mathematically, you need find the price formular of call and put and then take derivative of these formulars wrt interest rate, which is also called rho. You can see that rho(call) is positve standing for same direction movement between r and price of call.

Economicaly, if r is goes up, normally stock price goes up, then you have the results.

   I think zzrays made a slim mistake when he expained in terms of economic .

   In reality when r goes up , the spot price of stock will be lower but not higher. As what hull said ,present value will be lower ,thus the spot price is lower. However , when we use BS model . we tend to assume the spot price doesnt change , the further price SPOTPRICE* e^{rt  _{WILL  RISE THEN the price of the call option rises.}} in  other words the time value rises.

  I think that is the process how r affects option price .

[此贴子已经被作者于2008-7-17 18:17:45编辑过]

‘ In reality when r goes up , the spot price of stock will be lower but not higher. ’

where you got this?  I　believe that the time value will rise how do you explain the put?

1. the stock price is the total sum of the future cash flows , r reflects the discounted rate.

2.money will flow from stock markets to other markets

3the cost of the company will go up

In reality when r goes up , the spot price of stock will be lower but not higher. As what hull said ,present value will be lower ,thus the spot price is lower. However , when we use BS model . we tend to assume the spot price doesnt change , the further price SPOTPRICE* ert  WILL  RISE THEN the price of the call option rises.

I THINK THIS EXPLAINATION WOULD BE BETTER

THANKS FOR UR CORRECTION .