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Basic Question 9 of 9
Which type of call options on non-dividend-paying stock are worth more?
B. European-style call options
C. They are worth the same.
A. American-style put options
B. European-style call options
C. They are worth the same.
User Contributed Comments 6
| User | Comment |
|---|---|
| aco2012 | I do not agree. An option of exercise is always an option. On the 1st level it was explained that arbitrage makes the floor value of MAX(0,S-X) for American call but MAX[0,S-X/(1+r)^T] for European one. It looks contradicting. Am I right, and should I just treat above quote to be wrong? Because it is from reliable source. |
| ohai | In theory, early exercise is never optimal for American call option on non-dividend stocks. Hence, early exercise has zero value. Consider that MAX[0,S-X/(1+r)^T] > MAX[0,S-X] for positive r. So these formulas don't show that the value of an American call option is greater than the value of a European call option. To show that early exercise has no value for American call options, consider these two scenarios for an American call option (assuming ITM, r >= 0 and zero volatility): 1) Exercise today: value is S-K 2) Exercise at time T: Since forward price of the stock is S*(1+r)^T, value at time T is S*(1+r)^T - K. Value today is S-K/(1+r)^T. Since S-K/(1+r)^T >= S-K, late exercise is optimal. |
| dreary | What benefit do you get if you exercise early? The only time it makes sense is when option liquidity is a problem, other than that it makes no difference, European or American. In fact, even if it was dividend-paying stock, it makes no advantage, contrary to what the book says. |
| aco2012 | Wow guys, thanks a lot, it seemed strange to me but you are right. To self-explain in most simple way is that a call is the right to buy something paying nominal price which is constant in the future. Because of time value of money it is always better to pay the same nominal price later than earlier. So it is better to exercise later. So it seems American calls on non-dividend paying stocks make no sense if markets are liquid. Their floor of MAX(0,S-X) makes no sense as well as more complicated arbitrage makes a floor of MAX(0,S-X/(1+r)^T) also for American call. |
| ohai | Yeah, I think you got it. That's pretty good - a lot of people just gloss over this part. Dreary: In theory, early exercise of American call options can be optimal for dividend paying stocks. Consider the extreme case where a stock pays a high dividend, like 80%, At the ex-date, S falls to zero. So intuitively, S-K will have a very small or negative value on the ex-date. Naturally, you would want to exercise early to avoid the stock price drop on the ex-date. I'm too lazy to write a formula with a discrete dividend, so consider this modification to my previous post. Now, we assume a annually compounded dividend, q, and we can exercise the option now or at time T. 1) Exercise today: value is S-K 2) Exercise at time T: Since forward price of the stock is S*(1+r-q)^T, value at time T is S*(1+r-q)^T - K. Value today is S*[(1+r-q)/(1+r)]^T - K/(1+r)^T. It's harder to tell from this formula, but for large values of q, S-K > S*[(1+r-q)/(1+r)]^T - K/(1+r)^T. Early exercise would be optimal in these cases. |
| dream007 | ohai, theory is not in line with reality! Do this: If you think the option price is going to drop because the underlying is going to drop by the amount of the dividend, short the call! Reality is that the options market prices in "everything". |
I just wanted to share the good news that I passed CFA Level I!!! Thank you for your help - I think the online question bank helped cut the clutter and made a positive difference.
Edward Liu
Learning Outcome Statements
calculate the no-arbitrage values of European and American options using a two-period binomial model;
identify an arbitrage opportunity involving options and describe the related arbitrage;
CFA® 2025 Level II Curriculum, Volume 5, Module 32.