The spot delta of an FX option is the amount of the base currency, per unit of notional, to trade in the spot market to hedge it: , with for a call and for a put. The forward delta is the amount to trade in the forward market, . The premium-adjusted delta corrects either for a premium paid in the base currency, which is itself a position in that currency: (spot) or (forward).
Exemples
Example 19.6 (Two smiles from one screen)
USDJPY three months: ATM 9.5%, risk reversal (dollar puts over), butterfly 0.3. By Equation 19.1 the 25-delta dollar call is at 9.2% and the put at 10.4%. With regular spot deltas their strikes are 160.85 and 150.71; with premium-adjusted spot deltas, the pair’s convention, 160.68 and 150.52. A trader who priced the 150.71 put at 10.4% while the market meant 150.52 would misprice it by the smile’s slope over 19 pips of strike (Figure 19.2).