#### Option Basics

Episode I.

Is there a Trekkie out there who can help me out? I understand the Black-Scholes option pricing formula, but I just can’t comprehend Star Wars.

People with tents sleeping in line waiting to buy tickets to a movie. Not just any movie, but a movie that’s playing everywhere. Multiple theaters, gobs of seats, and plenty of screenings.

I have a few thoughts as to why anyone would go through all the trouble to be among Star War’s first viewers.

Crowd Mentality! The media hypes the movie, and a feeding frenzy begins.

Bad Math Skills! Until there’s a scarcity of theaters, there’s no scarcity of seats. Each theater has hundreds of seats, one per person. Don’t forget they empty the theater and show the movie again. Over and over, infinitum.

Bragging Rights! Every time a day one viewer watches the video, he will remember he’s able to tell his grand kids he saw the movie on May 19^{th} not May 20^{th}.

Bad Business Skills! Who is smarter? The guy in a tent for a week, or his buddy who pays him $20 to buy an $8 movie ticket?

Too Much Free Time! Hello, don’t people have anything better to do than wait days to buy a ticket to a movie?

Am I missing something? I just don’t get it. While you’re at it, explain to me how Episode One can come 20 years after the first movie.

I haven’t seen the movie yet, was it worth the hype? Was the expectation greater than the event?

What does this have to do with option pricing?

I get e-mails from many mathematically challenged, crowd following option traders who don’t know the value of time and can’t brag about good trades. Besides, even I have to jump on a bandwagon every once in a while.

Don’t forget the suspense. Our last column ended in a cliff hanger. Will the sequel be worth the hype? Does understanding **Implied Volatility** and **Vega** help traders to win more often and lose less frequently?

Enough excitement, back to option pricing.

In mathematical equations you solve for the unknown. Two plus two equals what number? That’s too easy. Let’s use multiplication instead of addition. Two times two equals? Still too simple, how about option pricing? Without going into tremendous detail of option pricing formulas, here’s the gist.

The price of the stock compared with the strike price has a value. The amount of time to expiration is easily calculated. As are interest rates and dividends. You take all these components plus the expected volatility, plug them into the pricing formula, and solve for the unknown; the option’s price. Actually the option’s theoretical price.

While mathematical formulas determine theoretical value of options, market forces determine the price at which options trade. The market consists of buyers and sellers. Supply and demand.

More buyers equals higher prices. You can’t pitch a tent to be one of the lucky, you need to write a check. On the flip side of the coin, excessive sellers and/or insufficient buyers drive prices lower.

Market Makers estimate with formulas. Charging according to whatever the traffic will bear. If the market won’t support higher prices, it drops.

The Dark Side of the Force.

Back to our make believe world, where nothing changes unless we allow it. Without any movement to the stock price, interest rate, dividend, and time to expiration; the price of an option can still vary.

The funny thing about all our previous make believe examples, this one might not be so made up. In reality, an option’s price may fluctuate without any other circumstantial difference. This situation can happen.

A rumor may spread about a take over possibility. The interest rates and dividends could certainly remain the same before and after the rumor. The stock price might not move. In no time at all the price of the options could sky rocket. The hype could end just as sudden and the stock price not falter, but the option price melts. Could it be, the expectation was greater than the event?

What about earnings reports? After the announcement, there is no guess work, no unknown, no expectation. Option prices tend to drop, the sizzle is gone and all that is left is steak, or gristle. Don’t fuel the fire by over paying for options.

Comparing **Implied Volatility** to **Expected Volatility** tells if an option is fairly valued. If the Implied Volatility is less than Expected Volatility the option is said to be undervalued. If Implied Volatility is greater than Expected Volatility the option is overvalued.

Vega measures option price changes based on volatility. Although Vega is considered one of the “Greeks,” it’s not actually Greek. It’s Spanish. Or as most would say, A foreign language.

“May the **Implied Volatility** be with you.”

