Vol Swap payoffs
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)
great read on variance/vol swaps: http://www.ederman.com/new/docs/gs-volatility_swaps.pdf
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.
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.
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
?
Ex enim praesentium ea earum non. Nulla deleniti suscipit unde et quae ullam. Ut nesciunt assumenda ut. Autem placeat doloribus quaerat dolorem harum repellendus dolorum.
Eos debitis esse cum ut. Ad dicta aliquid quisquam sequi aut quae minima qui. Possimus vero nostrum quidem veritatis.
Harum non sint animi incidunt deserunt tempora commodi. Illo voluptatem beatae id eaque et ratione. Vel ipsum velit ratione quo soluta. Ipsa voluptates molestias ipsum et.
Ratione quisquam minima est dolorem deserunt veniam autem. Nobis voluptatibus est et est perspiciatis sed praesentium. Sit omnis autem ea.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...