Why Historical Payoffs Do Not Directly Estimate American Put Premiums

Summary

The document asks whether historical data can estimate American put premiums in the same way that expiry payoffs are used to estimate European put premiums. It proposes replacing the expiry return with the minimum return during the option’s life, then reports that this approach produced estimates about twice as high in the author’s trial. The author suggests this could serve as an upper bound and asks whether an American premium can be approximated from a European premium and strike.

The material frames the issue but does not derive a valuation method, provide a dataset, or establish the proposed bound. It offers no numerical evidence beyond the author’s reported comparison, and the chart mentioned for European premiums is not included. The key limitation is that early exercise decisions affect American option value, so a path minimum alone does not provide a validated estimate. The discussion is therefore a research question rather than a tested pricing procedure.

Key ideas

• Expiry payoff histories are proposed as a way to estimate European put premiums.
• Using the minimum underlying return during an option’s life is suggested as an approximation for American puts.
• The author reports that this path-minimum approach produced premiums about twice as high in their trial.
• The proposed relationship between European and American premiums is not demonstrated or validated.

Tags

# Realised American Put Premiums from Historical Data?


# Realised American Put Premiums from Historical Data?












It's possible to calculate European Put Premiums from historical data (see plot below) as:

$$P_{eu}(K|Q_{vol}) = E[(K/S_T-S_T/S_0)^+|Q_{vol}]$$

It's not possible to estimate Americal Premium same way. But maybe it's somehow possible to estimate it approximately?

Like - instead of return on the expiration date, use min return during option lifetime (doesn't work I tried and got premiums x2 times higher, although it could be considered as upper boundary for American option, i.e. $P_{eu} < P_{au} < 2P_{eu}$)?

Any other ideas? Or heuristics to somehow derive it from European $P_{am}(K) = F(P_{eu}(K), K)$?

Plot for European Premiums for 10 vol deciles:

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.