## Spot

Subtype of Delta DefThe spot delta

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

*Δˢ***of the currency pair**

*s***, with**

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

*FOR***the domestic currency, is defined as the first derivative**

*DOM***, where:**

*∂V(s)/∂s***is the option's price expressed as a function of the spot fx rate**

*V(s)***according to the Black Scholes formula Black Scholes FX formula**

*s*It can be shown that it equals (expressed as a function of K,σ,φ):

Δˢ(K,σ,φ) = φDᶠN(φd₊)

Solving for

**yields:**

*K*K = fe

^{-φN⁻¹(φΔˢ/Dᶠ)στ¹ᐟ² + ½σ²τ}

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 Δˢ leads to the put-call delta parity relation:**

*K*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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