# The effect of changes in the risk-free rate on call and put options

Does anyone know why changes in the risk-free rate affect prices of call and put options?

Q) A decrease in the risk-free interest rate will have what effects on the values of a call option and a put option?

Value of a call option Value of a put option

• A. Decrease Increase
• B. Increase Increase
• C. Increase Decrease

Call options typically have positive rho, and puts have negative rho.

And it has to do with the interest that can be earned when long a call, or must be forgone when long a put.

Why would the put option be worth more? Are we looking at this in terms of the holder or issuer?

If I was the holder of a bond and I had a put option and interest rates fell wouldn’t the value of my put option be worth less? If I can put at 104 but the bond price is 105 i wouldn’t exercise. The put option only becomes valuable once interest rates rise so if my bond price went to 103 the put would have value since I can exercise the put and get 104?

I suppose it depends your underlying asset.

Look at put-call parity:

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

If r increases, then X/(1 + r) decreases; to maintain equality, either c0 must increase or p0 must decrease (or both). Conversely, if r decreases, either c0 must decrease of p0 must increase (or both).

Hi S2000, intuitively speaking I’m not sure I understand this, would you mind explaining in layman’s terms please?

If you have a call option and the risk free rate decreases, the present value of the strike price (what you would have to pay) would increase. This is a negative thing if you are holding the call, so the call value should decline (easy to see in Black-Scholes OPM or Put-Call Parity [as Magician referenced]). If you are holding a put and the risk free rate decreases, the present value of the strike price (what you would receive) would increase. This is a good thing from your perspective, so the put value should increase. The reverse situations also are true.

If I remember correctly, minimum value of a *European call option is {0,S+X/(1+R)^t.}. and the European Put is {0, X/(1+R)^T - S}

Decrease in (1+R) makes X higher, hence Call worth less and Put worth more.

*American call is worth at least equal the European Call. American Put = (X-S) due to immediate exercise availability. http://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91316225 Check out carthurj post, it’s amazing for understanding this.