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- NicoLondon
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Gamma Variance Swaps
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.
Gamma Variance Swaps
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.
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- NicoLondon
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Gamma Variance Swaps
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.
Gamma Variance Swaps
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.
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- NicoLondon
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Gamma Variance Swaps
Antonio, Thanks again for your help.I really need to have a look at this article ;-)Nicolas.
Gamma Variance Swaps
You can find the article at http://www.math.nyu.edu/research/carrp/ ... fig.pdfAnd the formula is on page 4.
Gamma Variance Swaps
The firewall prevents me from answering to pm (weird). So could you send me an email, that will be easier.