Effect of Dividends on Option Pricing

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Dividends, Interest Rates and Their Effect on Stock Options

While the math behind options-pricing models may seem daunting, the underlying concepts are not. The variables used to calculate a fair value for a stock option are the price of the underlying stock, volatility, time, dividends, and interest rates. The first three deservedly get most of the attention because they have the largest effect on option prices. But it is also important to understand how dividends and interest rates affect the price of a stock option, especially when deciding to exercise options early.

Black Scholes Doesn’t Account for Early Options Exercise

The first option pricing model, the Black-Scholes model, was designed to evaluate European options, which don’t permit early exercise. So Black and Scholes never addressed when to exercise an option early or how much the right of early exercise is worth. Being able to exercise an option at any time should theoretically make an American option more valuable than a similar European option, although in practice there is little difference in how they are traded.

Different models were developed to price American options accurately. Most of these are refined versions of the Black-Scholes model, adjusted to take into account dividends and the possibility of early exercise. To appreciate the difference, these adjustments can make you first need to understand when an option should be exercised early.

In a nutshell, an option should be exercised early when the option’s theoretical value is at parity, and its delta is exactly 100. That may sound complicated, but as we discuss the effects interest rates and dividends have on option prices, we will use an example to show when this occurs. First, let’s look at the effects interest rates have on option prices and how they can determine if you should exercise a put option early.

The Effects of Interest Rates

An increase in interest rates will drive up call premiums and cause put premiums to decrease. To understand why you need to think about the effect of interest rates when comparing an option position to simply owning the stock. Since it is much cheaper to buy a call option than 100 shares of the stock, the call buyer is willing to pay more for the option when rates are relatively high, since he or she can invest the difference in the capital required between the two positions.

When interest rates are steadily falling to a point where the federal funds’ target is down to around 1.0% and short-term interest rates available to individuals are around 0.75% to 2.0% (like in late 2003), interest rates have a minimal effect on option prices. All the best option analysis models include interest rates in their calculations using a risk-free interest rate, such as U.S. Treasury rates.

Interest rates are the critical factor in determining whether to exercise a put option early. A stock put option becomes an early exercise candidate anytime the interest that could be earned on the proceeds from the sale of the stock at the strike price is large enough. Determining exactly when this happens is difficult since each individual has different opportunity costs, but it does mean early exercise for a stock put option can be optimal at any time, provided the interest earned becomes sufficiently great.

The Effects of Dividends

It’s easier to pinpoint how dividends affect early exercise. Cash dividends affect option prices through their effect on the underlying stock price. Because the stock price is expected to drop by the amount of the dividend on the ex-dividend date, high cash dividends imply lower call premiums and higher put premiums.

While the stock price itself usually undergoes a single adjustment by the amount of the dividend, option prices anticipate dividends to be paid in the weeks and months before they are announced. The dividends paid should be taken into account when calculating the theoretical price of an option and projecting your probable gain and loss when graphing a position. This applies to stock indices, as well. The dividends paid by all stocks in that index (adjusted for each stock’s weight in the index) should be taken into account when calculating the fair value of an index option.

Because dividends are critical to determining when it is optimal to exercise a stock call option early, both buyers and sellers of call options should consider the impact of dividends. Whoever owns the stock as of the ex-dividend date receives the cash dividend, so owners of call options may exercise in-the-money options early to capture the cash dividend. Early exercise makes sense for a call option only if the stock is expected to pay a dividend prior to the expiration date.

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Traditionally, the option would be exercised optimally only on the day before the stock’s ex-dividend date. But changes in the tax laws regarding dividends mean it may be two days before if the person exercising the call plans on holding the stock for 60 days to take advantage of the lower tax for dividends. To see why this is, let’s look at an example (ignoring the tax implications since it changes the timing only).

Exercising the Call Option Example

Say you own a call option with a strike price of 90 expiring in two weeks. The stock is currently trading at $100 and is expected to pay a $2 dividend tomorrow. The call option is deep in the money and should have a fair value of 10 and a delta of 100. So the option has essentially the same characteristics as the stock. You have three possible courses of action:

  1. Do nothing (hold the option),
  2. Exercise the option early, or
  3. Sell the option and buy 100 shares of stock.

Which of these choices is best? If you hold the option, it will maintain your delta position. But tomorrow the stock will open ex-dividend at 98 after the $2 dividend is deducted from its price. Since the option is at parity, it will open at a fair value of 8, the new parity price, and you will lose two points ($200) on the position.

If you exercise the option early and pay the strike price of 90 for the stock, you throw away the 10-point value of the option and effectively purchase the stock at $100. When the stock goes ex-dividend, you lose $2 per share when it opens two points lower, but also receive the $2 dividend since you now own the stock.

Since the $2 loss from the stock price is offset by the $2 dividend received, you are better off exercising the option than holding it. That is not because of any additional profit, but because you avoid a two-point loss. You must exercise the option early to break even.

What about the third choice, selling the option, and buying stock? This seems very similar to early exercise since, in both cases, you are replacing the option with the stock. Your decision will depend on the price of the option. In this example, we said the option is trading at parity (10), so there would be no difference between exercising the option early or selling the option and buying the stock.

But options rarely trade exactly at parity. Suppose your 90 call option is trading for more than parity, say $11. If you sell the option and purchase the stock, you still receive the $2 dividend and own a stock worth $98, but you end up with an additional $1 you would not have collected had you exercised the call.

Alternately, if the option is trading below parity, say $9, you want to exercise the option early, effectively getting the stock for $99 plus the $2 dividend. So the only time it makes sense to exercise a call option early is if the option is trading at or below parity, and the stock goes ex-dividend the next day.

The Bottom Line

Although interest rates and dividends are not the primary factors affecting an option’s price, the option trader should still be aware of their effects. In fact, the primary drawback in many of the option analysis tools available is they use a simple Black Scholes model and ignore interest rates and dividends. The impact of not adjusting for early exercise can be great since it can cause an option to seem undervalued by as much as 15%.

Remember, when you are competing in the options market against other investors and professional market makers, it makes sense to use the most accurate tools available.

Understanding How Dividends Affect Option Prices

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:

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.

Effect of Dividends on Option Pricing

Cash dividends issued by stocks have big impact on their option prices. This is because the underlying stock price is expected to drop by the dividend amount on the ex-dividend date.

Meanwhile, options are valued taking into account the projected dividends receivable in the coming weeks and months up to the option expiration date. Consequently, options of high cash dividend stocks have lower premium calls and higher premium puts.

Effect on Call Option Pricing

Options are usually priced with the assumption that they are only exercised on expiration date. Since whoever owns the stock as of the ex-dividend date receives the cash dividend, sellers of call options on dividend paying stocks are assumed to receive the dividends and hence the call options can get discounted by as much as the dividend amount.

Effect on Put Option Pricing

Put options gets more expensive due to the fact that stock price always drop by the dividend amount after ex-dividend date.

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