Option Pricing Models

OddTrader · Feb 26, 2016

Investopedia said:
http://www.investopedia.com/articl...ding-how-dividends-affect-option-prices.asp
Understanding How Dividends Affect Option Prices "

The payment of dividends for a stock has an important impact on how options for that stock are priced. Stocks generally fall by the amount of the dividend payment on the ex-dividend date. This 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 in order to make informed trading decisions.

Drop of Stock on Ex-Dividend Date

There are two important dates investors need to know for the payment of dividends. The first is the record date. This date is set by the company when a dividend is declared. An investor must own the stock by that date to be eligible for the dividend. However, this is not the full story.

If an investor buys the stock on the record date, the investor does not receive the dividend. This is because it takes three days for a stock transaction to settle. This is known as T+3. It takes time for the exchange to do the paperwork to settle the transaction. Rather, the investor must own the stock before the ex-dividend date. The ex-dividend date is essentially the cut-off date for the payment of the dividend. Any shares that trade on the ex-dividend date are not eligible for the payment.

The ex-dividend date is therefore the crucial date. If a company is making a decent-sized dividend payment, investors are willing to pay a premium for the stock in the days leading up to the ex-dividend date to receive the dividend. On the ex-dividend date, the exchanges automatically reduce the price of the stock by the amount of the dividend. For example, assume the stock for ABC, Inc. is trading at $50 the day prior to the ex-dividend date and is paying a $1 dividend. The exchange automatically adjusts the price of the stock to $49 since the dividend is not included in the price. This is known as the stock going ex-dividend. Some stock quote systems and newspapers list an “x” next to the stock quote to signify it is going ex-dividend.

Some exchanges also move any limit orders for the stock. Using the same example, if an investor had a limit order to buy stock in ABC, Inc. at $46, the exchange automatically moves the limit order down to $45.
Impact of Dividend of Options

Both call and put options are impacted by the ex-dividend rate. Put options are more expensive since the exchange automatically drops the stock price by the amount of the dividend. Call options are cheaper due to the anticipated drop in the price of the stock.

Put options gain value as the price of 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 deliver the underlying stock at the strike price if the option is exercised. The seller collects the premium for taking this risk.

On the flip side, call options lose value in the days leading up to the ex-dividend date. A call option on a stock is a contract where 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.
American Vs. European Options

Investors also need to understand the difference between European options and American options to understand the impact on option prices. European options can only be exercised on the date of expiration. This is different than American options. American options can be exercised at any point up until the date of expiration. This difference can have an impact on how options are priced. Most stock options in the U.S. are American options.

The holder of a call option in the money on a dividend-paying stock may decide to exercise the option early to receive the dividend amount. If the option is exercised early, the seller of the call option must deliver the stock to the holder. In general, it only makes sense for the holder of the call option to exercise if the stock is going to receive a dividend prior to the expiration of the option.

Black-Scholes Formula

Most options are priced according to the Black-Scholes formula, which is the seminal method for pricing options. However, the Black-Scholes formula only reflects the value of European style options that cannot be exercised early and do not pay a dividend. Thus, the formula has limitations when being 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 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 come up with ways around this limitation. One common method is to subtract the discounted value of a future dividend from the price of the stock.

The implied volatility in the formula is the volatility of the underlying instrument. Some state the implied volatility of an option is a more useful measure of an option’s relative value than the price. Options are often used in delta neutral trading strategies. These strategies offset the risk of an option position with a long or short position in the underlying stock. More complex strategies can be used to profit from drops in the implied volatility.

Investors 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 goes down. Thus, the implied volatility on put options is higher leading up to the ex-dividend date due to the price drop.
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botpro · Feb 26, 2016

stoic said:
I would like to hear from option traders that utilize option pricing models on just how important they feel dividends are in the calculation. From my own research, using option price models with the dividend and without on the same security produce differences of only a few pennies. The dividend seems to have a relatively minor impact on the option price.
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Studying the following dividend case will prove you wrong, as having the dividends in the model is very important:
http://www.elitetrader.com/et/index...es-of-estx50-atm-options-so-different.298090/
It was a very educational case also for me, I learnt much about the BIG impact of dividends on the Call and Put prices.

As spindr0 correctly stated, and I cite him here, "dividends are priced into the options. It makes no sense to use a model that doesn't price the dividends",
so it doesn't make to think otherwise; the markets work like they work, you have to follow the rules of the market.

Using BlackScholesMerton with dividends is the mathematical correct way,
and there are countless research papers on this, all verifyable by anyone with enough math skills.

OddTrader · Feb 26, 2016

https://books.google.com.au/books?i...ved=0ahUKEwiru6_B25bLAhWMj44KHbt2AEkQ6AEIFDAA

botpro · Feb 26, 2016

stoic said:
they read, but do they comprehend?
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It could be up to the writer... ;-)

It is unclear what you want to demonstrate (or ask?) with your 2 calculation cases.
Yes, both are used. So, then what is your question?

botpro · Feb 26, 2016

I don't get it! I've unknowingly replied to a 6 year old thread... ;-)
Never mind... ;-)

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Option Pricing Models

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