Looking only at the math, one would expect stock prices to decrease by the same amount as the dividend, which should impact the price of options on that stock. However, the market is rarely ever about just the math and many other factors going into stock pricing, and by extension, options pricing.
The normal dividend cycle looks something like this: A company’s board of directors announces a dividend payment and sets a record date, or the last day on which a person can be listed as a shareholder and receive the dividend payment. Since stock transactions take two days to settle, an investor must buy the stock in question at least two days prior to the record date to be eligible to receive the dividend. The last business day prior to the record date is considered the ex-dividend date, or the first day in which the stock trades without the dividend factored into the stock price.
Back to the math—the expectation, if not always the fact, is that the stock price will drop by the amount of the dividend payment, because that cash is transferred off the company’s books and into the hands of the shareholders.
By that logic, call options should also drop in price while put options would rise. Remember, a call option gives the holder the right to buy a particular stock at a particular price, so if the price of the stock is expected to go down on news of a dividend, the call option would also be less expensive. A put option would become more expensive, because a put option gives the owner the right to sell a stock at a particular price, and if the option writer also expects the price to drop, the premium for that option would logically go up.
However, math and logic rarely drive the market. Imagine company XYZ is currently trading at $100 and announces a 2.5% dividend payment, or $2.50. Keep in mind that dividends are paid quarterly, so a $2.50 dividend would amount to $0.625. It’s completely normal for a stock trading at $100 to move $0.625 or more in a day without any particularly noteworthy news or events taking place. In other words, a stock expected to open down $0.625 could very easily close higher rather than lower, because dividend payments are relatively small.
In the chart below, courtesy of Yahoo Finance, Pepsi’s ex-dates for an announced $0.9275 dividend were 12/6/18 and 2/28/19, and on both days, the stock gained rather than lost during the trading day, as one would expect based on pure math.