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Interest Rate Models

S

Sunit_K

Member
Hi,
The derivations for these models(Vasicek, CIR, Hull White) seem rather daunting and the final formulas aren't simple either.

Are we expected to memorize the final formulas, say for B(t,T), and the derivations too? Or is it enough to remember the SDEs?
Have these proofs been previously asked?

Also the formula in the tables (Vasicek model) seems a bit different than the one provided in the Core Reading. Can someone shed a light on how they relate or if they are identical albeit with different notation?

Thanks,
Sunit
 
These kind of proofs have been previously asked. Luckily the new syllabus means that if you can get, say, 50% on CT8, you could probably still pass CM2 assuming you get all marks in Ruin Theory, Run-off triangles and stochastic CT1, all three of which I find easier than CT8 as a whole. (Funny though that the sample paper is like 94% CT8, counting both papers A and B)

The Vasicek model has some constants added because they want you to know your stuff e.g. how to derive it.
 
Oh boy, those proofs sure are something.
Ruin theory is usually accompanied by reinsurance, it would be interesting to see how the examiners split it considering reinsurance is now in CS2, but they can always make the assumption of some prior knowledge of reinsurance although I'm not sure if that can be called 'fair'.
Ruin theory and Run-off triangles feature prominently in the past papers for about 25% combined, it would nice for these two to carry similar significance in the CS2 paper, but the chances of that are very thin.

Thanks anyway!
And all the best!
 
This particular split doesn't bother me too much as I'm doing NTU's CT6 and IFoA's CM2 and CS2 all this April. IFoA did state that there will be ~25-30% from non-CT8 topics in CM2. But it's possible that the paper A could somehow still be your traditional CT8 paper, and the paper B is these three easier topics (I hope this isn't the case)...

All the best to you too!
 
Hello Sunit

Good questions!

The final formulae for B(t,T) have been tested in the past, eg CT8 April 2015 Q10 (quote the Vasicek bond pricing formula) and CT8 April 2016 Q8 (derivation of Vasicek bond pricing formula result). Also Vasicek derivations in April 2014 Q5, April 2012 Q6, April 2011 Q10, April 2010 Q4. I also have a vague memory that the CIR pricing formula result has been asked for in the distant past but not the proof.

In short, sadly, yes, I would recommend that you learn this, in particular for the Vasicek model. The Vasicek model for interest rates is an example of an Ornstein-Uhlenbeck process, which the CM2 syllabus (4.4.6) specifically singles out as one that you need to be able to solve. The other one is Geometric Brownian Motion (4.4.5). You should not be expected to solve the CIR and H&W SDEs as these are off syllabus. However, the final bond pricing formulae may be tested.

The formulae in the Tables for the SDEs for the various interest rate models hark back to the old Subject 103. Since the Tables haven't been updated since then, these formulae are a little out of sync with what's in the Core Reading. The exam question usually gives you a formulation of the SDE to use but if not, I would opt for the Core Reading ones.

Hope this helps
Anna
 
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