## PA Fwd

Subtype of Delta DefThe premium-adjusted forward delta

**of an fx option on the spot fx rate**

*Δᶠₚₐ***of the currency pair**

*s***, with**

*FOR/DOM***the foreign currency and**

*FOR***the domestic currency, is defined so that it represents the number of forward**

*DOM***units that need to be held as a hedge against a short position on a**

*FOR***option on one**

*FOR/DOM***unit in the case where the option's premium is paid in**

*FOR***currency.**

*FOR*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

**analytically and a numerical procedure must be employed.**

*K*The put-call parity relation

**implies that the implied vol**

*Call Price - Put Price = s - KDᵈ***is the same for a call and put on the same strike**

*σ***and then the above formula for Δᶠₚₐ leads to the put-call delta parity relation:**

*K*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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