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State price deflator

J

Jeremy Lim

Member
Hi admin,

I would want to clarify if the state price deflator approach will no longer be tested although it still appears in the CMP.
 
Hi Jeremy

Although state price deflators haven't been examined for a while, they are still very much on the syllabus and in the Core Reading.

They are most likely to come up in the context of the binomial model and that's where you should concentrate your efforts for deflators. They may also appear in a question on risk-neutral pricing so I would learn what's on the Summary Page (Page 31) of Chapter 17.

Useful past exam questions on state price deflators to look at are:

CT8 April 2005 Q10
CT8 April 2007 Q3
CT8 Sep 2011 Q7
CT8 Sep 2013 Q6
CT8 April 2005 Q8
CT8 Sep 2009 Q5

Hope this helps
Anna
 
Hi,

Regarding State Price Deflator, I am unable to understand how its adapted to price a derivative at time t as mentioned in the notes Vt = Ep[AT*VT] / At.

I am thinking that Ep[At*Vt] = Ep[AT*VT] = V0.

Can someone please suggest how to arrive at the formula mentioned in the notes.
Thanks.
 
Hi
Ep[AT*VT] gives the value at time 0 of a derivative with a payout at time T, so V0=Ep[AT*VT].
Ep[At*Vt] gives the value at time 0 of a derivative with a payout at time t. So this is essentially a different derivative, and therefore won't equal Ep[AT*VT].
If you have a look at the definition of AT you'll see that it's driven by the random variable NT - the number of up-steps between time 0 and time T, and the discount factor exp(-rT). Let's pretend we're at time t rather than time 0, and so we've already had Nt up-steps (and this quantity is definitely known at time t). So between time t and time T there are NT-Nt up-steps remaining, and we want the discount factor to be exp(-r(T-t)) instead. If you write out AT/At and perform the necessary algebraic simplification this is exactly what you'll get.
Hope that helps.
 
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