Vol vs var swaps

[gver]

Hi .. Is trading Volatility against variance swap helps to trade the curvature of the vol smile curve ? If yes, could you pls help me with an intuitive understanding .. Thanks

 

[financeguy]

A varswap vs volswap spread put in place in equal vega amounts at onset of the trade (as a package also known as a convexity swap), does allow you to trade the 'curvature' or convexity of the smile. Volswaps are linear in vol by definition, meaning they don't have any dvega/dvol, while varswaps are linear in variance, meaning they are convex in vol and have positive dvega/dvol. Therefore a vega neutral portfolio of a long varswap and short volswap with have no implied vol exposure, but will have positive dvega/dvol, or volga, exposure. The value of volga is primarily determined by the convexity of the volatility smile, and so the price of the var vs vol swap spread will be priced based on that. You can trade this strategy by simply waiting for the trade to expiry and get paid the difference between realized variance and volatility less the entry point strikes, or you can rebalance the vega exposure using vanillas or additional volswaps as vol goes up and down (sell vol when vol goes up, and buy vol when vol goes down to monetize the long volga). You can also trade longer dated or forward starting spreads to bet on the curvature of the smile being different in the future, and then close out the trade once the pricing changes.

 

[gver]

thanks @financeguy .. that explanation made things pretty clear .. do you have any paper/mathematical stuff on this ..

 

[financeguy]

thanks @financeguy .. that explanation made things pretty clear .. do you have any paper/mathematical stuff on this ..

I don't have any one paper on this stuff, but the profiles of varswaps and volswaps are well known; there's plenty that will come up if you just google them. Varswaps are priced via a vanilla replication using a continuous strip of options along the volatility smile for a given expiration date (perfect under the assumption of constant interest rates, which is not realistic but usually close enough). Volswaps are not as model independent, but can be priced with a 'convexity adjustment' down from the varswap price. The amount of this convexity adjustment is the value of the varswap vs volswap spread. I would recommend looking into that as a starting point.

 

[gver]

Thanks a lot, will have a look