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Delta of a put option formula

Description of the Delta of a put option formula

Formula for the calculation of a put option's delta. The delta of an option measures the amplitude of the change of its price in function of the change of the price of its underlying.

Formula

\[ \delta = N(d1) - 1 \] \[ {\small where: d1 = \frac{ln \left( \frac{S}{K} \right ) + \left(r+\frac{\sigma^{2}}{2}\right)t}{\sigma\sqrt{t}} } \ \]

Symbols

\(K\ \)       
Option strike price
\(N\ \)       
Standard normal cumulative distribution function
\(r\ \)       
\(σ\ \)       
\(S\ \)       
Price of the underlying
\(t\ \)       
Time to option's expiry