The payment of dividends for a stock impacts how options for that stock are priced. Stocks generally fall by the amount of the dividend payment on the ex-dividend date (the first trading day where an upcoming dividend payment is not included in a stock's price). This movement impacts the pricing of options. Call options are less expensive leading up to the ex-dividend date because of the expected fall in the price of the underlying stock. At the same time, the price of put options increases due to the same expected drop. The mathematics of the pricing of options is important for investors to understand so they can make informed trading decisions.

## Stock Price Drop on Ex-dividend Date

The record date is the cut-off day, set by the company, for receipt of a dividend. An investor must own the stock by that date to be eligible for the dividend. However, other rules also apply.

If an investor buys the stock on the record date, the investor does not receive the dividend. This is because it takes two days for a stock transaction to settle, which is known as T+2. It takes time for the exchange to process the paperwork to settle the transaction. Therefore, the investor must own the stock before the ex-dividend date.

The ex-dividend date is, therefore, a crucial date. On the ex-dividend date, all else being equal, the price of the stock should drop by the amount of the dividend. This is because the company is forfeiting that money, so the company is now worth less because the money will soon be in the hands of someone else. In the real world, all else does not remain equal. While, theoretically, the stock should drop by the amount of the dividend, it could rise or fall even more since other factors are acting on the price, not just the dividend.

Some brokers move limit orders to accommodate dividend payments. Using the same example, if an investor had a limit order to buy stock in ABC Inc. at $46, and the company is paying a $1 dividend, the broker may move the limit order down to $45. Most brokers have a setting you can toggle to take advantage of this or to indicate that the investor wants the orders left as they are.

## The Impact of Dividends on Options

Both call and put options are impacted by the ex-dividend date. Put options become more expensive since the price will drop by the amount of the dividend (all else being equal). Call options become cheaper due to the anticipated drop in the price of the stock, although for options this could start to be priced in weeks leading up to the ex-dividend. To understand why puts will increase in value and calls will drop, we look at what happens when an investor buys a call or put.

Put options gain value as the price of a stock goes down. A put option on a stock is a financial contract where the holder has the right to sell 100 shares of stock at the specified strike price up until the expiration of the option. The writer or seller of the option has the obligation to buy the underlying stock at the strike price if the option is exercised. The seller collects a premium for taking this risk.

Conversely, call options lose value in the days leading up to the ex-dividend date. A call option on a stock is a contract whereby the buyer has the right to buy 100 shares of the stock at a specified strike price up until the expiration date. Since the price of the stock drops on the ex-dividend date, the value of call options also drops in the time leading up to the ex-dividend date.

## The Black-Scholes Formula

The Black-Scholes formula is a method used to price options. However, the Black-Scholes formula only reflects the value of European style options that cannot be exercised before the expiration date and where the underlying stock does not pay a dividend. Thus, the formula has limitations when used to value American options on dividend-paying stocks that can be exercised early.

As a practical matter, stock options are rarely exercised early due to the forfeiture of the remaining time value of the option. Investors should understand the limitations of the Black-Scholes model in valuing options on dividend-paying stocks.

The Black-Scholes formula includes the following variables: the price of the underlying stock, the strike price of the option in question, the time until the expiration of the option, the implied volatility of the underlying stock, and the risk-free interest rate. Since the formula does not reflect the impact of the dividend payment, some experts have ways to circumvent this limitation. One common method is to subtract the discounted value of a future dividend from the price of the stock.

The formula as an equation is:

$\begin{aligned} &C=S_tN\left(d_1\right)-Ke^{-rt}N\left(d_2\right)\\ &\textbf{where:}\\ &d_1=\frac{\ln{\frac{S_t}{K}}+\left(r+\frac{{\sigma_v}^2}{2}\right)t}{\sigma_s\sqrt{t}}\\ &\text{and}\\ &d_2=d_1-\sigma_s\sqrt{t}\\ &\textbf{where:}\\ &\text{C = Call premium}\\ &\text{S = Current stock price}\\ &\text{t = Time until option exercise}\\ &\text{K = Option striking price}\\ &\text{N = Cumulative standard normal distribution}\\ &\text{e = Exponential term}\\ &\sigma_s=\text{Standard deviation}\\ &\text{ln = Natural log}\\ \end{aligned}$

The implied volatility in the formula is the volatility of the underlying instrument. Some traders believe the implied volatility of an option is a more useful measure of an option’s relative value than the price. Traders should also consider the implied volatility of an option on a dividend-paying stock. The higher the implied volatility of a stock, the more likely the price will go down. Thus, the implied volatility on put options is higher leading up to the ex-dividend date due to the price drop.

## Most Dividends Cause Barely a Flutter

While a substantial dividend may be noticeable in the stock price, most normal dividends will barely budge the stock price or the price of the options. Consider a $30 stock that pays a 1 percent dividend yearly. This equates to $0.30 per share, which is paid out in quarterly installments of $0.075 per share. On the ex-dividend date, the stock price, all else being equal, should drop by $0.075. Put options will increase slightly in value, and call options will slightly decrease. Yet, most stocks can easily move 1 percent or more in a day with no news or events at all. Therefore, the stock could rise on the day even though it should technically open lower on the day. Therefore, attempting to predict micro movements in stock and option prices, based on dividends, may mean missing the bigger picture of what is going on with the stock and option prices over the course of the days and weeks around the event.

## The Bottom Line

As a general guide, put options will increase slightly prior to a dividend and call options will fall slightly. This assumes all else remains equal which, in the real world, is not the case. Options will start pricing the stock price adjustment (related to the dividend) well ahead of when the stock price adjustment actually occurs. This implies micro movements in the option price over time, which are likely to be overwhelmed by other factors. This is especially true with small dividend payments, which are a very small percentage of the share price. Dividends that are substantial, such as high yield dividends, will have a more noticeable impact on share and option prices.