The Big IF

The biggest battles of the Cold War were often fought during the Olympics. No matter what flag you saluted, it was US verses that “Evil Empire.” I don’t know about you, but I always felt the other country’s athletes used performance enhancing drugs. Not to mention their judge’s scores reflected definite political bias. Biased scoring could award a gold medal to a silver or bronze performance.

You’ve seen the kids who score and rank everything and anything. Holding up a card that is either a 6 or a 9, depending on which end is up. “Solid nines, but a six from the Russian Judge.” Simultaneously in Russia kids are jokingly scoring, “A six from the American Judge.” It’s all perspective.

Option pricing has its own “Russian Judge,” volatility. If you don’t understand volatility’s role in option pricing, your gold medal trades might not make it to the platform.

Option prices are based on a number of components; time, interest rates, dividends, price (stock & strike) and potential. Potential, also known as volatility, is the most subjective. Hence the ability to be the kink in our attempt for the gold.

Time is constant with all options. Three days from now or three weeks from now is the same, no matter if you are trading Amazon.Com or AOL.

Interest rates may change up or down, but it’s the same rate for every stock.

Dividends will vary stock by stock. General Electric’s dividend has nothing to do with General Motors. So dividends are figured on a stock by stock basis. The dividends will be the same no matter what strike price, no matter if it’s Puts or Calls, no matter if you’re buying or selling.

Options are priced as a snapshot in time. The math between price and strike prices at a given point in time is easily figured.

The simplicity of option pricing ends here. (As if you thought it was simple so far.)

**Volatility** is the **MOST IMPORTANT** component in option pricing. Simultaneously, it may be the **MOST DIFFICULT** to understand.

Mathematically speaking, volatility is the annualized standard deviation of daily returns. Translated, it measures the stock’s price fluctuation. The more the stock moves the higher the volatility.

Volatility scores potential movement of the underlying stock. The “Greek” symbol Vega measures volatility. Proving the point volatility is complex, Vega isn’t actually a Greek letter.

With me so far? It gets worse. Concerning option pricing, there are four types of volatility; Historical, Future, Expected, and Implied.

**Historical Volatility**

Simply stated, how much the price of a stock has moved in the past.

Without going deep into math, let me explain the concept. If you have two $ 50 stocks, the price is currently the same, but historical volatility may differ.

If one stock’s 52 week high/low is $ 40/60, while the other’s is $ 45/55, it is easy to see which stock trading range is greater. The more a stock’s price moves, the higher historical volatility.

If you have two $ 50 stocks with equal 52 week high/lows, their historical volatility may still be different. If one had a daily trading range of $ 5, its historical volatility would be higher than a stock with a daily trading range of $ 2. (Daily trading range equals the difference between the high and low during a one day period.)

Easily verified, historical volatility measures the actual prior price movement.

**Future Volatility**

An almost useless concept. Future volatility is historical volatility before it happens. Price movement before it moves. After it moves, it’s not in the future, it’s not in the present, it’s in the past. Confirmed after it happens. Future volatility is accurately measured in the future looking backwards, after it became fact. Of the four, it is the least important Volatility.

**Expected Volatility**

Expected volatility deals with the future. Generally based on prior price movements, it assumes the stock will move in a certain pattern. Not the what it’s moved, not the what it will move, but the what it should move.

Fairly valued options are calculated according to expected volatility. However, not all options are fairly valued. Some options are undervalued and many more are overvalued. As with anything, buy low sell high.

Certainly more important than future volatility, arguably more important than historic volatility, but definitely less important than implied volatility.

Volatility prices options, but as you will see option pricing determines volatility.

**Implied Volatility**

The Big IF, the “Russian Judge,” the other side of the coin, the pick pocket of option pricing. Call it what you want. Implied volatility costs option traders more money than anything else.

Understanding Implied volatility and Vega allows traders to win more often, but more important to potentially lose less often.

Next we will discuss implied volatility and its ramifications in greater detail.

**Time Passes**

Beginning traders go broke taking big losses. Novice traders fall victim to attrition through multiple small losses. Advance traders falter taking small profits. Where are you on the evolutionary chain of traders?

The ability to pick market direction reigns as the most important factor for success for all option traders. Understanding option pricing helps traders magnify gains, and avoid losses.

