Hello,I'm looking for a method to calculate the implied volatility for FX options which are not quoted.For example I know the implied vol for USD-CHF and AUD-CHF and I want to deduce the implied vol for AUD-CHF.I think that I could use the formula vol AUD-CHF = vol USD-CHF + vol USD-AUD + 2* correlation*sqrt(vol USD-AUD)*sqrt(vol USD-CHF) but I don't know is this formula holds whatever is the moneyness.I'd like to know if there is a practical way to deduce the cross FX implied vol.Thanks for your help

excuse me , there's a typo:I know the implied vol for USD-CHF and USD-AUD and I want to deduce the implied vol for AUD-CHF

As you seem to be yourself aware, you are on muddy groud. Normally the cosine type formula you have quoted is used to find implied correlations, given all three volatilities. Even this is a bit dubious because1. of the skew2. correlation per se is a dubious concept.So, as far as I am aware, your problems are1. the skew is going to muck up your formula2. correlation is a very difficult concept. In particular, you can run into major pathology if you mix implied correlations with historical vols.

Hi, the method i was taught is as follows:vol AUD-CHF = sqrt(varianceUSD-CHF + varianceUSD-AUD - 2*correlation*std dev(vol USD-AUD)*std dev(vol USD-CHF))i also concur with Graeme in that the skew will be a problem so adjustments may need to be made and that the concept of the correlation itself is difficultSpoona

thank you for your help.for the correlation I think my shortcut will be to use the correlation between USD-CHF and USD-AUD whatever is the moneyness or the time to expiry. We will see where it goes.

Graeme,Could you please develop your thoughts on implied (correlations) and historical volatility?I'm planning to extract implied correlations and spot volatility from forward option prices, using the formula sigma_implied(T)^2 = sigma_spot^2 + sigma_dom_int(t, T)^2 + sigma_for_int(t, T)^2 - 2*corr_spot_for*sigma_spot*sigma_for_int(t, T) - 2*corr_spot_dom*sigma_spot*sigma_dom_int(t, T) + 2*corr_dom_for*sigma_dom_int(t, T)*sigma_dom_int(t, T).Probably unreadable... But the spot volatility (sigma_spot) and the correlations are assumed to be constant while the interest rate volatilities (bond prices) are assumed to be dependent on time period.Here the bond price volatilities are to be estimated using historical prices, while the implied forward option volatilities are used on the left-hand side. Hence I'm mixing historical volatility and implied volatility to attain some sort of implied spot volatility and implied correlations, how do you feel about this?I'm doing it this way to avoid estimating correlations since I'm told this can be tricky/uncertain. But now the outcome is very sensitive to my estimation of historical bond price volatility....Of course anyone can comment.

I'm not understanding why you'd use the variance of the sum of the individual FX rates instead of the product. CHF/USD + USD/AUD doesn't yield much, however CHF/USD * USD/AUD = CHF/AUD. Non?