# Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the perspective of using Black-Scholes to price them and calculate the Greeks?

As you probably know without dividends it's is never optimal to early exercise a call option on a non dividend paying stock because then the time value is lost, if $r$ is non-negative.
Early exercise of an American put option can be optimal if the option is sufficiently far in the money and $r > 0$. Then you can earn interest on the money gained.
In the rare case that $r < 0$ it can be optimal to exercise call options. However $r$ rarely, if ever, goes sufficiently negative on its own.
• Technically, call options can be optimal to exercise early if $r<0$. $r$ rarely if ever goes sufficiently negative on its own, though. Commented May 7, 2012 at 12:31