> For the complete documentation index, see [llms.txt](https://docs.knox.premia.finance/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.knox.premia.finance/appendix/delta-strike-formula.md).

# 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:

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

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

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

$$
K\_{delta} = S e^z
$$