PA FwdSubtype of Delta Def
The premium-adjusted forward delta Δᶠₚₐ of an fx option on the spot fx rate s of the currency pair FOR/DOM, with FOR the foreign currency and DOM the domestic currency, is defined so that it represents the number of forward FOR units that need to be held as a hedge against a short position on a FOR/DOM option on one FOR unit in the case where the option's premium is paid in FOR currency.
It can be shown that it equals (expressed as a function of K,σ,φ):
Δᶠₚₐ(K,σ,φ) = φ(K/f)N(φd₋)
The above equation cannnot be solved for K analytically and a numerical procedure must be employed.
The put-call parity relation Call Price - Put Price = s - KDᵈ implies that the implied vol σ is the same for a call and put on the same strike K and then the above formula for Δᶠₚₐ leads to the put-call delta parity relation:
Δᶠₚₐ(K,σ,+1) - Δᶠₚₐ(K,σ,-1) = K/f
The meaning of symbols and more details in Black Scholes FX formula
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