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Show equivalent martingale measure Sept 2009 Q6

M

Michael Truscott

Member
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. 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. 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. e_sitActive Member
    ↑
    Thanks John!! I get it now :)

    e_sit, Apr 13, 2014 Report
    #3 Like Reply


  4. 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!
 
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
 
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