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Hi all,I am naively trying to derive a pseudo close solution for a Gamma Variance Swap based on the same idea of static replication used for standard Variance Swaps when we suppose that the underlying is lognormal. At one point, I end up with a term E[0_int_T {vol_t^2.S_t^2dt}] which i do not know how to manage. Do we need to make any approximation at this point ? Thanks for your help. Nicolas.

Hi,Replication of the Gamma Swap (I suppose this is the one you refer to : sum of daily variances weighted by the level of the Stock) can be replicated using the Carr-Madan formula.

Hi Antonio,Thanks for your reply. I actually try to value a variance gamma swap in a continuous framework. With respect to my previous mail i realised that i made a mistake in my calculus. I actually end up with a term of type: integral of S_t. log(S_t). r_t . dt ... that i do not know what to do with ... I do find the formula with terms in 1/K but i am stuck with this term. Thanks for your help or hint.Nicolas.

I don't exactly know how you end up with this (hard to figure like that). But, I did the calculus, and you have two steps to follow : - First, write the Itô fomula for the function f(F(t))=exp(rt)*[F(t)ln(F(t)/F(0))-F(t)+F(0)]- The use the Carr-Madan formula for the function phi(.)=r(-rT)f(.)- Then, setting the liquidity threshold at the ATM forward price, you get the desired formula.Hope I am clear. Feel free to pm otherwise.

Antonio, Thanks again for your help.I really need to have a look at this article ;-)Nicolas.

You can find the article at http://www.math.nyu.edu/research/carrp/ ... fig.pdfAnd the formula is on page 4.

I am working on it ... thanks

The firewall prevents me from answering to pm (weird). So could you send me an email, that will be easier.

Ok thanks

Received your email. Many thanks again.Nicolas