Why At-The-Money Calls are Frequently Priced Higher than At-The-Money Puts – May 20, 2024
Intuitively, at-the-money (ATM) calls and puts should be priced the same. In most instances, this is not the case. ATM calls are generally priced higher than ATM puts. Why? The reason would center around the cost of carry. The buyer of a call can keep cash in their account, instead of purchasing the shares and earn interest on that cash; while the put buyer foregoes the opportunity to receive cash benefit of a similar amount. We would expect the difference in price between the ATM call and put to closely resemble the cost of carry of the strike price, which relates to the current short-term interest rate. In this article, we will investigate this with Apple Computer (Nasdaq: AAPL), an options calculator – using a 0% interest rate then start moving the rate higher and observing how the call and put prices change. We are making the assumptions of no dividend or hard to borrow scenarios (stocks that are hard to borrow for short sale transactions).
What is Rho?
Although not considered a major Greek, Rho measures the change in the option price due to a change in interest rates.
AAPL: $185.00 ATM call strike: 0% interest (red arrow top)
AAPL: $185.00 ATM put strike: 0% interest (red arrow top)
The theoretical option price for the $185.00 call is $5.137 per share (exact price as the call option). We inserted the ATM implied volatility stat of 23% (as with the call).
AAPL: $185.00 ATM call and put strikes: 1% interest
With interest rate now a factor, we would expect the cost of carry to enhance call value when compared to put value. In the screenshot above, we see call value at $5.095 per-share, compared to put value at $4.942 per-share. Let’s increase the hypothetical interest rate by 100 basis points to 2%.
AAPL: $185.00 ATM call and put strikes: 2% interest
In the screenshot above, we see call value at $5.175 per-share, compared to put value at $4.872 per-share. The difference between call and put value increased as the interest rate increased, accounting for the disparity between ATM call and put strike premiums.
Discussion
Interest rates (Rho) play a minor role in option prices, but is a factor, nonetheless. This relates to the cost of carry benefit inherent in buying call options which is not implicit with put options. Exceptions can occur due to the existence of dividends or a hard to borrow situation on the shares.
Author: Alan Ellman