How Does the ‘Risk-Free Rate’ Factor into the Time Decay of an ITM Call Option?

The risk-free rate (r) slightly reduces the time decay (Theta) of an In-the-Money (ITM) call option. The Black-Scholes model accounts for the fact that the strike price is a future payment, and its present value is discounted by the risk-free rate.

A higher risk-free rate reduces the present cost of exercising the call in the future, thereby making the call more valuable today. This small positive effect counteracts the negative Theta, resulting in a slightly slower time decay compared to a scenario with a zero risk-free rate.