When American and European Put Values Coincide

Summary

The note asks whether a non-dividend-paying American put can have the same no-arbitrage value as a European put at particular strikes. It gives a simple condition: if the interest rate is zero, the two contracts are priced equally at every strike, so no special strike is needed.

The explanation offers no derivation, pricing framework, market data, or numerical example. Its result is therefore limited to the stated zero-rate assumption; it does not address how positive rates, exercise timing, or other contract and market assumptions affect the comparison. Readers seeking a fuller argument would need a separate treatment of early exercise and option valuation.

Key ideas

• With zero interest rates, American and European puts have equal prices for every strike, under the stated no-dividend assumption.
• The equality does not depend on choosing a particular strike.
• The note provides the conclusion without a supporting derivation or empirical evidence.

Tags

# Are there values of the strike price for which an American put and European put have the same no-arbitrage price?


# Are there values of the strike price for which an American put and European put have the same no-arbitrage price?












Assuming the options do not pay dividends, is there a strike price that satisfies this?

## Answer by Valometrics.com (score 1)

https://quant.stackexchange.com/a/53090

If there is no interest rate, the european and american put prices are the same for every strike.

More details can be found in my answer for the question below:

Longstaff Schwartz Algrorithm in R

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.