Hi,my question is how variance swaps are replicated in practice. Further how big is typically the difference between the price obtained from the "unperfect replicating portfolio" and the price obtained from the theoretical replication portfolios (which involves an infinite number of strikes available).Thanks.

it is an art, not a scienceI know some traders just hedge the vega with the most liquid option available on the market and subsequently follow some dynamic vega-hedging strategy... and hope for the best!e.

Nowadays variance swaps on the major indexes (Eurostoxx, SPX, etc.) are such commoditized "flow" products that someone who trades a book of them manages their inventory more like a book of single stocks or variance swaps than like a single option which has to be constantly delta hedged, and the risk left over after this is usually hedged with 2-4 options (including the OTMs) to try and minimize the risk in a few key scenarios (implied vols go up/down, stock makes a large move, etc.)

I am not a specialist of variance swaps, but it's not so simple : on this position, you don't have gamma risk, only vega risk, so I think you have to combine options (long call and short put) in order to eliminate gamma movements ....

The replicating portfolio for a var swap consists only of long option positions, plus a daily delta hedge (if your swap has daily settings). See the paper by Neuberg (1990) which I posted not long ago.

Erstwhile, could you please give me the link for your paper ?? Thanks a lot.

There is a lot of literature on volatility derivatives, including recent advances toward a general theory of pricing derivatives on volatility and variance. This is the paper that kicked off the entire variance swap business (three years after its publication):Link to thread on Neuberger paper

Last edited by erstwhile on May 10th, 2005, 10:00 pm, edited 1 time in total.

Thanks all. From your experience, is the theoretically calculated var swap price using the spectrum of observable strikes and some inter- and extrapolation close to the market quote. If not, how could one obtain a better estimate of a tradable swap rate from a given smile.

this paper (GS - 1999) will be very helpful for you (replicating variance swaps) :

I haven't priced a var swap from fundamentals in quite awhile, but when i was doing it, there was one major "gotcha": the var swap price depends a lot on what you assume for very low strike put implied vols! That is, strikes below the bottom of the exchange. This is because in the replicating portfolio of options, the weighting of an the option is inversely proportional to strike^2.But nowadays with these liquid var swaps, there would be an implied downside skew. The options above the top strike in the exchange also in general matter to the price, but not as much as the low puts.Given the liquidity of the market this is probably not an issue nowadays. But it might be interesting to back out the market assumption for very low strike options. Might be interesting to compare this "implied distribution tail" to the behavior of the credit indices, as they are ultimately linked to longer dated deep OTM puts (sort of).

I heard that Long / Short equity desks were hedging their exposition to volatility by shorting Variance Swaps ; it's a good idea, but how do you determine the amount of hedge ?????I think that tentation is big to be over-hedged, especially since last year ...

QuoteOriginally posted by: BLOBYI am not a specialist of variance swaps, but it's not so simple : on this position, you don't have gamma risk, only vega risk, so I think you have to combine options (long call and short put) in order to eliminate gamma movements ....In a way, variance swaps are pure gamma risk, since the payout of the floating leg is the sum of the squares of the log returns of the underlyer. Every day/week/etc, you are paying/receiving a fixed amount (or accruing its future value) in exchange for receiving/paying the square of that period's return. A 1Y variance swap is very similar to a 1Y IR swap against O/N or 1w Libor, only you know the libor rate in advance, but you don't know the square of the stock return in advance.Offsetting risk between var swaps and options really is quite simple. If you are worried about what side you are on, see erstwhile's Song for the Gamma Long QuoteOriginally posted by: BLOBYI heard that Long / Short equity desks were hedging their exposition to volatility by shorting Variance Swaps ; it's a good idea, but how do you determine the amount of hedge ?????The amount is sometimes called the skew delta, and no matter what you call it is basically a trade on the correlation between spot return and variance (which is often significantly negative, meaning if you are net long, you should be long variance as a hedge.).

Last edited by exotiq on May 12th, 2005, 10:00 pm, edited 1 time in total.

it's very interesting ; exotiq, can you develop this thesis around the "skew delta" ?

Variance swap on an index has two underlying priced components - individual stock vol and stochastic priced correlation between stocks. The latter is a very important factor, and contributes probably up to 50% to index vol changes... There are also correlation swaps nowadays... does anybody know how those swaps are replicated in practice? Is there finally a way of isolating correlation and vol components in dispersion deals? Thanx, Greg

GZIP: On