approximate price of variance swap from implied vols

patzoul · November 15th, 2006, 4:02 am

any suggestion for a forumla to get the price of a variance swap based for example on the implied vols of the 90%, ATM and 110% vanillas?

asd · November 15th, 2006, 4:56 am

Not sure, I think Derman's paper on Variance swap has approximation formulas for the sameHope it helps

JohnLaw · November 15th, 2006, 5:17 am

have you NumeriX libs? in this case I can send you a spreadsheet in excel or a C++ dll that price them.......J.

eiriamjh · November 15th, 2006, 11:51 am

Derman is a good referencealso the last chapter of Gatheral's book covers variance swaps and vol derivatives, and there is this formula based on BS implied vol in function of log-moneyness:hope this helpse.

Forde · November 17th, 2006, 2:56 am

it's all in herehttp://finance.eller.arizona.edu/documents/seminars/2004-5/PCarr.Bifrost03-05.pdf

Forde · November 17th, 2006, 2:58 am

this is interesting as well - model indept. upper and lower bounds for variance callshttp://www.math.uchicago.edu/~rl/vocs4.pdf

flairplay · November 17th, 2006, 6:39 am

QuoteOriginally posted by: Fordeit's all in herehttp://finance.eller.arizona.edu/documents/seminars/2004-5/PCarr.Bifrost03-05.pdfMartin, This is NA from your previous institution. I have taught all my traders how to price all variance swaps in their head - they get to within 0.05% vol. Certainly not more than 0.10%, which is still tighter than standard bid offer in our markets.Of course the far out wings extrapolation have an impact but they can somewhat adjust for that too.

eiriamjh · November 17th, 2006, 9:55 am

What I don't like about the Carr-Lee approach is that it assumes continuous, frictionless trading of futures AND options on the underlying. This is is far from what happens in practice.e.

Alzone · December 12th, 2006, 11:52 am

in the derman et al approach where you weight the option prices by a constant times the inverse of the square of the strike how do you estimate the constant?thanks

newbee · December 12th, 2006, 4:15 pm

patzoul, I came across a JPM paper on Variance swaps, everything was explained very well, and it had "quick" calculations as well. Sorry, I don't have it, but you should ask some friends at JPM.Juan

quantman · December 13th, 2006, 9:10 pm

Hello,by popular demand, here's the JPM pdf file on variance swap.Enjoy !

pedrogarcia · March 25th, 2007, 10:26 am

Hi!!!I am very interested in the excel file for pricing variance swaps. Could you send it to me please? My email is cgeacar@gmail.comThank you very much in advance,Carlos

olive · March 27th, 2007, 9:08 am

savvysoft · March 28th, 2007, 1:21 pm

Having read the Derman et al paper but not the others, I wonder if anyone can say if they are measuring both:the volatility of volatilityandthe realization (or sampling) volatilityI think the Derman paper (and perhaps others) only captures the first concept: that the stochastic process has a parameter which is not stable over time, and the smile is used to quantify the amount of instability.The second term says that the ex-ante volatility is the uncertainty of returns around the known and constant (ex-ante) risk free rate of Black-Scholes, while the variance swap payoff is calculated as the variance around the realized mean.We can imagine a binomial world where the price might follow the up up up etc only path. The variance swap would use a vol of 0, while the tree would say (if it could talk) that the vol was the same v it is in every other path, since in every node it always deviates by the same amount from the risk free rate.Do any papers explicitly model the second term? The true value ought to be based on the sum of the two.