Black Scholes price, Black, option, increase

dandman

why does the call option price increase with increase in risk free rate?
why does the put option price fall?

brainsX

The call option price falls when rf increases because the call option is similar to a leveraged position in the underlying, and an increase in the risk free rate makes the leverage ("borrowing") more valuable.

The put option price decreases for a different reason. The holder of the put option is going to get paid the strike in exchange for the stock if the option is in the money at expiration. The higher rf, the lower the present value of the strike.

Rasec

Call = Put + S - X/(1+rf)

If risk free rate increases, X/(1+rf) decreases, which will increase Call

jarobi04

under risk-neutral measure all assets are supposed to grow at the risk free rate. as the risk free rate goes up, assets are supposed to grow faster -> difference with the strike price is supposed to increase for calls -> call price goes up. similarly, put price goes down.