What is the formula for calculating the Duration of an option?

The calculation of the Duration of an option is an essential concept in the context of option pricing and its sensitivity to changes in interest rates. The correct formula represents the relationship between the option's sensitivity (measured by Delta), the underlying asset's Duration, and the relative pricing of both the option and the underlying.

The first part of the formula, Delta, reflects the sensitivity of the option's price to changes in the price of the underlying asset. Duration, specifically the Duration of the underlying, indicates how sensitive the price of the underlying asset is to changes in interest rates.

The components that follow demonstrate how these sensitivities interrelate. By multiplying Delta by the Duration of the underlying and then adjusting for the relative prices of the underlying and the option, this formula effectively provides a comprehensive measure of the option's Duration.

The correct approach ensures that the impacts of both the option and its underlying asset are accurately combined, allowing for a clearer understanding of how changes in interest rates will influence the pricing dynamics of the option. This is particularly crucial for financial analysts and portfolio managers who aim to manage interest rate risk effectively in their investments involving options.

Thus, using this formula, one can ascertain how an option's price will respond in relation to changes in the underlying