How Interest Rates Affect Option Prices

The direct effect on stock options

In standard stock-option pricing, a higher interest rate tends to increase a call’s value and decrease a put’s value when the stock price, strike, time, volatility and dividends are held constant. This is a comparison between otherwise identical pricing assumptions.

One intuition is that a call lets its holder postpone paying the strike to acquire shares. The value of postponing that payment increases when money can earn more interest. A put’s strike receipt is a future amount whose present value falls as the discount rate rises.

Rho measures rate sensitivity

Rho estimates how much an option’s theoretical value changes for a change in the interest rate. It is a local estimate: it does not promise that the market will move by that amount. Longer-dated options can have greater rate sensitivity than near-term contracts.

Check the units in a calculator. Rho might be displayed per one-percentage-point change in rates, per share, or per contract. A move from 4% to 5% is one percentage point, also called 100 basis points.

A simple rho example

Assume a stock call is priced at $4.00 per share and its rho is $0.08 per share for a one-percentage-point rate increase. If the pricing rate rises from 4% to 5% and all other inputs stay fixed, the first-order estimate is $4.08.

For a 100-share contract, that is an estimated $8 increase. If the stock falls at the same time, the call can still lose value overall. The example uses invented inputs and omits higher-order effects and costs; it is not a forecast.

Why a rate hike can still hurt a call

A central-bank announcement can move the stock price, expected dividends and implied volatility together. The stock-price effect can easily outweigh the direct interest-rate effect. An announcement already anticipated by the market may produce little reaction or a move in the opposite direction.

Separate two questions: what changes in the pricing model when only rates change, and what happens to the investment when the entire market reacts. They are different calculations.

Options on rate futures are different

A SOFR call follows the SOFR futures quotation, which rises as the implied rate falls. A Treasury futures call follows bond prices. Neither should be interpreted using the shortcut that higher rates help stock calls.

For a futures option, begin with the price of the specified futures contract. Then consider how time, volatility and the contract terms affect the premium. A change in the policy rate alone cannot tell you whether that option will make money.

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