hey all, posted this in forex forums but seems this area is better: if I have say 1month implied vol of AUD/USD is 9.4 1month implied vol of EUR/USD is 9.3 and correlation between these 2 vols is 57%, what is the implied 1month vol of EUR/AUD? thanks!
I think you can calculate it like this ... First pair return is A, second pair return is B , third pair return is C = B/A Ln(C) = Ln(B) â Ln(A) Ln(B) normally distributed with sigmaB = 0.093 Ln(A) normally distributed with sigmaA = 0.094 Ln(C) normally distributed with sigmaC = sqrt( sigmaA^2 + sigmaB^2 - 2 * 0.57 * sigmaA * sigmaB )
thx for your reply. with the particular numbers I gave it comes out as eur/aud vol is 8.72 just thinking, this isn't a no arbitrage type figure though, right? because vol itself is traded so eur/aud vol could really be anything? if it doesnt follow the mathematical relationship (i.e. related in a particular way to the vols of the first two pairs), wouldn't there be arbitrage opportunities? curious for thoughts.