Can somebody suggest me the most used model for pricing variance swaps (is there something in Excel?) and how are they hedged in practice?Thanks.Pier

derman (see www.derman.com) wrote a nice article about variance swap pricing, including an approximation of the fair strike when ony a finite set of options is available.

More practical techniques?

quick and dirty: varswap = ATM fwd vol * SQRT ( 1 + T * skew^2) and skew = [vol (90,T) - vol(100,T)]*[90 - 100]

Pricing and hedging are obtained via a static replication with calls and puts of differents strikes. There is no need for any model in the most general case. See Carr and Madan for further explanations.

QuoteOriginally posted by: tontonkumPricing and hedging are obtained via a static replication with calls and puts of differents strikes. There is no need for any model in the most general case. See Carr and Madan for further explanations.To see the failure of your statement, try to price a 1y varswap on a single name, say GM. Collect 1y option quotes apply that weighting formula across all traded strikes and think whether your hedge makes sense at all (especially the put wing) and calculate how pricey it would be to buy that strip taking into account bid/ask spreads for less liquid strikes.

To tell that hedging can't be done via static replication is one thing, but to tell that valuation can't be done via the formula is another ...Of course, if you hedge with a 80-120 smile available, your hedge becomes very very partial (if you still dare to call it a hedge), but however, the formula is quite robust when it comes to valuation : the only argument that can be opposed to the formula is the possible anticipated huge jump (which would be consistent with the skew) that would distort the formula !

The fact that the static replication is practically difficult may however explain big differences between variance swap quoted strikes and the theoretical formula (up to several points), variance swap market makers being more interested in flows than in the actual fair price !

g000RRRe,just curious if you know - when you use this static formula to hedge a long position in varswap, what is the shape of your final PnL distribution?

hmm you mean theoretically, if you can hedge with the whole strip of options + delta hedge continuously, and in absence of jump ?then, your hedge is perfect, isn't it ?

In practice, you can use equity or index options to hedge your var swaps. Exact replication by using calls and puts to hedge is very costly and a loser.

One more thing, usually traders use variance swaps to hedge off their vol risk that one might have from some other product. It is hard to make money trading pure variance swaps (just being long) because they trade at fairly high premium above ATM vol. If you buy var swaps you are betting that realized vol will be higher than the level you buy and that happens mostly on some news triggers of market crashes. One can also be a pure seller of var swaps, but then again you are taking shots in the dark.Here is something in Excel for pricing.http://www.fincad.com/support/developer ... Swaps.htm-> Check out this sectionValuation of a Variance Swap using a Portfolio of European Options Example

QuoteOriginally posted by: sepparQuoteOriginally posted by: tontonkumPricing and hedging are obtained via a static replication with calls and puts of differents strikes. There is no need for any model in the most general case. See Carr and Madan for further explanations.To see the failure of your statement, try to price a 1y varswap on a single name, say GM. Collect 1y option quotes apply that weighting formula across all traded strikes and think whether your hedge makes sense at all (especially the put wing) and calculate how pricey it would be to buy that strip taking into account bid/ask spreads for less liquid strikes.seppar:Yep the hedge is not good, I misread the question (How to hedge in practice...), but it's meant to get a fair price/hedge. However, even with the whole strip of options and in a BS world, the replication is not exact since we first made a third order approximation of the varswap payoff formula to get the Carr madan formula.ariliveitup:Hedging with the equity is nice, but, guessing you're not using BS to do so (!), how do you get your model params ? on the vanillas ?Furthermore, how do you price it ? Monte-Carlo ? Equivalent Vol Swap Formula for Heston ?