Does a Change in the Risk-Free Rate Have a Greater or Lesser Impact on OTM Option Delta than on ATM Option Delta?
A change in the risk-free rate generally has a lesser impact on the Delta of OTM options compared to ATM options. The risk-free rate is a component of the option's extrinsic value.
Since OTM options have a lower probability of expiring ITM, their Delta is less sensitive to the marginal changes in the extrinsic value components, which include the risk-free rate. The impact is marginal for all options, but less so for OTM.