Hi Everyone,
I am struggling a little with understanding why call options increase in value when interest rates increase.
I am reading Natenberg’s book on Volatility Trading. In it, he mentions that for stock-type settlement futures options, an increase in interest rates results in decreased call option price. This is because the carrying costs increase. This makes perfect sense to me.
However, he also says that for stock options, the inverse relation is true. Precisely, he states that if interest rates increase, so does the value of the call option. Why is this true? I do see why increased interest rates would make people choose options over underlying (thus increasing option value), but wouldn’t the increased rates also increase carrying costs and thus decrease the option value?
Thank you!
Interest Rates and Option Values
byu/Terrible_Ad5173 inoptions
Posted by Terrible_Ad5173
1 Comment
EDIT: Sorry, I should have read further into your post.
It’s the same argument, only I had it backwards. In the equity trade (e.g., buying shares on margin), you have a cost of carry due to interest payments on the loan. If interest rates rise, those payments increase, so you have less money at the end of the trade, all else equal.
But for an equity call, you get the right to own the shares at the strike price *without having to take out a loan*. Therefore, no interest payments that increase if the interest rate goes up. Similary, if no loan is involved but we’re considering the opportunity cost of cash that can’t be invested at the risk-free rate, the value of money is the factor. Since the call needs less cash up front to be bought, the lower cost of the call means more of your cash can be invested at the risk-free rate, compared to buying shares with cash. So increasing interest rates increase the risk-free return of the excess cash left over after buying a call.
Therefore, the options market adds a premium to the call trade over the stock trade to reflect the advantageous difference in carrying cost that a call has over buying shares, when interest rates rise. In short, rho is a positive value for long calls.