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_variance2Φ1(Δ)volatility_factor)z = \Big(\frac{{total\_variance}}{2} -\Phi^{-1}(\Delta)\cdot{volatility\_factor}\Big)
Kdelta=SezK_{delta} = S e^z