How Expected Dividends Affect Stock and Call Option Values
Summary
The document examines how an announced future dividend affects a portfolio containing stock and calls when the stock price does not move on the announcement. Its central point is that information can already be reflected in both stock and option markets, so a dividend announcement alone does not imply a new change in the portfolio’s value. Option pricing should use an underlying adjusted for the expected dividend over the option’s life, rather than treating the full stock price as the dividend-free input.
Expected dividends generally reduce call values because call holders do not receive the dividend paid to stockholders. The explanation assumes the calls remain alive through the dividend date and that option markets share the relevant information. It is a conceptual clarification, not a numerical valuation exercise; it does not specify a discrete-dividend model or discuss cases where market expectations change at announcement.
Key ideas
- A dividend announcement need not change portfolio value if its information is already reflected in both markets.
- Expected dividends generally lower call values because option holders do not receive the stock dividend.
- Option valuation should account for expected dividends during the option’s remaining life.
- The explanation assumes the call maturity is on or after the dividend date.
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Full text
# Black Scholes Model and Dividends
# Black Scholes Model and Dividends
My question can be summarised as such:
- Consider a portfolio. Say it has a price $\Pi = x$.
- Portfolio consists of a stock and a sequence of call options underlying on the stock.
- It has been announced that a dividend will be paid in half year. However, assume that the stock price does not change today.
- How will the value of the portfolio change today?
My argument:
- If the stock price does not change today due to announcement, then we can assume the dividend is already priced into the stock value.
- In order to use the Black-Scholes-Merton option pricing model, the underlying stock price must only consist of a risky component, and not the certain dividend component as it must be assumed that stock prices follow a geometric Brownian motion.
- Since the stock price used for the model decreases (subtracting the present value of the dividend in half year), and the delta of the portfolio is positive, the value of the portfolio must decrease.
Where is the flaw in my argument (if there is one) ?
## Answer by emcor (score 1)
https://quant.stackexchange.com/a/17981
The option portfolio would not change its value because the dividend also has been already priced in as you can assume that option markets have the same information on the underlying as the stock market.
A dividend in general decreases the value of the call options because these are foregone relative to holding the asset as soon as the market has as an expectation about it. You should assume though that the maturity of your call options is greater or equal the dividend payment date.
The fact that the dividend was already priced in upon the announcement is not relevant because it may change the underlying price (or not) $S_t$, but not the calculation of the underlying for the option pricing $S_te^{-d(T-t)}$.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.