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I am trying to compute the calibration of an FX market volatility surface, and especially I want to retrieve the strikes from the deltas quoted.

I don't have any trouble reverse-engineering the formulas for non premium-adjusted deltas. However, for many currency pairs, the convention is to use premium-adjusted deltas, which are not monotonic in strike. For example, for a premium-adjusted forward delta (Source: Clark - FX Option Pricing - Chap3 p47): $$ \Delta_{F;\%} = \omega\frac{K}{F_{0,T}}N(\omega d_{2}) $$

Following this source, p14:

One common solution to this problem is to search for strikes corresponding to deltas which are on the right hand side of the delta maximum.

What is the argument or the intuition behind this statement?

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  • $\begingroup$ I guess the intuition behind this is that the market tends to quote out-of-the-money options. For calls, these are on the upside and thus right of the max. delta strike. $\endgroup$ – LocalVolatility Dec 19 '16 at 17:53

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