Why do call option prices rise with a rise in interest rates?

In risk-neutral world, all assets grow on average with the same risk-free rate. If interest rates go up, the underlying asset is expected to grow more. Therefore, call option price goes up. Does that help?

An intuitive way to think of it is that a call option gives you the option to defer payment for an asset at a later date at a known price. In a high interest rate environment, the call option has a greater value since you defer payment and you are able to invest the money (which you would otherwise use to buy the asset now) at that higher interest rate and buy the asset when the option expires. Hope this helps.

because it gives the investor the option to save more money … if you are delaying your investment in the asset, when interest rates go up, you can get more money from your investments the situation is different for fixed-income investments in which the price goes down when interest rate goes up … this makes your call option (buying at a higher price) less attractive … OA

Thanks, all good explanations. I got it now.

if you understand perimel’s explanation, then you can take it back to put-call parity: c = p + S - Ke^(-rt) If r increases, the PV of strike decreases, and the value of the call must increase to avoid arbitrage. The same goes for an increase in T or stock price.

Very good comment SeesFA! Sometimes a popular formula can answer a lot of questions.