I try to use the finite difference method to get the approximately gamma value, but there is an issue I can't solve.
First, I set $h$ to 1 basis point of underlying asset value, but the result is not right; then I use market value of gamma find $h$ to compare it with my original setting. I found the different value of underlying assets give different h. For example, to get market gamma, 500 underlying asset should set h to 0.35 basis point of underlying value and 20 underlying asset should set h to 0.58 basis point of underlying value.
How to set the step size(h) for the finite difference method? I wonder if there is a $h$ to optimal result.
The formula I used:
f(x)'' = (f(x+h)-2*f(x)+f(x-h ))/h^2