## Risk Neutral Measure vs Forward Measure

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### Risk Neutral Measure vs Forward Measure

Dear all
I have a technical doubt in the following facts.Especially pricing a forward and future on a tradable underlying we do everything wrt a risk neutral measure.But if the underlying becomes non-tradable then I have seen people switching over everything to a forward measure where the Numeraire is given by a zero coupon bond.The logic behind this is I guess in the first case when the underlying is tradable we can set up a replication strategy with the underlying and money market account(numeraire in risk neutral measure ) while giving no arbitrage arguements for both forwards and futures.But if the underlying is not tradable we shift to the forward measure to construct a replication strategy using the numeraire(a zero coupon bond ) and money market account. Please correct me if I 'm wrong .

thanks.
ram1234

Posts: 14
Joined: Mon Sep 19, 2011 10:23 pm

### Re: Risk Neutral Measure vs Forward Measure

Neftci's book has a very good explanation on the difference between risk neutral measure and forward measure, Ch17.

I don't think the replicating portfolio argument really apply for interest rate derivative, that is why the risk-neutral measure kind of ran into problems.

He used the arbitrage free argument to compute payoff or of different instrument, cash account, interest rate derivative(in this example FRA), bond maturing at the same time as the FRA expiration date, bond expirying after FRA expiration date, etc. If you work with risk-neutral measures, you will end up discounting the FRA payoff with spot rate which is itself a random process. But if you work with the fwd measure, where Bond expirying at the same time as FRA contract with some simple algebra, then you simplify the problem done to only need to model the libor rate process. And under fwd measure, it has the martingale property udner forward measure which is very desirble for modelling purpose.

It is best you read that chapter, very well explained.

Yi
wuyiquant_tobe

Posts: 7
Joined: Mon Oct 29, 2012 1:13 pm