Many new option traders dig themselves such a deep hole they can’t climb out. At least, can’t climb out fast enough. Stock prices go up, they go down, they may end up where they started, but time always passes. Sometimes, there just isn’t enough time.

Have you heard the joke, “Convicts are the number one buyers of options, nothing makes time fly like owning an option.” If you break a Law of option pricing, you don’t go to the jail house, you go to the poor house!

What does all this mean?

An option’s rate of erosion shouldn’t surprise or scare anyone. Option buyers can calculate time’s expense before buying. This is done with the Greek called **Theta**. Option sellers can predetermine maximum returns. Traders can know the cost of carrying option positions, both long and short. Hedged position traders can profit from the continual and constant passage of time.

**Time’s Effect on Option Pricing:**

Time value and time decay ranks as one of the easiest components of option pricing to understand. The time value of an option includes everything but the intrinsic value. Time costs money! More time, more money. Less time, less money. It’s that simple.

But options can’t be simple, they have to have some complexity. Time passes rhythmically with the tick of a clock, but time value erodes at a different tempo. Time value decays at its square root.

The square of a number is the product of a number multiplied by itself. 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, etc. The square root is the other side of the equation. It’s the equal divisor. The square root of 1 is 1, the square root of 4 is 2, the square root of 9 is 3, etc.

The Laws of option pricing dictate time value is highest for the At the Money (ATM) option. Not sometime or most of the time but always. Time value drops as the strike prices move In and/or Out of the Money (ITM, OTM). Strike prices Deep In and/or Out of the Money (DITM, DOTM) have the lowest time value. Not sometime or most of the time but always.

To better understand time value and its rate of decay, one should think in price units and time units. Price units include dollars and cents; In the case of options, dollars and fractions of dollars. Time units can be days, weeks or months. You can even use hours, minutes or seconds. We won’t discuss an option’s blink of an eye decay rate, but we could mathematically figure it out.

A Hypothetical Example of At the Money (ATM) Call options, (All other option pricing components being constant):

One Time Period = The Square Root of One Price Unit

Two Time Periods = The Square Root of Two Price Units

Three Time Periods = The Square Root of Three Price Units

Four Time Periods = The Square Root of Four Price Units

Insert the time period of your choice, months, weeks, days. Insert the price unit of your choice dollars or fractions of dollars. For our example, lets make it months and dollars.

1 Month = $ 1.00 (Square Root of 1 = 1)

2 Months = $ 1.41 (Square Root of 2 = 1.41)

3 Months = $ 1.73 (Square Root of 3 = 1.73)

4 Months = $ 2.00 (Square Root of 4 = 2)

We could extrapolate, the nine month option would cost only $ 3.00 (Square Root of 9 = 3), the 16 month option’s price would be $ 4.00 (Square Root of 16 = 4).

We could replace months with weeks and dollars with fractions, such as 1/2. Therefore if the one week option were priced at $ .50, the four week option should be $ 1.00, the 16 week option would be $ 2.00.

If we assume four weeks per month, the consistency of the pricing of time becomes evident. We can see the one month option and the four week option are both priced at $ 1.00. $ 2.00 buys the four month option and/or the16 week option. Continuing the math, the 16 month/64 week (LEAP) option would be priced at $ 4.00.

Both equations provide an equal answer:

16 Time Periods = The Square Root of 16 Price Units.

16 Months = The Square Root of 16 Dollars.

16 Months = 4 Dollars.

64 Time Periods = The Square Root of 64 Price Units.

64 Weeks = The Square Root of 64 ½ Dollars.

64 weeks = 8 x .50. = 4 Dollars.

Stock prices go up, they go down, they may end up where they started, but time always passes. The passage of time can be a profitable journey.

Any Car Racing Fans Out There? Stock Car Race Fans? Drag Race Fans?

I like to think of Stock trading like Stock Car Racing. (Convenient?) Your car races the track at a constant 100 mph. (Delta of 1.00) As long as you don’t spin out and hit the wall, (drop in price) or take too many pit stops (stagnant price movement), you will win your race and claim the prize of profits in your account.

