Converting FX Delta Volatility Surfaces to Strike Volatility

Summary

The document asks how to obtain an FX option’s volatility from a surface quoted by delta and tenor. The proposed workflow first reads the at-the-money volatility, determines the option’s corresponding delta, then interpolates the volatility surface at that delta, using bilinear interpolation and flat extrapolation. The question asks why the quoted deltas cannot instead be converted into strikes to build a strike-tenor surface and interpolate directly, and assumes that an option’s strike is at the money when entered because its delta would be 50%.

The answer points to a specialist paper on constructing FX volatility smiles and converting deltas into strikes. Its key caution is that “at the money” can have different meanings across currency pairs and maturities. The document does not provide the conversion equations or resolve when each interpolation approach is suitable. In practice, the surface construction depends on the relevant delta and ATM conventions, so a simple 50% delta assumption is not enough to establish that strike and ATM coincide.

Key ideas

• FX volatility surfaces are often quoted by delta and tenor rather than strike and expiry.
• The question compares iterative delta-based lookup with conversion to a strike-tenor surface.
• Converting quoted deltas to strikes requires a volatility-surface construction method.
• The meaning of at the money can vary by currency pair and maturity.
• The document points to a specialist reference but does not provide conversion formulas.

Tags

# Getting option volatility off vol surface


# Getting option volatility off vol surface












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?

## Answer by Antoine Conze (score 2)

https://quant.stackexchange.com/a/43606

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.