Estimating American Option Early Exercise Premiums with Discrete Dividends

Summary

The document asks how to estimate the early exercise premium for an American option when the underlying pays discrete cash dividends. The proposed approach integrates a probability term over possible asset prices and times before the ex-dividend date, then uses those contributions to estimate the premium at the current time. It also compares this estimate with a continuous dividend model.

The author reports that the continuous dividend estimate aligns with the American option bid when carry and volatility are inferred from European option prices, while the discrete dividend estimate is much smaller and appears to put the American option below its payoff. They also describe inferring a borrow or lending fee as carry for the discrete dividend model. The document is a question rather than a worked solution: it gives no derivation, validation, or resolution of the apparent pricing problem. The linked research paper concerns early exercise premiums for American puts on dividend-paying stocks, but its findings are not summarized here.

Key ideas

• The question proposes integrating an exercise probability term across price and time before a discrete dividend date.
• The resulting integral is intended to estimate the current early exercise premium.
• The author reports a discrepancy between discrete and continuous dividend premium estimates.
• The document does not establish whether the proposed integral or the reported implementation is correct.

Tags

# Early exercise premium with discrete cash dividends using integral approximation


# Early exercise premium with discrete cash dividends using integral approximation












From my understanding, we have to integrate $N(d1(S_x-D,B,t))$ on both asset-price and time-space to derive the Early Exercise Premium $EEP(B,t)$ on each $t$ before the ex-date to get current early exercise premium $EEP(S,0)$. Where $$S_x = S \exp((r-\sigma^2/2) t + x \sigma \sqrt{t})$$ Is this correct?

When I use carry and vol backed out from European option prices, continuous div EEP is at bid of American quotes, which is correct. But when I use discrete cash div version EEP is a fraction of the continuous one, which takes American price below payoff which is wrong. I apply the same method on backing out carry with discrete div which only returns implied borrow/lending fee that I use to plug in as q.

Thanks.

https://www.researchgate.net/publication/251443198_The_early_exercise_premium_for_American_put_options_on_stocks_with_dividends

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.