I like to compare option trading to Drag Racing. You buy at a point, desiring your option to slingshot in speed to a much higher price. The quicker the better.

With Stock Racing you have time on your side, a 500 mile course gives you opportunities to get back on top. Time is also on the side of stock traders. Stock prices can rise sooner or later. Sooner being better. Timing is much more important to the option trader. In Drag Racing, if you jump the gun they don’t restart the race, you’re red flagged, you lose. With option trading you need to be not only right, but right on time.

With Drag Racing and option trading you want to be lined up from the start because there is less room for mistakes.

To win a Stock Car Race you need sustained speed over a long distance. Winning a Drag Race isn’t based on speed, but acceleration. The fastest car doesn’t win, the quickest does.

Option trading, like Drag Racing is based on acceleration.

Back to Option Pricing (very necessary to understand for option strategy) :

**Delta** measures the change of an option relative to the change of the underlying. Delta is quoted like a snapshot in time, however, it is dynamic. Delta changes, it responds to the passage of time and to the movement of the underlying asset. The change of Delta is measured by **Gamma**.

Beginner option traders have probably never heard of Gamma. Novice traders might be aware of the term, but don’t understand Gamma’s significance. Professional option traders and Market Makers understand and trade Gamma. To a hedge trader, those with large multiple positions, Gamma is the most important component of option pricing.

Knowledge of certain concepts is necessary before attempting to understand Gamma.

Everyone should know what In the Money (ITM), At the Money (ATM), and Out of the Money (OTM) means regarding strike prices. These terms indicate if an option has any intrinsic value. Does the option have equity, in addition to potential. On expiration day, the time is gone, the potential has passed, the only options with value are the In the Money (ITM) options.

Traders buy options hoping the intrinsic value increases, or the extrinsic value decreases. Extrinsic is the opposite of intrinsic. Intrinsic measures the amount in the money, extrinsic measures the amount out of the money.

Example:

Let’s say a stock is at $ 20.00, the $ 17.50 call is In the Money (ITM) $ 2.50. It has $ 2.50 of equity, or intrinsic value. The $20.00 call has no equity, no intrinsic or extrinsic value, it is At the Money (ATM). The $ 22.50 call has no equity, no intrinsic value, but the extrinsic value is $ 2.50, it is Out of the Money (OTM). As a general rule, extrinsic value is not used. Most traders consider Out of the Money (OTM) options as having zero intrinsic value. This is true, but you should be aware of the existence of extrinsic values.

If in our example, the stock were to rise to $ 22.50 the $ 17.50 call’s intrinsic value would increase $ 2.50 to $ 5.00. It is now Deep in the Money (DITM). The $ 20.00 call would now have intrinsic value. It changed from At the Money (ATM) to In the Money (ITM). The $ 22.50 call lost its extrinsic value, it went from Out of the Money (OTM) to being At the Money (ATM).

Delta varies according to the Laws of option pricing. The more In the Money, the higher the Delta. As an option’s intrinsic value increases, so does its Delta.. Options with extrinsic values have low Deltas, but as they move from Out of the Money (OTM) towards being In the Money (ITM), their Deltas increase. The higher the Delta the more dollar for dollar the option moves relative to the underlying.

**Gamma** measures the rate of change of Delta. Suppose in our previous example, the $ 20.00 call (ATM) had a Delta of .50 (fifty) if the stock rose $ 2.50, the Delta might rise to .65 (sixty-five) as the option went ITM, the total Gamma would be .15. Gamma usually shows up in pricing models measuring the change of Delta for a $1.00 move in the underlying. Simplistically said, the Gamma in our example on the $ 20.00 ATM call was .06. Delta increased .06 (six) for each $1.00 move of the stock. 2.5 times .06 equals .15. In reality, the Gamma might have started at a slightly different figure and changed with the stock price. Don’t worry, there isn’t a “Greek” to measure the rate of change of the rate of change of the rate of change etc.

