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After having taken a look at this question about American and European options I was under the impression that the main difference between American and European options in Black Scholes pricing was factoring in dividends. When discussing options on futures is that difference mitigated due to the lack of dividends from futures?

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    This question might be more appropriate for quant.stackexchange.com
    – 0xFEE1DEAD
    Commented Jul 31, 2017 at 17:37

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I don't think your understanding is correct. The main difference between American-style and European-style option is the timing of the right to exercise the option. In American-style options, the option can be exercised at anytime whereas it is a point-in-time for European-style options.

Models used for those scenarios are different because the time horizon that is looked at is quite different. Therefore, when you ask:

When discussing options on futures is that difference mitigated due to the lack of dividends from futures?

The answer is no, simply because that is not the core difference between both option types. One can easily think of the possibility of the price fluctuation such that at one point in time prior to maturity, the option would be in the money and the back out of the money such that it could have been profitable to exercise the American-style option before maturity. This needs to be priced in whereas it would not for European-style options.

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  • I mean this strictly in terms of black scholes pricing. I know the fundamental difference between the types of options Commented Jul 31, 2017 at 16:04
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  1. I was under the impression that the main difference between American and European options in Black Scholes pricing was factoring in dividends.
  2. When discussing options on futures is that difference mitigated due to the lack of dividends from futures?

The Black-Scholes model is used to price European options. The lack of dividends is part of the underlying assumptions but the model can be extended to account for dividends. However, the model is still limited to European options because this isn't the main problem (see below).

The problem of finding the price of an American option is related to the optimal stopping problem of finding the time to execute the option. Since the American option can be exercised at any time before the expiration date, the Black–Scholes equation becomes an inequality. [...] In general this inequality does not have a closed form solution[.] source: Wikipedia

To value options on futures, the slightly different Black model is used:

The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, Interest rate cap and floors, and swaptions.

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I believe your question is mixing two concepts:

  • Early exercise decision: it can be shown that early exercise of American Call options on stocks makes only sense iff D > K(1-e(-r)), where D is the dividend, K is the strike and r is the interest rate.
  • Modelling: The treatment of dividends is complex in professional setups as the payments are not continuous and uncertain. Either way, dividends always need to incorporated.

Early exercise

Since you have dividends as the deciding factor, it makes intuitively sense to assume that one would never early exercise an American call option on futures.

However, there is a different argument for futures, namely interest on margin that you forgo if you only hold the option. This applies to type of futures options trading in the US for example.

On the other hand, many options on futures mark to market the premium, meaning they are subject to futures-style premium posting (FSPP). In this case, it can be shown that it is indeed never optional to exercise early.

Modelling

With regards to modelling, the distinction between Black Scholes Merton (stocks) or Black-76 (stock futures) is not important. In fact, both use the same idea, just applied to a different underlying. If there is no early exercise possible (or optimal under any circumstances), there exists this simple closed form formula most people are familiar with (for Black Scholes Merton and Black-76). It can even be used interchangeably to get to the same result as shown here. The link is for FX options but the only difference is that dividends are swapped for a second interest rate.

Black (Scholes) is still the most frequently used tool for pricing American options, you just don't have a closed form formula and rely on a PDE solver. Generally, a finite-difference solver of the PDE or Monte Carlo (MC) simulation of the SDE should result in the same value. However, MC is computationally more intensive and only used more exotic path-dependent structures.

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