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 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 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 e_sitActive Member ↑ Thanks John!! I get it now e_sit, Apr 13, 2014 Report #3 Like Reply 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
