# How sensitive are vertical spreads to changes in implied volatility?

How sensitive are vertical spreads to changes in volatility / implied volatility in the money, at the money, and out of the money?

I'm thinking for 1 point spreads this would be very small / neutral for ITM, ATM, and OTM, but I'm not sure. If you have thoughts on this, perhaps please confirm in a comment or answer.

For larger spreads, it would become larger / less neutral, but does it follow any specific "formula"? Is it just a subtraction of vegas, with a large implied volatility skew causing a great difference?

• Intuitively it's going to go like the first derivative of vega, meaning very small ATM, increasing as you move away (either ITM or OTM), but then back to zero as you move even farther away. – Pete Nov 17 '11 at 5:25

Net the vegas of the individual options in the spread.

Inherently, the closer together the strikes, in the spread are, the less sensitive to changes in implied vol the spread is.

The opposite is true for wider spreads.
Technically, the wider the spread the more it follows the dynamics of the skew itself, depending on where the spread is relative to at-the-money. (which is to say that it varies)

Graphically, you can think of it this way...
A general increase in implied vol causes the PnL line of the spread to flatten (move to the middle between the max profit/loss potential of the spread.

A general decrease in implied vol causes the PnL line of the spread to steepen (move towards the max profit potential of the spread.

• Thanks Glyphard. I'm curious, is there a reason for what you noted in regard to the PnL line, i.e. flattening on an increase in volatility, or steepening on a decrease in IV? – Ray Jan 9 '12 at 4:52
• Yes, because an increase in vega means an increase in option premium, so if you're long an option that's an increase in your PnL line, and the opposite is true if you're short an option. In a verticle spread, you're long and short options for the same expiry. When the strikes of these options are somewhat close to each other, this effect (higher vega increases option premium) causes the PnL from both options to offest giving the PnL graph the flattening tendancy that I mentioned. – glyphard Jan 9 '12 at 17:20
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