**Delta** is speed. **Gamma** is acceleration.

I buy options because of Gamma. I’m a Drag Race fan.

I hope people are getting some useful information from these “Basic” posts. Don’t worry we will be getting more specific about option strategies especially using weekly options.

Introducing: **Delta**

Options are complex! Their value being determined by a long mathematical equation, with many sub-equations and variables. I can’t write the formulas out for you. Not because they’re secret, but because my keypad doesn’t contain the crazy looking symbols used in the formulas.

Each aspect of option pricing is a separate component of the formula. To remove confusion, each component has a Greek title; Delta, Gamma, Theta, Vega, and Rho. Do you wonder? Should that last sentence read, “To ADD confusion?” Everyone knows Vega is not Greek. It’s a Chevrolet.

The first and most important of the “Greeks” is **Delta**. It is probably one of the most common known of the “Greeks,” but it can be looked at three ways. Two of which are widely accepted. The third is far less important and really only theoretical. Most quasi-knowledgeable traders only know one or two.

The first and most important way to look at Delta: Delta measures the rate of change in an option’s price compared to a one point ($1) movement in the underlying security.

Since the rate of change in the price of a stock is measured dollar for dollar, their movement is 100%. Stocks have a Delta of 1.00. Don’t worry; stock prices do not have any other “Greeks,” only Delta.

Option prices, which don’t move the same dollar for dollar as stock prices, have lower Deltas. Think of it as a percentage of the movement of the stock price. If a stock goes up $1 and an option on that stock went up 1/2, it had a Delta of .50.

Many times Deltas are not mentioned with decimals but as whole numbers. Since options trade 100 shares of stock per contract, the decimals are dropped. Example: .50 x 100 = 50.

Deltas can never be over 1.00 (one hundred). If you ever see an option move greater than the underlying, it was caused by another of the “Greeks.” In our examples, we will assume everything else remains constant. In reality, the other “Greek” forces are at work, but for explanation sake, they will remain silent.

The at the money (ATM) Call will typically have a delta of .50. In the money (ITM) will have a higher delta. The Delta is still higher on deep in the money (DITM). The opposite is true for out of the money (OTM) and deep out of the money (DOTM) options, their Deltas are lower.

An understanding of Delta helps option traders choose strike prices. To be profitable with small price movements, you will need to buy ATM or maybe even ITM options. The difference between the Bid/Ask spread may be too great to overcome with OTM options.

The parameters of our hypothetical example: $30 stock, $25 Call price $6 Delta .75, $30 Call price $2 Delta .50, $35 Call price $1 Delta .25. If the stock price increases $1 to $31, the $25 Call would increase .75 to $6.75. The $30 Call would rise to $2.50, the $35 Call would increase to $1.25.

Let’s say the Bid/Ask spread on the $35 Call was .75/1.00 when the stock was $30. After the $1 price rise in the stock the Bid/Ask spread might have become 1.00/1.25. If you buy @ $1 and can only sell @ $1, you lose the cost of commissions.

**Delta** is dynamic. When the stock price moves, the Delta changes. Delta will increase as the stock price increases. Delta will decrease if the stock price falls. This change is known as Gamma. Think of Delta as speed and Gamma as acceleration. We will go into Gamma later in much greater detail.

Delta also changes as time passes. As option expiration gets closer the Delta for the ITM option increases towards 1.00, and the Delta for the OTM option decreases towards .00, while the ATM option’s Delta will almost hold at .50, right until expiration.

OTM options are usually a bad deal. There’s generally not enough time for the price to rise and the Delta is too low, the exception is with Leaps. The Deltas on Leaps will be closer to .50. ITM Leaps will have lower Deltas than short term options. OTM Leaps will have higher Deltas than short term options. Most people are unaware of this phenomenon. It can be used to great advantage in calendar spreads.

Every option trader should know Delta! Its okay not to know Rho, but knowledge of Delta is essential. You will need to understand Delta before trying to grasp Gamma (my favorite).

In order to understand option strategies, especially using weekly options it is necessary to understand Delta – hopefully you do now. As always if you have any comments please leave them below.

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