Gamma of futures

[ajsa]

Hi David,

I know gamma of forward is 1.. i wonder if gamma of futures is 1 as well or some other fomula?

Also if the underlying has dividend, is gamma of forward still 1?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

0 for both, with/without dividend...you can inuit: ask if the deltas change when the underling changes? They don't change:
d^2forward/dS^2 = d(exp(-qT))/dS = 0
d^2future/dS^2 = d(exp(r-qT))/dS = 0

Gamma is our only 2nd partial derivative: it is the rate of change of delta. If delta does not change (i.e, very deep OTM & ITM options, where the delta curve is getting flat), gamma = 0

David