Libor and change of measure

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Libor and change of measure

Postby niski » Mon Mar 07, 2011 2:41 pm

Hello everyone!
Thinking about Lognormal Libor Models..

Let Q^T[k-1] martingale equivalent measure induced by taking the bond expiring at T[k-1] as a numeraire.
How to calculate E^(Q^T[k-1])[ L(T[k-1],T[k]) |F_t] ? (Where L is the future libor rate from one period to the another at t..)

I was thinking about change the measure going from Q^T[k-1] to Q^T[k] but how to do that? Using an advanced type of Bayes formula?

Thanks!
niski
 
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Re: Libor and change of measure

Postby sraks » Mon Mar 07, 2011 6:50 pm

Hi Niski,
I beileve conceptually the most striaghtforward way is to notice that the FRA with zero strike is a martingale under the
P(T-1) . Also remember that L=[P(T-1)/P(T)-1]/tau. Expressing everything in terms of L you get that (L/(1+L*tau)) is a martinagle. Assume dL/L=mu*dt+sigma*dW under P(T-1) . Now figure out mu.

You can also refer to the relevant chapter in "Concept" to see how this is done. "Concept" is the best book out there for internalizing the drfit calculation for change of measure.

Hope this helps.

Regards,
SR
sraks
 
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Joined: Tue Feb 16, 2010 3:31 am


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