The dividend payment of a stock will affect the pricing method of the stock’s options. Stocks usually fall in the dividend payment amount on the ex-dividend date (the first trading day on which the upcoming dividend payment is not included in the stock price). This change will affect the pricing of options. Since the price of the underlying stock is expected to fall, the price of the call option is lower before the ex-dividend date.

At the same time, due to the same expected fall, the price of the put option has risen. The mathematical principles of option pricing are important for investors to understand so that they can make wise trading decisions.

Key points

- Stock-listed options are affected by dividend payments, because holders of the underlying stock receive dividends, but holders of call and put options will not receive these inflows.
- When the underlying stock goes ex-dividend, the call option will fall, and the value of the put option will increase because the stock price reflects the dividend that will be paid.
- Holders of deep-priced American call options can choose to exercise these options in advance before the ex-dividend date to obtain dividend payments owed to the relevant stocks.
- The Black-Scholes formula is not suitable for the fair evaluation of American options on dividend-paying stocks.

### Share price falls on ex-dividend date

The record date is the deadline set by the company to receive dividends. Investors must own the stock before that date to be eligible for dividends. However, other rules also apply.

If an investor purchases stocks on the registration date, the investor will not receive dividends. This is because stock transactions take two days to settle, which is called T+2. It takes time for the exchange to process the paperwork to settle the transaction. Therefore, investors must hold the stock before the ex-dividend date.

Therefore, the ex-dividend date is a key date. On the ex-dividend date, if other conditions are the same, the stock price should decrease the dividend amount. This is because the company is confiscating the money, so the value of the company is now reduced because the money will soon be in the hands of others. In the real world, everything else is not equal. Although in theory the amount of dividends a stock should fall, it may rise or fall more because other factors affect the price, not just the dividend.

Some brokers move limit orders to accommodate dividend payments. Using the same example, if an investor has a limit order to buy ABC Inc. stock for $46, and the company is paying a $1 dividend, the broker might lower the limit order to $45. Most brokers have a setting that you can switch to take advantage of or indicate that investors want the order to stay the same.

## The impact of dividends on options

Both call options and put options are affected by the ex-dividend date. Put options become more expensive because the price will decrease the dividend amount (other conditions are the same). In anticipation of falling stock prices, call options have become cheaper, although for options, this may begin to be priced in the weeks before the ex-dividend. In order to understand why the value of a put option increases and a call option decreases, let’s look at what happens when an investor buys a call option or a put option.

Put options increase in value as stock prices fall. A put option on a stock is a financial contract in which the holder has the right to sell 100 shares at a specified strike price until the option expires. If the option is exercised, the seller or seller of the option is obliged to purchase the underlying stock at the exercise price. The seller charges a premium for taking this risk.

Conversely, call options lose their value a few days before the ex-dividend date. A call option on a stock is a contract under which the buyer has the right to purchase 100 shares at a specified strike price before the expiry date. As the stock price fell on the ex-dividend date, the value of the call option also fell before the ex-dividend date.

## 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 options that cannot be exercised before the expiry date and the underlying stock does not pay dividends. Therefore, this formula has limitations when it is used to value American options on dividend-paying stocks that can be exercised early.

In fact, due to the loss of the remaining time value of the option, stock options are rarely exercised early. Investors should understand the limitations of the Black-Scholes model when evaluating dividend-paying stock options.

The Black-Scholes formula includes the following variables: the price of the underlying stock, the execution price of the related option, the time until the option expires, the implied volatility of the underlying stock, and the risk-free interest rate. Since the formula does not reflect the impact of dividend payments, some experts have Ways to bypass this restriction. A common method is to subtract the discounted value of future dividends from the stock price.

The formula as an equation is:

C = S t N (d 1) − K e − rt N (d 2) where: d 1 = ln S t K + (r + σ v 2 2) t σ st and d 2 = d 1 − σ st where : C = call option premium S = current stock price t = time before option exercise K = option exercise price N = cumulative standard normal distribution e = exponential term σ s = standard deviation ln = natural logarithmbegin{aligned } &C=S_tNleft (d_1right)-Ke^{-rt}Nleft(d_2right)\ &textbf{where:}\ &d_1=frac{ln{frac{S_t} {K}}+ left(r+frac{{sigma_v}^2}{2}right)t}{sigma_ssqrt{t}}\ &text{and}\ &d_2=d_1- sigma_ssqrt{t }\ &textbf{where:}\ &text{C = call option premium}\ &text{S = current stock price}\ &text{t = option line Time before weighting}\ & text{K = option exercise price}\ &text{N = cumulative standard normal distribution}\ &text{e = exponential term}\ &sigma_s= text{standard deviation}\ &text{ ln = natural logarithm}\ end{alignment}

C=secondTonN(d1)–Potassiumelectronic–rTonN(d2)Where:d1=σsecondTonenterPotassiumsecondTon+(r+2σv2)Tonandd2=d1–σsecondTonWhere:C = call premiumS = current stock pricet = the time before the option is exercisedK = option strike priceN = Cumulative standard normal distributione = exponential termσsecond=Standard deviationln = natural logarithm

The implied volatility in the formula is the volatility of the underlying instrument. Some traders believe that the implied volatility of options is a better measure of the relative value of options than prices. Traders should also consider the implied volatility of dividend-paying stock options. The higher the implied volatility of the stock, the more likely it is that the price will fall. Therefore, the implied volatility of put options before the ex-dividend date is higher due to the fall in prices.

## Most dividends cause little volatility

Although large dividends may appear in stock prices, most normal dividends hardly affect stock prices or option prices. Consider a $30 stock that pays a 1% annual dividend. This is equivalent to $0.30 per share, paid in quarterly installments, at $0.075 per share. On the ex-dividend date, under other conditions, the stock price should fall by $0.075. The value of put options will increase slightly, and the value of call options will decrease slightly. However, in the absence of any news or events, most stocks can easily fluctuate by 1% or more in a day. Therefore, although it should technically open lower that day, the stock may rise on the day. Therefore, trying to predict microscopic changes in stock and option prices based on dividends may mean that it is impossible to understand the changes in stock and option prices in the days and weeks before and after the event.

## Bottom line

As a general guide, put options will rise slightly before dividends, and call options will fall slightly. This assumes that all other conditions remain equal, which is not the case in the real world. The option will begin pricing the stock price adjustment (related to dividends) long before the stock price adjustment actually occurs. This means that over time, option prices will undergo minor changes, and these changes are likely to be overwhelmed by other factors. This is especially true for small dividend payments, which account for a very small percentage of stock prices. Considerable dividends, such as high-yield dividends, will have a more significant impact on stock and option prices.

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