8
$\begingroup$

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?

$\endgroup$
7
$\begingroup$

All this assumes the absence of arbitrage:

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.

So yes, see also Hull, 7nd edition, chapter 9 'Properties of Stock Options', section 9.6 in particular.

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.

$\endgroup$
  • 2
    $\begingroup$ Technically, call options can be optimal to exercise early if $r<0$. $r$ rarely if ever goes sufficiently negative on its own, though. $\endgroup$ – Brian B May 7 '12 at 12:31
  • 1
    $\begingroup$ Great comment! I added it to the answer since I feel an answer should stand on its own. $\endgroup$ – Bob Jansen May 7 '12 at 18:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.