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# imp vol for forex options

Discussion in 'Options' started by erasmus, Jul 8, 2008.

1. ### erasmus

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!

2. ### gbos

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 )

3. ### erasmus

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.

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