When only the model interest rate rises, European calls without dividends become more expensive and puts cheaper in the Black–Scholes model. All other inputs stay the same
What Does Rho Measure?
Rho describes how sensitive a theoretical option price is to a change in the interest-rate input
CALL
Model price rises
Under these assumptions, a higher model rate increases the call price
PUT
Model price falls
Under these assumptions, a higher model rate decreases the put price
All else equal · European options without dividends · Rho in the BeInOptions calculator is per one percentage point change in the rate
Same Example. Only the Rate Changes
Stock€100
Strike€100
Time1 year
IV20%
Dividend0%
0 % model rate
Call€7.97
Put€7.97
5 % model rate
Call€10.45
Put€5.57
Black–Scholes model · per share · continuously compounded annual rate · European exercise · excluding fees5% is an educational scenario, not a current rate quote
The present value of the strike paid later depends on the interest rate
Call − Put = Stock − Present Value of Strike
For European options without dividends, C − P = S − K × e^(−rT). With a €100 strike and one year, the present value is €100 at 0% and about €95.12 at 5%; the call–put difference therefore grows from €0 to about €4.88
With a continuous dividend yield q, C − P = S × e^(−qT) − K × e^(−rT). Dividends and early exercise in American options change the relationship
ⓘCompare total outcome, risk and time horizon – not just the premium
A covered call combines stock exposure with an option premium and caps gains above the strike. T-Bills are US Treasury debt; yield to maturity assumes a given purchase price and holding to maturity. Savings account rates and bank terms can change; check the relevant deposit protection separately
Frequently Asked Questions
No. The 0% and 5% rates are model inputs for this comparison only. A suitable rate depends on currency, maturity and model convention
With more time to expiry, the strike is discounted for longer. Other factors also affect the option price; Rho isolates the rate change
That direction applies here to European calls in the Black–Scholes model with all other inputs fixed. Actual market prices can move differently because of volatility, dividends, the stock price and other factors
No. An option premium pays for rights and obligations under an option contract. A covered call still carries stock risk, capped upside and possible assignment
