dVegadVol in SABR model

[tigger]

Hi guys

I have been studying the SABR model for rates options, and have come across the concept of dVegadVol over various strikes. I understand the maths behind it, but am struggling to grasp the intuition.

Why is the sensitivity of an option's price to a bump up in vol unchanged by the level of vol (i.e. dVegadVol = 0) for ATM options, but positive for wing strikes? Can someone please try to explain intuitively why wing strike options have higher vega sensitivity at higher levels of vol?

Thanks a lot to anyone who can help

 

[xandman]

Your a more advanced trader than I am, but let me take a guess.

The answer probably lies in the pricing model itself. At higher volatilities, the IV component has a higher composition weighting in the option price.

With wing options, you have additional skew effects that raise the IV component even higher.

What has me wondering is that I recall that Vanna sensitivity drops off at the single digit deltas after peaking around the meaty options.

 

[longthewings]

Hi guys

I have been studying the SABR model for rates options, and have come across the concept of dVegadVol over various strikes. I understand the maths behind it, but am struggling to grasp the intuition.

Why is the sensitivity of an option's price to a bump up in vol unchanged by the level of vol (i.e. dVegadVol = 0) for ATM options, but positive for wing strikes? Can someone please try to explain intuitively why wing strike options have higher vega sensitivity at higher levels of vol?

Thanks a lot to anyone who can help

Think of it this way.....increases in implied vol mean those wings are more likely to soon become at-the-money as you realize vol and the underlying moves out into the wings. The market is making the wings more sensitive to shifts in IV. Moreover, you don't really realize volatility, you realize variance. Variance is a squared term, so it's convex. So you're moving further out into the wings at an accelerating rate, meaning the wings need to be increasing in value in a convex manner, hence a positive second derivative (dVegadVol).

Hope this helps.