How Discrete Dividends Affect European and American Call Values
Summary
The document explains why a predictable stock price drop on an ex-dividend date does not create a simple arbitrage by shorting calls. Option prices should account for known dividends before the payment date, so the anticipated loss in the stock’s value is reflected in the option’s price in advance. A European call cannot be exercised early, and its payoff at expiry depends on the stock value after the dividend. In the example, a stock priced at 100 will pay a dividend of 4 before expiry; a European call with strike 90 is valued using the post-dividend forward level of 96, giving an intrinsic value of 6 under the stated zero-volatility, zero-drift assumptions.
An American call may be exercised just before the dividend date, which can preserve the pre-drop value when early exercise is optimal. The answers emphasize continuity of option value across the predictable stock-price jump and note that actual pricing depends on correctly modeling the dividend and exercise features. The example is deliberately simplified and does not establish a general trading rule.
Key ideas
- Known dividends are incorporated into option prices before the stock goes ex-dividend.
- A European call holder does not receive the dividend and faces the post-dividend stock value at expiry.
- American calls may be exercised before a dividend when doing so is advantageous.
- A predictable stock price drop alone does not imply an arbitrage from shorting calls.
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Full text
# Option arbitrage with dividends?
# Option arbitrage with dividends?
If a stock pays a discrete dividend, the stock price falls by the amount of the dividend. There is no arbitrage opportunity from this predictable jump, because the investors receive the same amount of price depreciation back in cash from the dividend.
But how about options? If the underlying jumps down at the dividend payment, the call option holder receives a direct loss without any compensation in cash as the dividend is only paid to the stock owners and the stock price is now worth less for exercise. So isnt there an arbitrage opportunity to short all call before the dividend and buy them back cheaper afterwards?
## Answer by Ulysses (score 3, accepted)
https://quant.stackexchange.com/a/18271
Fact 1: if you are not good at pricing options, of course you can create a lot of arbitrage opportunities for the rest of the market. It does not matter whether the reason is in dividends or anything else.
Fact 2: if you are good in pricing options, you price the dividend effect in advance. Consider the situation of the European calls, and suppose that both the volatility and the drift are zero. The stock is at a 100, and there is gonna be a dividend of 4 before expiry. If you hold an ITM option with a strike 90, you would not price is at 10 = 100 - 90, rather you would price it at 6 = (100 - 4) - 90. They also say that European options expire on the forward rather than on the spot, notice that the forward for that expiry would be exactly 96 = 100 - 4. At the same time, American call would still be 10 worth since you would exercise it just before the dividend drop out time. Essentially, when pricing option around dividend one makes sure that the price of the option along the path of the stock (which does feature the jump) stay continuous: $V(S_{t-},t-) = V(S_{t+},t+)$ - see any book by Wilmott, perhaps also appears in Hull (maybe M. Joshi also has that). That's done exactly to avoid arbitrage. It's like you know in advance that your call would not be worth that much, so why would you buy it for such price?
## Answer by Victor123 (score 2)
https://quant.stackexchange.com/a/18269
Generally no, because 'dividends' are already 'priced into' the options. Which means, if an ATM call cost 0.50, and stock price drops by 1.00(amount of dividend), the ATM becomes OTM, but it may still cost 0.50, because the initial price of 0.50 already factored in the dividend.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.