HiI have some simple questions about the paper "The Vanna-Volga Method for implied Volatlities" RISK jan2007.(same paper, downloadeable, www.fabiomercurio.it/consistentfxsmile.pdf )1)The authors apply Ito Formula to justify the method (p107) if we need to use 3 options + the stock to make the portofolio non-risky --> we have four noises and not just 2 as in the ito formula written by the authors. Any explaination? 3) did some tests using fake prices and the formula can violate call convexity. Is it frequent in practice? ("...leads to prices arbitrage-free in practice" does not seem very quantitative) Does it appear more often when using the approximations (i am not talking about the wings)? Thanks very much

my answer might not help very much...but i had the same problems, when reading the remark about arbitrage violations...Probably one might be able to proof some general result concerning convexity within that interpolation...this would be interesting.I am not quite sure, why you're having problems with the application of the ito formula...adding the three options gives you an unique solution of the portfolio weights (kind of saying something like "complete market")....I think the formula is correct

Hi, just a comment on the convexity violation: unfortunately it is not possible to prove that the second derivative w/r to the strike is always positive, but in practice (at least on the FX market where I 've been using the interpolation for 6 years), I never found cases where the smile was convexity-wise not arbitrge free.It may happen when the three options used for hedging imply a very high butterfly. Anyway, the smile will be convexity arbitrageble not for too much out-of- the-money options, since the method produces extreme wings reverting towards the atm level (interpolation does not increase the risk of generating this kind of smile). As for a formula for the check, we will think about it.