American Options versus European Options

This post assumes a basic understanding of options – for a primer on options, you can read a guest post I wrote for The Million Dollar Journey here.

Options can be either American-Style Options or European-Style Options and the only difference is that the holder of an American style option can exercise their option any time before and at expiration of the option contract whereas a European option holder can only exercise their option on the expiry date of the option contract.

Since this is the only difference, an American style option with all the same terms as a European style option (underlying security, strike price, expiry date) will theoretically always be worth no less than a European style option since there may be extra value in being able to exercise early.

If we dig a little deeper we find the following relationships:

For a non-dividend paying stock, a call option with American terms should be the same price as a European call option

This is because the cash required to buy the stock if you exercised the option could instead be invested at the risk-free rate and earning interest if you didn’t exercise your option. This is true until expiry, which means there is no economic incentive to exercising your option early on a non-dividend paying stock.

For a dividend paying stock, a call option with American terms CAN be higher than a similar European style call option

For a dividend-paying stock, it’s a bit more tricky. If you exercise your call option before the ex-dividend date you will receive the dividend payment. Now you have to figure out if that dividend payment (plus interest) is greater or less than the interest earned at the risk free rate on the cash NOT used to purchase the stock’s shares if you didn’t exercise your option. If the dividend payment is higher, then the American style call option is worth more since you could indeed exercise the call option and claim the dividend.

I should explain in more detail:

You own a December 55 Call option on ABC stock that is trading at $55/share. Therefore the call option is at-the-money. ABC pays a quarterly dividend of $0.25/share. It is November 1st, and the stock goes ex-dividend tomorrow, which means if you own the stock today you get the next scheduled dividend payment of $0.25/share (which is paid on November 30th). The risk free rate is 3%.

If you exercised your option contract, you would purchase 100 shares of ABC at $55/share for an outlay of $5,500. You then receive $25 in dividends on November 30th.

If you didn’t exercise your option contract, you could instead invest $5,500 at the risk-free rate of 3%, for 51 days which is the time between now, November 1st, and December 21st (options expire after the third Friday of the expiry month). This would earn you $23.05 in interest, calculated as:

$5,500 x 3% Interest x 51/365 Days = $23.05

Since this is less than the dividend payment, the option to exercise early and claim the dividend is, in this case, desirable – and hence carries a premium. Therefore, the American style option would be worth more than the European style option in this case.