrong to take it for granted.

 

But Mike in my solution I had written that assuming that; S0uS1d < S0 and the same will be for the down-up move. I hate unclear questions, do you get penalized for stating an assumption?

I remember April 2008_q3, the question wanted the value of a derivative after one year when the information before just spoke about periods, it was unclear whether a year was one period or two periods. I simply assumed it was one period and the examiner's report used two periods.

Thanks.

 

Generally, if something is unclear, yes, it's best to state an assumption and proceed from there and you shouldn't get penalised.

However, in this case, your assumption would contradict the value of the derivative as stated later in the question and so can't be correct. As this isn't immediately obvious though, I have some sympathy, but expect the examiners wouldn't.

I see your point and agree the wording could have been better, but I have less sympathy here.

The question starts with "Consider a two-period Binomial model ...". I think it should be clear it means "Consider and use a two-period Binomial model ..." rather than "Consider a two-period Binomial model, but only use the first period of it for this question (the second period being considered just for fun)".

Sorry if that sounds a little harsh! But I'm totally with you on unclear questions. There's no excuse for them and it's something you shouldn't have to deal with in the exam.

 

It's not nice at all. I used to hear that some people are made to sit a paper before it's given to us in order to clear ambiguities. Is this true????

 

Yes. All questions are reviewed internally by the examining team themselves and then by the staff actuary for the relevant subject and at least twice externally by what is known as the "guinea-pig" process.

 

Ok...thanks. One more question, why is it that the CT8 Examiner's reports don't have comments on how students tackled each question?

I think the comments are extremely helpful.

 

The Principal Examiners are meant to include these comments and this has happened for both 2011 CT8 exam papers, so it looks hopeful that it will be a regular feature now.

 

Ok...thanks,i haven't went as far as 2011 April exams.