Call Rho
Sensitivity of call price to a 1.00 (i.e. 100 percentage point) change in the risk-free rate. Positive for calls — higher rates increase call values via the present-value-of-strike channel.
When to use: Use to size interest-rate exposure on call positions. For typical retail trading horizons rho is small relative to delta, gamma, theta, and vega — but matters for long-dated LEAPS and rate-sensitive environments.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Rho | Rho | Change in option price per 1.00 (i.e. 100%) change in the risk-free rate | $ |
| S | Stock Price | Current price of the underlying | $ |
| Strike | Strike Price | Exercise price of the option contract | $ |
| Rf | Risk-Free Rate | Continuously compounded annual risk-free rate as a decimal | % |
| Sigma | Volatility | Annualized volatility of the underlying as a decimal (e.g. 0.25 for 25%) | % |
| T | Time to Expiration | Time to expiration in years (e.g. 0.25 for 3 months) | years |
Real-Life Examples
Example 1: ATM Call Rho, 30% Vol, 90 Days
Stock at $100, $100-strike 90-day call, r = 4%, σ = 30%.
Given
Step-by-Step
A 1.00 (100 percentage point) rise in r increases the call price by ~$12.29. Per-1%-rate convention: ~$0.123. Small relative to the other Greeks for short-dated options, more material for LEAPS.
Frequently Asked Questions
Higher rates lower the present value of the strike (which the call holder pays at exercise), increasing the call's value. Equivalently, higher rates raise the forward price of the stock, pushing more options ITM under the risk-neutral measure.
For long-dated options (LEAPS), in volatile rate environments, or when comparing calls across different rate scenarios. For short-dated retail trades rho is rarely the dominant Greek.
Divide by 100. The output here is per 1.00 (100%) move in r; brokers conventionally display the per-1%-point figure (rho ÷ 100).