# Understanding Rho: Definition, Uses, and Calculations for Options

## What Is Rho?

Rho measures how the price of an option changes in response to shifts in the risk-free interest rate. It reflects the [sensitivity](https://www.investopedia.com/terms/p/price-sensitivity.asp) of calls and puts to rate changes; calls typically gain value as rates rise, while puts often lose value.

Though generally less influential than other "[Greeks](https://www.investopedia.com/terms/g/greeks.asp)," like [delta](https://www.investopedia.com/terms/d/delta.asp) or [theta](https://www.investopedia.com/terms/t/theta.asp), rho becomes more significant for options with long times to expiration. As part of the Greeks used in the Black-Scholes pricing model, rho helps traders and portfolio managers assess and [manage](https://www.investopedia.com/terms/r/riskmanagement.asp) interest-rate risk.

### Key Takeaways

*   Rho measures how an option's price changes with a 1% change in interest rates.
*   Options with longer time to expiration have a higher rho and are more sensitive to interest rate changes.
*   Call options generally have positive rho, increasing in value when interest rates rise, while put options have negative rho.
*   Rho is a minor factor in options pricing but is part of the Black–Scholes model.
*   The Greeks help manage risk by isolating changes in value due to specific market factors like interest rates.

## Understanding Rho Calculations and Practical Applications

Rho is calculated as the first derivative of an option's value concerning the risk-free rate. Rho predicts how an option's price changes with a 1% change in the risk-free rate of a U.S. [Treasury bill](https://www.investopedia.com/terms/t/treasurybill.asp).

For example, assume that a [call option](https://www.investopedia.com/terms/c/calloption.asp) is priced at $4 and has a rho of 0.25. If the risk-free rate rises 1 percent, say from 3 percent to 4 percent, the value of the call option would rise from $4 to $4.25.

Call options usually increase in price with rising interest rates, while put options decrease. Thus, call options have positive rho, while put options have negative rho.

Assume that [put option](https://www.investopedia.com/terms/p/putoption.asp) is priced at $9 and has a rho of -0.35. If interest rates were to decrease from 5 percent to 4 percent, then the price of this put option would increase from $9 to $9.35. In this same scenario, assuming the call option mentioned above, its price would decrease from $4 to $3.75.

Rho is larger for in-the-money options and decreases as options become out-of-the-money. Also, rho increases as the time to expiration increases. [Long-term equity anticipation securities (LEAPs)](https://www.investopedia.com/terms/l/leaps.asp), which are options that generally have expiration dates that are greater than one year away, are far more sensitive to changes in the risk-free rate and, thus, have larger rho than shorter-term options.

Although rho is key in the [Black-Scholes](https://www.investopedia.com/terms/b/blackscholes.asp) model, interest rate changes only slightly affect option prices. Because of this, rho is usually considered to be the least important of all the option Greeks.

## The Bottom Line

Rho measures how an option's price responds to changes in the risk-free interest rate. Rising rates typically boost the value of call options while lowering the value of puts. Though rho is part of the Black-Scholes model, it's often viewed as the least influential of the Greeks.

Its impact becomes more pronounced for long-duration options such as LEAPs, which are more sensitive to rate shifts. Understanding rho can help investors anticipate these effects and adjust their portfolios to better manage interest-rate risk.