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September 2012

T

Turtlelord

Member
Opinions on the CT8 September 2012 paper.

I was disappointed it had pretty much no stochastic calculus questions.
 
My main gripe was the 20% reduction = 1/1.2 in the binomial tree question (3, was it?). How something like that gets [past] reviewers I'd love to know.
 
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I agree. I feel the exam was far too heavily weighted towards the first 6 chapters of the course.
 
While the first 6 chapters were mentioned (finally got Chapter 2 mentioned!), I think the hardest questions were still from the latter part of the course, namely Black Scholes and Merton. I slipped up on number 1 amazingly! *Shrug*
 
Unless I missed something there was no EMH! That sucked

Also, it did feel very different to the way last few years of papers were weighted wrt parts of the syllabus... and of course you tend to prepare more where the weight is historically greater... oh well, wait and see now... :rolleyes:
 
Was there an easy way to find the volatility in the Black Scholes question. For 2 marks that trail and error thing is just not worth it it takes too long
 
Question 1 was basically "do you have an intuitive understanding of what risk-neutral probability means". To do part (i), you're looking for the probability q that makes the expectation of the portfolio equal to the risk-free rate (ie solve

r = q*r_a + (1-q)*r_b

At least, I hope that's right!
 
And yes, I spent about twenty minutes banging my head off a brick wall calculating that implied volatility. Still need to sit down and see what was going wrong.
 
Implied volatility was between 400 and 500%

Think about this:
If risk-free return is close to zero (0.5%) and a call on underlying with current price =1.2 and strike = 1.3 has a price of 0.85, the volatility must be crazy, as it can go both up and down.. (It roughly implies there's a 50% chance the price would be 1.3+0.85*2 = 3 at maturity - otherwise no-one would buy the call since both downside and upside needs to be included in the price)

I stopped at 400% because I was running out of time, and I'm probably going to be FA. I stopped because the question said to calculate it to within 1%, meaning that even once you find it between 400% and 500%, linear interpolation itself won't be good enough as you may be off on the 1% margin, which means you probably had to calculate 10 or so call option prices for 2 marks...
 
I had calculated implied volatility as 400% odd but thought it was wrong so used a more "sensible" number for the rest of the question. :mad:

Bit annoyed now!
 
I can feel a "candidates failed to think widely" or "surprisingly badly answered" coming on...
 
Calum it took me until Friday to figure that Question #1 risk neutral probability. Threw me off completely for the rest of the question but yes I do think you're right. These 2 mark implied volatility questions are a bit ridiculous lol. I just assumed one and moved on.
 
Isn't risk neutral prob from the bond section? 1 - exp(integral of r(u)du)?
 
I think there was a mistake with the implied volatility question.

I tried looking at the rest of that question in the last five minutes of the exam, only to realise that in the final part it said that the strike price is $1.20, i.e. same as the current price.

I can't remember the exact wording, but I think that it involved calculating the price of a put option with strike price of $1.20, which makes me think that that's what it should have been at the start of the question.

This would have made the calculation for part (i) so much easier, and the 2marks a lot more reasonable.

Does anybody know what happens if there is a mistake in the exam?
 
romeodunn said:
I think there was a mistake with the implied volatility question.

Does anybody know what happens if there is a mistake in the exam?
Click to expand...

April's paper had a VaR question with an error in, where they gave credit for any reasonable approach.
 
romeodunn said:
I think there was a mistake with the implied volatility question.
Click to expand...

The paper is up, if you can bear to look(!).

I don't think it can be a simple misprint because the volatility is still over 400% even at K=1.2 - there's a handy calculator at:

http://www.soarcorp.com/black_scholes_implied_volatility_calculator.jsp

This question continues to baffle me. I can understand the argument that the numbers should have warned us volatility would be unusually high (not that I think an exam is the place for testing this sort of thing). I can't understand how calculating it to 1% is only worth two marks, when waffling about, say, characteristics of a term structure model is worth eight.
 
Calum said:
My main gripe was the 20% reduction = 1/1.2 in the binomial tree question (3, was it?). How something like that gets [past] reviewers I'd love to know.
Click to expand...

I thought they were using the approximation ud=1.

That's really bad I used d=1/1.05 in the folowing question instead of 95%...:mad:
 
Calum said:
Question 1 was basically "do you have an intuitive understanding of what risk-neutral probability means". To do part (i), you're looking for the probability q that makes the expectation of the portfolio equal to the risk-free rate (ie solve

r = q*r_a + (1-q)*r_b

At least, I hope that's right!
Click to expand...

This paper was messier than I thought... I used the CT1 formulae 1/(1+ia)= q*(1/(1+i)), where q = 1-exp(-a), i.e. q-rate discrete equivalent of "a" transition intensity.

I though they were referrring to effective yields, and the difference between the risk-free bond and the risky bond was the risk-neutral probability of default

CT8 is really traumatising me, a brutal paper I really wish I stop taking...
 
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