# Risk Free Rate and Puts/Calls

"An increase in the risk-free rate increases the values of call options on equities and decreases the values of put options on equities. " Can someone explain the above statement, possibly with an example? Why is it true?

There are a bunch of ways of seeing that. The direct way is to go to the B-S formula and graph it a few times for fixed everything else or do some calculus. A hand-waving kind of explanation is to use put-call parity. Call + Bond = Stock + put If bonds are paying high interest you would like to be holding the bond. That means that you are willing to pay more money to own the call. Since you would rather own the bond than the stock, you will reduce the amount of money you are willing to pay for the put.

Thanks, but still a bit confused… you’d be willing to pay more for the call if the bond is paying more interest why exactly?

Remember Value of the call Max ( 0, S- X/(1+r)^t ) Value of Put Max( 0, X/(1+r)^t - S ) When rate(risk free) is up X/(1+r)^t will go down because r in denominator. In case of call you are subtracting less value from Stock price (S), that makes call value higher. Opposite is true in other case. Read more on derivatives section.

> you’d be willing to pay more for the call if the bond is paying more interest why exactly? Look at Joey’s formula (I don’t mean he invented it :-)): Call + Bond = Stock + put Thus: Call = Stock + put - Bond If interest rates rise, Bonds value goes DOWN, so Call value will be greater than otherwise.

Dreary Wrote: ------------------------------------------------------- > > you’d be willing to pay more for the call if the > bond is paying more interest why exactly? > > Look at Joey’s formula (I don’t mean he invented > it :-)): > How do you know that?

Ah yes, i understand now. thanks!

…nor do I mean he didn’t invent it either.