# Variance Swap Vega

I am currently reading the paper of Derman and al for my master thesis on Variance Swap. At one point one says that "The variance vega is largest when the option is ATM", considering here a call option on a stock.

I must say, I am having some difficulties to understand that. The only reason I came up with is that vanilla option are almost linear in volatility at ATM.

Edit:

In order to clarify my questions which is not clearly explicit.

• What is the option? How is it related to a variance swap? – Gordon Mar 15 '17 at 17:45
• Sorry I just edited my post: a call option on a stock and the variance exposure is highest when the call is ATM – Axel Haddar Mar 15 '17 at 17:51
• What do you mean "Variance vega"? Should it be option vega? – Gordon Mar 15 '17 at 17:53
• It is basically the same apparently yes, except the notation here is dC/ variance – Axel Haddar Mar 15 '17 at 17:54
• So then it is not the same. Rather "Variance Vega" is $\nu/(2\sigma)$ where $\nu$ is the usual (volatility) Vega. – Quantuple Mar 15 '17 at 18:38