March 06

8 questions, some thoughts:

Quite a few definitions, particularly those ones where we were told to relate it to Binomial trees.

Didn't even attempt that product of two share price processes question, the Ito formula scared me

Felt more doable than previous ones though that's not saying much

There were three of us who sat it where I was, all retaking...

I'm sure more will come back to me in due course

 

it was a fairly tough paper i think. Although a lot of the questions had been taken from an old ACID paper (which I really had only skimmed over a few weeks back ... doh!)

The binomial tree via no arbitrage was a tricky one, I think the correct approach was setting up a portfolio P = V - Delta x S and then working from the end nodes backwards...

The question with the generalised Ito formula was a bit unfair i think, ok the formula was usable, but the stuff on risk neutral measure seemed beyond the syllabus - speculated on using a n-factor Cameron-Martin-Girasov theorem to get from P to Q, and found the two gamma_i(t) functions to rewrite d(s1s2) in terms of Q (so it had no drift), but was at a loss of where to proceed from there.

The FRA / interest rate futures were ok, but I didn't know what the two legs bits was about.

Right at the start, finding B(0,T) seemed tricky, you had to find the distribution of a double integral of Brownian motion, which I suspect I got wrong, and then use the normal MGF to evaluate e^{integral of r_t}

Oh and what did other people get for the fixed rate in the 1 year CMS swap based on floating payments equal to the 4 yr swap rate? I thought the fixed rate would also have to be the 4 yr swap rate, as it only had a single payment. I didnt know what to put for the wordy bit at the end of the question, said it was to do with convexity, but couldnt really take it any further.

The prove d(W_t^2) is not 2W_t was pretty tough! I managed to recall the riemann sum formula for the ito integral, but could not prove it.

I can't recall much else now, oh except that someone at Croydon clearly had a bad stomoch (everyone looked round when some guy at the back farted at about 100 decibels!)

...oh and apparently these were "artuarial" exams

 

this was no easy paper than last years...

i think 1 was ok...2 had that nasty newtonian approach thing...had no clue what i had to do...can't say anything abt 7 and 8...got me completely astounded...esp. the CMS swap one...

i think atleast 25% was undoable from my part...so it seems things are not looking good again from my side...this was a re-attempt...but was no better than the 1st....uurrgh....

it was just me in the exam center..the other guy didn't turn up...invigilator looking at me every 15 mins...was a bit scary (

 

I didn't think that the paper was too hard core, however, on the whole, I struggled with it. This was probabily due to not preparing enough for quesions sunch as 7 and 8. Up until those things weren't going to badly.

I was hoping for some more derivative mathsy questions, and not so much in the way of interest rates - however in fairness, some of this was in the core reading.

For the non arbitarge question see CiD 2002 question 6!

For the Ito question I messed up the derivation by the method the examiners proposed so instead found;

(s1+s2)^2 -s1^2 - s2^2 = 2 s1 * s2

Thought that the wordy parts were ok.

In light of students comments from the last two sittings this exam didn't seem off the wall.

 

Gareth,

For the d(W_t^2) =/= 2W_t dW_t question I used a taylor expansion with f(y) = y^2

d( f(y) ) = ft + f ' dy + 1/2 * f '' (dy)^2
= 2 w_t dw_t + dt

so the dt term forces the inequality - I think?

 

i also did that in the end, as i got nowhere with the limiting series approach, but i dont think that will get any marks

 

see page 3 of http://efinance.nease.net/StCalc4.pdf for the correct approach

I think no one could reasonably have done this under exam conditions, to do it you needed to know that:



where [0,t] is split into t_1,t_2,...t_n with t_0 = 0, t_n = t and t_i - t_{i-1}=t/n

without this "fact" the proof won't go anywhere.

So i would guesstimate that no one got this question right.

 

and for the d(s1 s2) question, see ACID A2002, Q4(iii). The entire question is the same, which is really annoying, since i'd not bothered much with ACID!!!!

I remember skimming over the answer when revising, but thought "nah that's much too complicated for ST6/CID". Stupid Stupid Stupid!

 

I was sitting ST6 for the 2nd time. Sat it first time in Sept 05 - what a nightmare that paper was! I thought yesterdays paper was more doable but still really tough - don't think i'll have picked up too many marks on 7 or 8.

Like propeller_dan i also used the taylor series expansion to show that d(W_t^2) = 2W_t dW_t was wrong.

As for the binomial question, thought it was real easy until i came on here and read Gareth's comments! For the 'no arbitrage approach' i just set up a replicating portfolio and then used the no arbitrage argument to say the portfolio must equal the value of the option now. But i guess i must admit that's just risk neutral valuation in disguise. Still used a ano arbitrage argument though!

