Why Is Delta Considered the First-Order Sensitivity of an Option’s Price?

Delta is the first-order derivative of the option price with respect to the underlying asset's price. It measures the immediate, linear change in the option's price for a one-unit change in the underlying asset's price.

As the first derivative, it is the most fundamental and direct measure of the option's exposure to the asset's movement. It is crucial for hedging, as a Delta of 0.5 means the option price will move half as much as the underlying asset price.