I am working on an option hedging simulation. In this context, I wanted to expand the simulation to include gamma. For testing purposes, I used among others the natural gas futures. When I calculate the greeks for an ATM-option for the current October contract
(f=2.86, st=2.90, days=30, vol=0.4, r=0.005),
I get a gamma of 1.21.
As far as I know, the gamma as the second partial derivative of the option price with respect to the underlying price, gives you the rate of change for the delta with respect to a change in the underlying. So if the natural gas futures would change by one point (which obviously would be a very large percentage move), the delta would change by more than one even if it has the boundaries of [0, 1].
Is my definition, calculation or interpretation of gamma not correct or am I missing something else ? (Before posting this, I looked gamma up in some option textbooks like Hull, Sinclair and Natenberg but could not find an explanation regarding this)
Thanks for help (and sorry for my trivial question ;-)