Why Non-Dividend American Calls Are Not Exercised Early
Summary
The document explains why an American call on a non-dividend-paying stock has the same value as its European counterpart, even though a binomial pricing algorithm may compare early exercise value with continuation value at each node. The key distinction is between the holder’s right to exercise early and whether exercising early is economically optimal. That right does not add value in this case, so early exercise should not improve the option price.
The answers also explain why general-purpose binomial code may retain the early-exercise comparison: it supports options on dividend-paying stocks and helps validate the model. If a calculation indicates early exercise is optimal for a non-dividend-paying stock, the implementation or assumptions should be checked. The discussion gives a conceptual explanation rather than a proof or a numerical example, and its conclusion is specific to calls without dividends; it should not be generalized to dividend-paying underlyings or other American options.
Key ideas
- An American call on a non-dividend-paying stock is not optimally exercised early.
- Its value matches that of an otherwise equivalent European call.
- A binomial model may still check early exercise to handle dividend-paying cases.
- An early-exercise result in the non-dividend case may indicate an error or different assumptions.
Tags
Full text
# pricing american calls on non dividend paying stocks # pricing american calls on non dividend paying stocks It is never optimal to exercise an american call option early if it is written on a stock that doesn't pay dividends, yet when pricing such an option, using a binomial model, we check whether or not it is optimal to exercise at each node. I find it strange that it is never optimal to exercise early yet we take into account in its price the payoff from exercising early. Does anyone know a good argument to explain this? Consider the following example of a call option it is clearly optimal to exercise early everywhere, so it implicit in the question that the stock underlying the option pays dividends? ## Answer by Mark Joshi (score 3, accepted) https://quant.stackexchange.com/a/21390 The argument that the American and European call are worth the same is model independent. So it holds for the binomial model. So there is no need to check to see if the early exercise occurs because it won't. Of course, if you have written general purpose code, it is much easier to test for early exercise and always have the test fail than to try and deal with special cases. ## Answer by SmallChess (score 1) https://quant.stackexchange.com/a/21391 It's been proven mathematically that it's never optimal to exercise an American call without dividend. If your spreadsheet shows otherwise, it has to be wrong. It's a bad idea to drop off the check for early exercising just because you know it'll never happen, because your code will break for anything else, say a dividend-paying American call. Furthermore, it's a good practice to keep the code for model validation. ## Answer by AfterWorkGuinness (score 0) https://quant.stackexchange.com/a/21377 Even though it is not optimal to exercise early, you still have that right, thus the price must reflect it ## Answer by nbbo2 (score 0) https://quant.stackexchange.com/a/21385 IMHO the code checks for early exercise because it is a general purpose code. That "if" statement will never be true for a non-dividend paying stock. It does not harm and it is good to make your code general.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.