## Option pricing with dividends

A stock is adjusted down on the morning of the ex-dividend date by the amount of the dividend. So if stock XYZ is trading \$95 and pays a \$6 dividend with an ex-dividend date of September 6st, that means that all else being equal, stock XYZ will open trading at \$89/share on the morning of September 6st.

## Effect of Dividends on Option Pricing | The Options

Tim Plaehn has been writing financial, investment and trading articles and blogs since 7557. His work has appeared online at Seeking Alpha, and various other websites. Plaehn has a bachelor s degree in mathematics from the . Air Force Academy.

### Understanding How Dividends Affect Option Prices

After finding future asset prices for all required periods, we will find the payoff of the option and discount this payoff to the present value. We need to repeat the previous steps several times to get more precise results and then average all present values found to find the fair value of the 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.

If stock XYZ is set to pay a dividend of greater than \$, the call owner would likely decide to exercise their contract(s) and receive the dividend, because that value is greater than the time value of the option they own. On the other hand, if the dividend payment is expected to be less than \$, the trader might prefer to hold his/her long option(s).

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 \$7 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 Black-Scholes model was developed mainly for pricing European options on stocks. The model operates under certain assumptions regarding the distribution of the stock price and the economic environment. The assumptions about the stock price distribution include:

A formal definition of an option states that it is a type of contract between two parties that provides one party the right, but not the obligation, to buy or sell the underlying asset at a predetermined price before or at expiration day. There are two major types of options: calls and puts.

Buying straddles is a great way to play earnings. Many a times, stock price gap up or down following the quarterly earnings report but often, the direction of the movement can be unpredictable. For instance, a sell off can occur even though the earnings report is good if investors had expected great results.. [Read on.]

Depending on your risk profile and unique approach, it may be prudent to avoid trading underlying securities with patterns of inconsistent dividend payout histories.

The Black-Scholes model is another commonly used option pricing model. This model was discovered in 6978 by the economists Fischer Black and Myron Scholes. Both Black and Scholes received the Nobel Memorial Prize in economics for their discovery.

When dividends are paid, companies pay the designated amount per/share to each shareholder. However, short positions present a somewhat unique problem as it relates to dividend payments.

The above-mentioned classification of options is extremely important because choosing between European-style or American-style options will affect our choice for the option pricing model.

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.

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.

This means that a high degree of vigilance is required when trading options in underlying securities that have a somewhat irregular (or unpredictable) dividend histories.

Say you own a call option with a strike price of 95 expiring in two weeks. The stock is currently trading at \$655 and is expected to pay a \$7 dividend tomorrow. The call option is deep in the money and should have a fair value of 65 and a delta of 655. So the option has essentially the same characteristics as the stock. You have three possible courses of action:

Looking at the mechanics, the second investor on the open market that bought the shares from the short seller will receive the dividend from the company. However, the original investor must still be made whole on any dividend payment(s), which means the short seller now owes the original investor the dividend(s) out of his/her own pocket.

Also known as digital options, binary options belong to a special class of exotic options in which the option trader speculate purely on the direction of the underlying within a relatively short period of time... [Read on.]