Why is the value of a European call option positively correlated with the risk free rate?
Edited - I just told craps 
If risk free rate is higher, the risk neutral expected return on the stock is higher - that is, in the risk neutral world that we are valuing in, we expect the return on the stock over 1 period to be higher. With a higher expected return, you would obviously pay more for a call option (as the payoff is expected to be higher).
Think about it this way - put call parity tells you that the value of a call is equivalent to a long put, a long position in the underlying asset and a short position in a bond equivalent to the strike price DISCOUNTED AT THE RISK FREE RATE. So if the risk free rate rises, the present value of the bond will decline and the value of the call will rise (as you are short the bond).
Mathematically speaking… Value of Eurpean call on maturity c = S - X/(1+r)^T Higher r ==> higher demominator in the 2nd term ==> lower -ve 2nd term ==> higher c
Value of call is actually: C = S + P - X/(1+r)^t your reasoning is correct though, you just forgot to add the value of the put in your formula. CFASniper – You just got Sniped! -jk
thank you…that helps but shouldn’t there be a put in the equation: c + X/(I+r)^T = p + S