ATM Conventions and Delta Premium Adjustment

Equity options usually quote "at-the-money" (ATM) as strike equals current spot price. FX options complicate this: because two currencies are involved and interest rates differ, the strike that actually splits the option's risk symmetrically is not spot — it is the ATM-forward or, more precisely, the strike where a call and put have offsetting deltas (delta-neutral straddle). Which convention a quote uses, and whether premium is paid in the base or quote currency, changes what "50-delta" and "ATM vol" mean in practice.

Why premium currency matters

If premium is paid in the quote currency (say dollars, for a EURUSD option), the option's delta is just the standard Black-Scholes delta. If premium is paid in the base currency (euros), the trader effectively already owns some euro exposure just from paying the premium, so the delta must be adjusted downward to net that out — this is premium-adjusted delta, and it shifts which strike counts as "25-delta" or "50-delta."

Worked example

A EURUSD 25-delta call has an unadjusted delta of 0.25. If the premium is paid in euros (the base currency), the trader already holds euro exposure equal to the premium amount just from paying for the option, so the premium-adjusted delta comes out lower — perhaps 0.22. Quoting the wrong convention when hedging would leave the desk short euros relative to what it intended, a small but real mismatch that grows with position size.