Why American Put Options Need Early-Exercise Pricing Methods

Summary

The document explains why American puts receive more attention than American calls in standard option-pricing discussions. In the usual case of an underlying asset that pays no dividends, exercising an American call early provides no advantage, so its value matches that of a European call. The American put can differ from its European counterpart because early exercise may matter, making it a distinct pricing problem.

That distinction motivates the use of specialized pricing methods for American puts, including trees, finite-difference schemes, and Monte Carlo approaches. The answer notes that methods developed for puts can be adapted to American calls when the underlying pays dividends. The explanation is scoped to vanilla options and the stated dividend assumptions; it does not compare the numerical performance or implementation details of the listed methods.

Key ideas

• For a non-dividend-paying asset, an American call has the same value as a European call.
• An American put can have a different value from its European counterpart because early exercise matters.
• American puts therefore provide a useful case for studying early-exercise pricing methods.
• Tree, finite-difference, and Monte Carlo methods can be generalized to dividend-paying American calls.

Tags

# Why the focus on American put options in literature?


# Why the focus on American put options in literature?












I've noticed that in the literature, whenever European vanilla options are to be priced, the classical approach is to price a European call.

I guess it doesn't matter because we have put-call parity.

However, almost every time I see somebody mention the pricing of American options, the standard approach is to consider an American PUT. We don't have a put-call parity, so considering American Call options seems equally relevant, and yet this doesn't happen.

Is there a reason for this?

EXAMPLE: Shiryev and Peskir's monograph on optimal stopping problems consider pricing American puts and perpetual puts... they don't even mention a call option.

## Answer by siou0107 (score 6, accepted)

https://quant.stackexchange.com/a/51192

That’s because in the case of a non dividend paying asset (the usual studied case), an American call is worth the same as a European call. Conversely for a non dividend paying asset the American put is different from the European put, so the American put needs special methods.

Nonetheless, once you study a pricing algorithm on an American put such as a tree, finite difference or a Monte Carlo method, you can generalise it to the case of an American call on a dividend paying asset

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.