Show equivalent martingale measure Sept 2009 Q6

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!