What Is Rho in Options?
Rho is the fifth and least discussed of the primary options Greeks. It measures the sensitivity of an option's price to a 1% change in the risk-free interest rate. A call option with a Rho of 0.05 will increase by $0.05 per share ($5 per contract) if the risk-free rate increases by 1%. Conversely, a put option with a Rho of -0.05 will decrease by the same amount when rates rise.
While Rho is often considered the least important Greek for short-dated options, it becomes significant in the current interest rate environment. With the Federal Reserve maintaining rates between 4% and 5.5% in recent years, Rho effects on long-dated options (LEAPS) can be meaningful. A 1% rate change on a 1-year at-the-money call option can affect the price by 3-5% of the option's value, which is not trivial for large positions.
Rho Formula
Rho Calculation Example
- 1T = 365/365 = 1.0 year
- 2d2 = [ln(100/100) + (0.05 - 0.03125) × 1.0] / (0.25 × 1.0) - 0.25 = 0.075/0.25 - 0.25 = 0.05
- 3N(d2) = N(0.05) = 0.5199
- 4Call Rho = 100 × 1.0 × e^(-0.05) × 0.5199 / 100 = 0.4947 × 0.5199 = 0.257
- 5If rates rise from 5% to 6%, the call price increases by approximately $0.257 per share ($25.70 per contract)
- 6LEAPS call price at 5% rate: approximately $13.18
- 7LEAPS call price at 6% rate: approximately $13.44
Why Interest Rates Affect Options Prices
Interest rates affect options through the cost-of-carry concept. When you buy a call option instead of buying the stock, the capital you do not deploy can earn interest. Higher interest rates make this advantage more valuable, increasing call prices. Conversely, a put option delays a stock sale, and higher rates make this delay more costly (you forgo earning interest on the sale proceeds), decreasing put prices.
| Expiration | Call Rho | Put Rho | Call Price | Rho as % of Price |
|---|---|---|---|---|
| 7 days | $0.01 | -$0.01 | $1.91 | 0.5% |
| 30 days | $0.04 | -$0.04 | $3.95 | 1.0% |
| 90 days | $0.11 | -$0.11 | $6.86 | 1.6% |
| 180 days | $0.19 | -$0.19 | $9.71 | 2.0% |
| 365 days | $0.26 | -$0.26 | $13.18 | 2.0% |
| 730 days (2yr) | $0.37 | -$0.35 | $18.41 | 2.0% |
When Rho Matters Most
- LEAPS positions: Options with 1-2 years to expiration have significant Rho exposure
- Large portfolios: Institutional options books can have millions of dollars of Rho exposure
- Rate decision events: FOMC meetings can cause sudden rate expectations shifts affecting all options
- Deep in-the-money options: ITM options have higher Rho because they behave more like the underlying asset
- Dividend-paying stocks: The interaction between Rho and dividend yield can compound the rate sensitivity effect
Managing Rho Exposure
With the Federal Reserve at 4-5% rates as of 2025-2026, Rho is more relevant than it was during the near-zero rate era (2009-2021). LEAPS traders and poor man's covered call investors should factor Rho into their analysis, especially when anticipating rate cuts or hikes.
Rates UP: Call prices increase, put prices decrease. Rates DOWN: Call prices decrease, put prices increase. The effect is proportional to time to expiration. Short-dated options are nearly immune to rate changes.
