Forward Measures

麻烦大神解释下FORWARD MEASURE, ASSUME RISK NEUTRAL, THEN S_T has mean = r, then dF_t(future) is a martingale under risk neutral?? I think this conclusion wrong, dF_t is martingale only under forward measure.--(根据Shreve的书） Where did I goes wrong?
详见PLOT,我觉得那个(matingale under risk neutral)是错的,,,但推导好像没问题啊

dabaozi 发表于 2013-11-6 06:05
It looks like under risk neutral, The future price's martingale property used the sigma of the stock ...

Ok, good question,

The problem is that forward and future are different.

Under forward measure forward is a martingale

Under risk neutral measure future is a martingale

when interest rate is constant, the two measures happens to be the same.

best,

It looks like under risk neutral, The future price's martingale property used the sigma of the stock, while under the forward measure, the volatility input has changed...

Chemist_MZ 发表于 2013-11-6 07:07
Ok, good question,

The problem is that forward and future are different.

I am confused more. Forget about all the arguments before.
Can I say forward are martingales under risk neutral only when r is a constant value.
because I think u can't calculate df_t given f_t= S_t/B(t,T) where B(t,T)=1/D(t)E[D(T)|f(t)] (when r is some process)

dabaozi 发表于 2013-11-6 08:36
I am confused more. Forget about all the arguments before.
Can I say forward are martingales unde ...

Yes, you can.

You can calculate, as long as you have a Bond process or short rate process (r).
best,