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?

  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) – 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.