State price deflator

Discussion in 'CM2' started by Jeremy Lim, Aug 7, 2019.

  1. Jeremy Lim

    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.
     
  2. mugono

    mugono Ton up Member

    All text in bold text (core reading) is examinable. Otherwise it is not.
     
  3. Anna Bishop

    Anna Bishop ActEd Tutor Staff Member

    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
     
  4. Sunil Chaudhary

    Sunil Chaudhary Active Member

    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.
     
  5. Steve Hales

    Steve Hales ActEd Tutor Staff Member

    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.
     
    Sunil Chaudhary likes this.

Share This Page