Rho

Rho measures how much an option's price changes when interest rates change by one percentage point. It is usually the least watched of the main Greeks because rates move slowly and the effect on short dated options is small. But rho matters for long dated options, for large portfolios and in periods when interest rates change quickly, as they did in 2022 and 2023 when US short term rates rose from near zero to over 5%.

Rho basics#

Why rates affect options#

Think about put call parity: a call plus cash equal to the present value of the strike equals a put plus the stock. See Put-Call Parity.

• Owning a call instead of the stock lets you keep cash and earn interest until you pay the strike. When rates rise, that benefit grows, so calls gain value.
• Owning a put means you receive the strike later. When rates rise, the present value of that future payment falls, so puts lose value.

How big is rho?#

When rho matters#

• LEAPS and long dated options used as stock replacements. See Option Expiration Dates.
• Deep in the money options, where the strike's present value is a big part of the price.
• Periods of rapid rate change, such as central bank hiking cycles. See Central Banks Explained.
• Large institutional portfolios where small sensitivities add up.
• Early exercise decisions for deep in the money puts, which become more likely when rates are high. See Early Exercise.

Rho for options on futures#

Options on futures behave differently. Because a futures position requires no upfront payment for the underlying, the cost of carry is already in the futures price. Under the Black 76 model, rho for futures options is small and negative for both calls and puts, reflecting the discounting of the option premium itself. See Black-76 and Bachelier Models.

Rho and dividends#

A related sensitivity, sometimes called phi or dividend rho, measures the effect of changes in expected dividends. Higher expected dividends lower call prices and raise put prices, because the stock price is expected to drop when dividends are paid. See Dividends.

Rho in practice#

Most retail traders can safely give rho a low priority on options shorter than a few months. Those holding long dated options, or managing large books, should track it alongside the other Greeks. See Managing Portfolio Greeks.

Common mistakes#

• Ignoring rho on LEAPS.
• Assuming rate changes only affect bonds. Option prices move too.
• Forgetting that futures options respond differently to rates.

Frequently asked questions#

What is rho in options?#

The change in an option's price for a one percentage point change in interest rates.

Why do call prices rise when interest rates rise?#

Because owning a call lets you delay paying the strike price and keep cash that earns interest, which becomes more valuable as rates rise.

When does rho matter most?#

For long dated and deep in the money options, and during periods when interest rates move quickly.

Next, explore the second order Greeks in Charm, Vanna and Volga.