Delta Strike Formula

• $S$ - spot price

• $\Delta$ - option delta

• $\sigma$ - implied volatility

• $\tau$ - time to maturity

• $\phi$ - normal cumulative distribution function

Delta strike price $K_{delta}$ is calculated as follows:

$${volatility\_factor} = \sigma \sqrt{\tau}$$

$${total\_variance} = \sigma^2 \tau$$

$$z = \Big(\frac{{total\_variance}}{2} -\Phi^{-1}(\Delta)\cdot{volatility\_factor}\Big)$$

$$K_{delta} = S e^z$$