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Rho

The sensitivity of an option's premium to a change in the interest rate.

Formula

\rho = \frac{\partial C}{\partial r}

r is the risk-free rate. The effect is largest in long-dated series: the further away expiry is, the longer the money stays tied up.

How to read the number

The rate sets the cost of money locked up until expiry, so it enters the option price alongside volatility.

When the metric lies

In short series the effect is lost against the noise of price swings and rho gets ignored. On long dates and after a sharp change in policy it is exactly what explains the gap from the model.

Also known as: option rho

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