Why a decrease in risk-free rate of interest will decrease call option values and increase put option values?

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thanhnam

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Dear my friends,
I read a question from question bank, and the answer include a sentence: “a decrease in risk-free rate of interest will decrease call option values and increase put option values” I couldn’t have a clear explanation for this work, could somebody help me?
 
I try to explain in very simple words.
When interest rates are higher call options prices are higher
when IR (interest rates) are higher opportunity costs of holding money is higher. By using call options investors save more money by not paying for the underlying until later date and earn higher interest meanwhile.
When interest rates are higher put options prices are lower
when IR are higher opportunity costs of waiting is higher because investors lose more interest while waiting to sell the underlying when using puts.
If u understand this then decrease in IR can be easily understood.
 
I would say the above is exactly correct. Stated another way however, in case you’re still struggling with it:
A call option can be looked at as the right to delay a purchase. The higher the interest rate you can earn on the cash you will use to make that purchase, the greater the benefit of being able to delay that purchase.
A put option can be looked at as the right to delay a sale. The higher interest rate you can earn on the cash generated from that sale, the less desireable it is to delay that sale.
Again I’d say it’s basically that same thing stated above, just worded differently.
 
Another way of looking at that. In the risk neutral world all assets are expected to grow at the RFR on average. If the RFR rate is lower, stock prices are expected to appreciate less. Therefore, your call price will go down, your put price will go up.
 
Technically, in a risk neutral world, there are other factors that influence forward rates, not just the risk free rate. However, the basic concept there is correct.
 
ohai wrote:
Technically, in a risk neutral world, there are other factors that influence forward rates, not just the risk free rate. However, the basic concept there is correct.
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Sssshhhhhh….!!! You’re gonna spoil Level 2 for everyone!
:D
 
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