# Option price when paying dividends. Dividends, Interest Rates and Their Effect on Stock Options

By Barclay Palmer Updated Oct 29, While the math behind options-pricing models may seem daunting, the underlying concepts are not.

The first three deservedly get most of the attention because they have the largest effect on option prices. Key Takeaways Dividends and interest rates are both components of options pricing models, and effect calls and puts differently.

Call options have positive rho, so an increase in interest rates will increase their values, while decreasing the value of puts, which have negative rho. Since stockholders, but not options holders, get paid dividends, when a stock goes ex-dividend, call prices decline and put prices rise.

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.

How Dividends Impact Option Pricing by Shelley Seagler Dividend stocks are a popular way to generate income, but they also impact several other investment strategies, including option strategies. Click To Tweet Stock Prices Fall on the Ex-Dividend Date Many companies pay dividends to their shareholders rather than retaining all of their earnings each year in order to attract income investors.

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 parityand its delta is exactly That may sound complicated, but as we discuss the effects interest rates and dividends have on option prices, we will use an option price when paying dividends to show when this occurs.

An increase in interest rates will drive up call premiums and cause put premiums to decrease. Thus, calls have positive rho while puts have negative rho.

### Effect of Dividends on Option Pricing

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 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. All the best option analysis models include interest rates in their calculations using a risk-free interest ratesuch as U.

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 costsbut 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.

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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 datehigh cash dividends imply lower call premiums and higher put premiums.

### Dividends, Interest Rates and Their Effect on Stock Options

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.

### How Dividends Impact Option Pricing

Whoever owns the stock as of the ex-dividend option price when paying dividends receives the cash dividendso 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. Traditionally, the option would be exercised optimally only on the day before the stock's ex-dividend date. To see why this is, let's look at an example ignoring the tax implications since it changes the timing only. So the option has essentially the same characteristics as the stock.

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You have three possible courses of action: Do nothing hold the optionExercise the option early, or Sell the option and buy shares of stock. Which of these choices is best?

If you hold the option, it will maintain your delta position. That is not because of any additional profit, but because you avoid a two-point loss.

### Understanding How Dividends Affect Option Prices

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 10so 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.

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- A first check of early exercise is: If this inequality is fulfilled, early exercise is not optimal, and the value of the option is where is the regular Black Scholes formula.
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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 options trader should still be aware of their localbitcoins html index bitcoin. 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.

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

The Bottom Line The payment of dividends for a stock impacts how options for that stock are priced.