Hi,

I'm looking into the differences between vol swaps and var swaps and from what I understand var swaps should always provide a better payoff than a vol swap if they have the same strike.

However, when looking at an example with vol strike of 20% and realised vol of 28.4% I find that my vol swap seems to have a better payoff than my var swap.

My Var payoff is 100k(0.081-0.04)=4,089
My Vol payoff is 100k
(0.284-0.2)=8,400

Am I doing something wrong or have I missed something?

Thanks!

youre using decimals instead of the actual numbers. when you square a decimal it will always go down, making the gap between sigma and k smaller. if you use the actual numbers you will see the reverse. also take note of whether or not you're using variance notional or vega notional (you didnt say)

http://www.ederman.com/new/docs/gs-volatility_swap...

we'll leave it in whole numbers since it may be more intuitive for you.

Say your vol strike is: 20%
We'll set your vega notional to 100k:

so as you know, if the vol goes up by 1% you should make 100k

Vol Swap Pnl = Vega Notional x (Realized Vol - Vol Strike)
ie. 100,000 x (21-20) = 100k. All good!

Now... You're expecting your var swap payout to be slightly higher.
To do a correct var swap pnl calculation like the vol swap above, you need your "variance" notional.

Variance Notional = Vega Notional / (2 x vol strike)

Therefore, variance notional = 100,000 / (2 x 20) = 2,500

So VAR swap Pnl = Variance Notional x (Realized Vol2 - Vol Strike2)
i.e. 2,500 x (212 - 202) = 102.5k

Let me know if you have any questions.

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If VAR PnL is Var N x (sigma squared - Vol K squared) how do you get (212-202) in the formula. Realized vol is 21 and 21 squared is not 212. Vol K squared is 20 squared or 400 so why do you have 202? Thanks.

that 212 is supposed to be 21^2 (21 squared) and 202 is 20^2 (20 squared)
so 2500 * (441-400) = 102,500

leveRAGE and FXTrader nailed it. Note that discussing notional for var swaps is sort of tricky. There's a notional specified in the swap contract and a vega notional. The two are not the same and the vega notional changes depending on the market strike. However, the swap notional is sort of meaningless and unintuitive, hence vega notional tends to be easier to think about from a market risk perspective.

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That's great - thanks all for your help!

why do people say that vol swap is safer than variance swap,. if the vol declines
var swap (20^2-19^2)*2500=-97500
vol swap (20-19)*100,000=-100000

?