# Why is the vega of an at the money option so insensitive to movements in volatility? I.e, why do ATM options have such little Vomma?

I've been trying to understand why at the money options have very little vomma. I was reading and came across a graph that showed vega as volatility changes and I couldn't grasp how the relationships work. Why is the vega of an ATM option just constant with respect to volatility?

well you are really asking why is the ATM value so linear in $\sigma.$ If you take a Taylor about $\sigma =0$ when ATM you get the well-known expression
$$\frac{1}{\sqrt{2\pi}} \sigma \sqrt{T} S_t +{\cal O}(\sigma^3 T^{3/2})$$ which gives the approximate linearity.