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Rho of a call option formula

Description of the Rho of a call option formula

Formula for the calculation of the rho of a call option. Rho is an option value's sensitivity to a change of the risk-free interest rate.

Formula

\[ \rho = Kte^{-rt}N\left ( d2 \right ) \\ {\small where: d1 = \frac{ln \left( \frac{S}{K} \right ) + \left(r+\frac{\sigma^{2}}{2}\right)t}{\sigma\sqrt{t}} ; } \] \[ {\small d2 = d1 - \sigma \sqrt{t}} \ \]

Symbols

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