1. Final Deadline dates for Mock Exam Marking have been revised as follows:

    CP2, CP3         Wednesday 25 March 2020

    CB2, CP1, SP1, SP5, SP7, SP8, SP9        Tuesday 7 April 2020

    CB1, SP2, SP4, SP6, SA1, SA2, SA3, SA4, SA7         Tuesday 14 April 2020

    Dismiss Notice

Show equivalent martingale measure Sept 2009 Q6

Discussion in 'CM2' started by Michael Truscott, Mar 18, 2020.

  1. Hello!

    This thread was originally in the CT8 thread, on which I have a follow-up question (at the bottom), and I was asked to move it here. Hopefully it reads ok!

    Any help much appreciated.....I hate this bit of the course. :)

    Cheers

    Mike

    1. [​IMG]
      e_sitActive 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!!

      e_sit, Apr 10, 2014 Report
      #1 Like Reply

    2. [​IMG]
      John PotterActEd TutorStaff 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

      John Potter, Apr 10, 2014 Report
      #2 Like Reply

    3. [​IMG]
      e_sitActive Member

      Thanks John!! I get it now :)

      e_sit, Apr 13, 2014 Report
      #3 Like Reply

    4. [​IMG]
      Michael Truscott
      Hello.....can I ask a follow up question please? I struggle a bit with the probability measure stuff.

      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!
     
  2. John Potter

    John Potter ActEd Tutor Staff Member

    P-lambda is a probability measure. A probability measure is an equivalent martingale measure if the discounted value of all assets is a martingale under that measure. This is useful because we know that this is also the fair price of that asset.

    Good luck!
    John
     

Share This Page