How Does the Cost of Carry for a Cryptocurrency (E.g. Staking Yield) Factor into Option Pricing Models?

The cost of carry for a cryptocurrency, such as a staking yield or a funding rate from a perpetual swap, is incorporated into option pricing models by adjusting the "risk-free rate" input. In the Black-Scholes framework, the dividend yield for stocks is subtracted from the risk-free rate.

Similarly, a continuous yield like staking reward or lending interest (the cost/benefit of holding the underlying asset) is factored in. This adjustment is crucial because it affects the forward price of the underlying asset, which in turn influences the option's theoretical value.