Risk free rate

[Professor]

Hi guys,

I have a quick query. In the Hull derivatives book it says that increasing the risk free rate leads to higher call option prices and lower put option prices (assuming all other variables are held constant). Does anyone know why this is?

Thanks

 

[Muppet06]

Call option means you won't buy the underlying asset until a future point in time - so if risk free rate of interest increases, then you can invest the money at a higher rate? Vice versa for a put option.

 

[Sherwin]

I think the key is the assumption that interest rates change while the stock price remains unchanged. If the assumption is true, you can image that the expected return from the stock in the future must increasse. That's why the value of call options will increase, I think.

What's more, Rho(call option)>0. That also means the positive relationship between interest rates and the value of call options, in mathematics.

 

[Elroy]

Hi guys,

I have a quick query. In the Hull derivatives book it says that increasing the risk free rate leads to higher call option prices and lower put option prices (assuming all other variables are held constant). Does anyone know why this is?

Thanks

Because a call requires short cash and long equity so increased borrowing cost increases price. Reverse for put. HTH