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I am currently looking into FX options. I am given a delta-tenor vol surface and I want to get the volatility of an option given its strike and time to expiry. I am reading about the method used and it seems to be an iterative method: first get the ATM volatility off the surface, then get the associates delta of the particular option. Afterwards you then get the implied volatility on the surface using this delta (using bilinear interpolation with flat extrapolation).

Why is it that one can't just convert those deltas into strikes (hence getting a strike-tenor volatility surface) and then use bilinear interpolation on the calculated strikes and the tenors? I assume that the strike of the option is the ATM strike because the delta of the option would be 50% when entered into, right?

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  • $\begingroup$ I am not quite sure what you are asking about. But have a look at my old question. It might help: quant.stackexchange.com/questions/29507/… $\endgroup$
    – Sanjay
    Jan 20, 2019 at 14:25
  • $\begingroup$ Thanks @Sanjay, will look into it and revert soonest should I have any questions.. $\endgroup$
    – acchan94
    Jan 23, 2019 at 10:36

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See the paper "FX Volatility Smile Construction, Dimitri Reiswich and Uwe Wystup" http://janroman.dhis.org/finance/FX/FX%20Volatility%20Smile.pdf for a comprehensive construction of the FX volatility surface, and in particular converting deltas into strikes.

In particular beware that even the notion of ATM may have a different meaning depending on the currency pair and the maturity.

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  • $\begingroup$ In my case, the volatility surface is a non-premium adjusted forward delta surface. $\endgroup$
    – acchan94
    Jan 23, 2019 at 10:39

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