Show equivalent martingale measure Sept 2009 Q6

Discussion in 'CT8' started by e_sit, Apr 10, 2014.

  1. e_sit

    e_sit Member

    In part (ii), we are asked to show that P_lambda is an equivalent martingale measure.

    The answer shows this by proving the discounted process: e^(-rt)D_t is a martingale under all scenarios.

    Why is showing the discounted price process is a martingale proves that P_lambda is an equivalent martingale?

    Shouldn't we try to show that D_t is a martingale instead?

    Thanks!!
     
  2. John Potter

    John Potter ActEd Tutor Staff Member

    No, in this question, Dt is the bond price process. In the risk-neutral world, we need the expected return on the bond to equal the return on cash.

    E[Dt|Fs] = Ds exp(t-s)r

    This is the same as needing the DISCOUNTED bond price process to be a martingale:

    exp(-rt)E[Dt|Fs] = Ds exp(-rs)

    E[Dt exp(-rt)|Fs] = Ds exp(-rs)

    John
     
  3. e_sit

    e_sit Member

    Thanks John!! I get it now :)
     
  4. Hello.....can I ask a follow up question please? I struggle a bit with the probability measure stufff.

    I think I get what John has written, but don’t understand what this has to do with p-lambda, or what p-lambda really is and so how this answers the question.

    Any help greatly appreciated!

    Mike
     

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