Why Do Higher Interest Rates Increase the Value of Call Options?

Higher interest rates increase a call option's value due to the effect on the forward price of the underlying asset and the cost of carry. Owning a call option is a leveraged way to get exposure to an asset without having to buy the asset itself.

The money not spent on the asset can be invested at the risk-free rate. A higher rate means more interest earned on this capital, which makes owning the call a more attractive alternative to owning the asset outright.

This added benefit is reflected in a higher call premium.