Spot
Subtype of Delta DefThe spot delta Δˢ 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 as the first derivative ∂V(s)/∂s, where:
V(s) is the option's price expressed as a function of the spot fx rate s according to the Black Scholes formula Black Scholes FX formula
It can be shown that it equals (expressed as a function of K,σ,φ):
Δˢ(K,σ,φ) = φDᶠN(φd₊)
Solving for K yields:
K = fe-φN⁻¹(φΔˢ/Dᶠ)στ¹ᐟ² + ½σ²τ
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 Δˢ leads to the put-call delta parity relation:
Δˢ(K,σ,+1) - Δˢ(K,σ,-1) = Dᶠ
The meaning of symbols and more details in Black Scholes FX formula
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