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American Option Pricing Around Ex-Dividend Dates

Article Quant Q&A · Author: volatile
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Summary

The discussion asks why an American option’s price should be continuous around an ex-dividend date and sketches an argument based on when early exercise is optimal. During periods when exercise is not optimal, the American option behaves like a European option. The answer suggests viewing the option as a sequence of European-style intervals separated by possible exercise dates, working backward from maturity and taking the greater of continuation value and exercise value at each opportunity.

For calls on dividend-paying stocks, the answer identifies the moment just before the stock goes ex-dividend as the key possible early-exercise point; puts can also have exercise opportunities that divide the life of the option into non-exercise intervals. The response offers intuition rather than a precise arbitrage proof. Its continuity claim depends on the model and conditions producing continuous European option prices, and it does not establish continuity at exercise opportunities or derive the result rigorously.

Key ideas

  • When early exercise is never optimal, an American option has the value of its European continuation value.
  • A call holder may find early exercise worthwhile just before the underlying stock goes ex-dividend.
  • At an exercise opportunity, the American option value compares continuation value with immediate exercise value.
  • The discussion gives intuition for continuity, but it does not provide the precise arbitrage proof requested.

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OptionsDerivatives pricing
Full text
# american option and cash dividends


# american option and cash dividends












Can someoe help with this : What is the precise arbitrage argument demonstrating that the price of an american option should be continuous around an ex-dividend date?

Thanks

## Answer by pincopallino (score -2)

https://quant.stackexchange.com/a/11459

If in the domain considered it is never optimal to exercise, then the price of an American option converges to the price of an European option. This means that the price of an American option is continuous in a domain of non-exercise as it is the case for European Options (1). This also means that the price of an American Option could be replicated by a portfolio of European options, one for each of the time-segment where early exercise is never optimal.

(1) I'd like to point out that this is, afaik, true for any model as option models give continuous prices for European products by design (with proper parameter choice) - it would be a trading/hedging hell otherwise.

The only time the holder of an American call option should consider early exercise is just prior to the stock going ex-dividend. There is where you may have your discontinuity as at exercise opportunity the value of American call is the max between the value of the product shall the owner not exercise and the value of the exit opportunity. Mark Joshi in "The concepts and practice of Methematical finance" explains better this, here I am just trying to pass along an intuition. The idea is to work backwards, from maturity to T=0, looking at the European replication and at the exercise opportunity work out the max. Similar argument applies to American puts where we could create a mesh of intervals where it is never optimal to exercise between points of possible early exercise, that over the entire life-time of the option.

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.