Interest rates and their effects on options

I’ve read in 2 totally unrelated sources that higher interest rates cause CALL options to increase in value. Someone plz explain why that is.The first time I shrugged it off, but then when when I read it a second time, my head started hurting.

If interest rates go up, it costs more for people to borrow money to invest into real estate, stock investments, and their own corporate expansion. If that’s the case, stock values should go DOWN, right? And if stocks come down in value, shouldn’t the CALL premiums be worth less too?

Take a look at put-call parity:

S0 + p0 = c0 + X / (1 + r)^t

If the risk-free rate r increases, the present value of the strike price X decreases; to maintain equality, either c0 (the price of a call option) must increase or p0 (the price of a put option) must decrease, or S0 (the price of the underlying) must decrease.

In a simpler version. An increase in interest rate signifies an increase in return on equity and traditional investment, while an increase in intrest rate causes a fall in the price of bond as a result of increased cost of borrowing.