February 10th, 2006, 9:03 am
Hi,I need help to understand the following.I have been trying to find the atm for different maturity terms 1w, 1m, ..., 1y etc. in the FX option marketIt seems that the ATM strike is found as by the 0-delta straddle, i.e.X(atm) = forward*exp(0.5*vol*vol*time)This formula works fine for FX options with a positive interest rate differential, (r_d-r_f) > 0. If the Interest rate differential is negative, (r_d-r_f) < 0, then the following formula works:X(atm) = forward*exp(-0.5*vol*vol*time)... but why this formula? Does any one know the argument behind this formula?(I have tested the formulas against superDerivatives.com and is able to match all atm strikes)Help would be appreciatedkind regards henrik