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.
Glossar
Risk-Free Rate
Rate ⎊ The risk-free rate represents the theoretical return on an investment with zero risk, serving as a critical input in option pricing models to calculate the cost of carrying an asset forward in time, particularly relevant for valuing longer-dated crypto options.
Atm Option
Strike ⎊ An At-the-Money (ATM) option is characterized by its strike price being precisely equal, or extremely close, to the current market price of the underlying cryptocurrency asset.
Delta of OTM Options
Definition ⎊ Delta represents the rate of change in an option's price relative to a one-unit change in the underlying asset's price.
OTM Option Delta
Characteristic ⎊ OTM option delta, representing an out-of-the-money contract, is characterized by an absolute value close to zero, typically ranging from 0.0 to 0.5 for calls and -0.5 to 0.0 for puts.