Delta Strike Formula

  • ​
    SS
    - spot price
  • ​
    Δ\Delta
    - option delta
  • ​
    σ\sigma
    - implied volatility
  • ​
    τ\tau
    - time to maturity
  • ​
    ϕ\phi
    - normal cumulative distribution function
Delta strike price
KdeltaK_{delta}
is calculated as follows:
volatility_factor=στ{volatility\_factor} = \sigma \sqrt{\tau}
total_variance=σ2τ{total\_variance} = \sigma^2 \tau
z=(total_variance2−Φ−1(Δ)⋅volatility_factor)z = \Big(\frac{{total\_variance}}{2} -\Phi^{-1}(\Delta)\cdot{volatility\_factor}\Big)
Kdelta=SezK_{delta} = S e^z