The best part of the exam was finding myself sat next to a bit of a stunner in the exam hall.

I really hope i don't have to resit this one again.

 

I thought it was a fairer exam than the last two but yeah, Gareths comments have taken some of the shine off.

The first question pi**ed me off a bit. It defined S(t) as exp(at).r(t) then asked you to find s(t). I assumed it meant find dS(t) which is the integrating factor clue you need to then find r(t). I think. This is how I approached it anyhow. What do others think?

At least the graphical questions were bookwork (albeit hull bookwork). I realised in the wee hours this morning that I'd mislabelled my axes though. Theta for t an vice-versa. Feel like a complete muppet for that one!

The CMS question came up last year so I didn't bother considering it much in my revision. How dumb. However I think the first part was trivially equal to the one year forward rate or whatever it was. Again, just like last year. The second part foxed me a little but I just gussed that you usually value a fixed / forward swap by valuing a fixed bond against a floating bond which you can assume to be equal at par. You can't do that in this instance as the floating rate payment would no longer be libor so the value would no longer be par. Anyone think that sounds reasonable?

Overall I came out pretty happy with my efforts and felt that if I fail this time I may not get so favourable a paper next time considering the previous two. Fingers crossed eh?
Best of luck everybody with the results.

 

Oh and if anyone gets too downhearted if they fail. Consider that there was a chap re-taking it in my exam sitting that had a Phd in stochastic calculus!

 

the s(t) bit in question 1 was very confusing. I mean it clearly was the integrating factor, but i found their hint misleading.

i ended up solving the sde in terms of s(t) just to keep the examiner happy, but really felt pissed off about the time I wasted trying to guess what exactly they wanted. Who got 1(ii)(b) about the bond price? I tried to simplify:



but could not find the distribution of the integral of r_t, because it involve finding the distribution of a double integral - in the notes on page 9 chapter12, Acted do this for question 12.8, but give you the variance of the double integral. This is what you need to proceed with the approach I took, and there's no way I could figure out that forumula in the exam.

So how exactly should I have approached that one?

 

Do you people work in investment and have to take this exam or something?

Compared to other ST's is sounds horrendous!!

The subject though sounds really interesting but the exam I think may put me off choosing to do this.

So why are you doing it?

 

i did it because i find the subject interesting, and i think future actuarial work will be heading in this direction (e.g.http://www.ma.hw.ac.uk/~andrewc/papers/ajgc38.pdf

plus initially it looked quite easy, as the notes are really thin and look like 109...little did i know it involved learning the contents of Hull and Baxter/Rennie!)

 

I had the same issue with q1.

Stupidly went straight into the question without reading it in enough detail! Solved the eqn for r(t) re-read the question and realised that I'd not solved for s(t) first.

anyway ST4 tomorrow...

 

btw...what did u guys/gals(if any) think of the last part of Q8...4 areas of risk where your assessment might be incorrect....i didn't have much of an answer...i mentioned Market/Credit/Settlement/Legal risks...as i knew that much only....any answers for that one???

 

I couldn't decide if it was the CALL SCROM things (as you mention), or whether it was to do with portfolio being delta and vega hedged but this only applied to small deviations so need to consider stress testing etc. Similarly if you need to look at the effect of one on the other, e.g. if interest rates AND volatility changed, how would this affect portfolio's value.

I don't think it was clear...

 

i dont think it was the MAC SCROLL thing, i wrote about whether they used a single interest model for the entire yield curve, and a bit about credit risk and stress testing.

oh and about volatility assumption used in blacks model (and smiles)

i wasn't really clear what they were after really.

i gotta go study for CT8 now, and my new title "Prefers posting to studying" is kind of a hint!

 

hi all,

I wish you all the best of luck when the results for st6 are released and hope you all do well.

what was the st6 paper like this year compared to last years exams?

did reading hull help in the end or were there any nasty suprises in the exam?


what do these acronymns/anagram exactly stand for
MACSCROLL / CALLSCROM

I presume they stand for some content of the little bookwork in this subject, but what inspired the construction of these….


someone on another post said there was a stunner in their ST6 exam ! lol
ummm.... i woudl have thought such "specimens" were in CT4 - or "models" as it is called -lol

 

I thought there were no real easy questions in this paper.
Q7 and Q8 were quite hard and written in a confusing way.
They will definitely be the questions that will make the difference between candidates and help them decide between Pass or Fail.

On the bright side, they still have to pass people but I would be surprised if there is more than a 20% pass rate this time.

Good luck.

 

Market Risk
Aggregation Risk
Credit Risk

Settlement Risk
Concentration Risk
Reputational Risk
Organisational Risk
Liquidity Risk
Legal Risk

I used an anagram website to come up with it. No way I can remember lists without this technique