Options for the Beginner and Beyond

Options for the Beginner and Beyond is an introduction to options and the corresponding trading strategies.

I found Options for the Beginner and Beyond an informative read. The first part – basic concepts – was an easy read as I already had some basic knowledge about options, but I could imagine that it's a tough read for an absolute beginner... I especially liked the second part about the trading strategies. They are well explained in a straight-forward way with many examples. Only the risk graphs took some time to understand because I was not familiar with them. The last part about special topics mainly covers theoretical things. I found this part too short.

My notes

Basic Concepts

Introduction

Why should someone who invests or speculates in the market learn to use options? The simple answer is that options can greatly enhance your profit from stocks and/or provide the means to protect your portfolio.

You need to understand the risks as well as the advantages of options in order to optimize your results.

One reason options are cheap is that they are time limited. A long or short position involving stock can be held indefinitely, but an option expires on a fixed date. The expiration date is typically the third Friday of the expiration month designated in the option contract.

The longer you want to hold an option, the more expensive it will be.

Another important aspect of being time limited is that the value of an option will decrease with time when there is no change in the stock price. [...] This is one of the risks of owning an option, namely that its value diminishes over time when the stock price remains unchanged.

As the stock price changes, the option price also changes, but by a lesser amount. How closely the change in the option price matches the change in the stock price depends on the reference price designated in the option contract. This reference price is called the strike price.

If the strike price of either a call or a put is close to the price of the stock, the option is said to be at-the-money. If the strike price of a call (put) is above (below) the stock price, the option is said to be out-of-the-money. If the strike price of a call (put) is below (above) the stock price, the option is said to be in-the-money.

When you buy an option, your maximum risk is limited to your original cost of that option.

Options associated with individual stocks trade in a manner called "American style", which permits the owner of the option to exercise the rights of the contract at any time before the option expires.

The buyer (owner) of a call option has the right to purchase 100 shares of stock at the strike price designated in the contract. This right to purchase can be exercised anytime before the contract expires. [...] The seller (writer) of a call option has the obligation to supply 100 shares of stock for purchase at the strike price, if so requested by the owner of the option. This obligation to supply the stock may be required at any time before the contract expires.

[...] this particular combination of owning a stock and selling a call is referred to as a covered call position.

The buyer (owner) of a put option has the right to sell 100 shares of stock at the strike price designated in the contract. This right to sell can be exercised anytime before the contract expires. [...] The seller (writer) of a put option has the obligation to buy 100 shares of stock at the strike price, if so requested by the owner of the option. This obligation to purchase the stock may be required at any time before the contract expires.

Time is money. This phrase should always be in the back of your mind as you deal with options. Remember that the value of an option decreases in time when everything else remains unchanged. When you own an option, time is your enemy. When you have sold an option, time is your friend.

Option Selection

Every option has a price that represents its intrinsic value plus a hyped value. In the language of option traders, the hyped value of the option is called its time value.

Whenever you consider buying an option, it is a good idea to identify just how much of its price is intrinsic value and how much is time value. It is easy to compute its intrinsic value by asking this question: What would this option be worth if it expired immediately today? When that intrinsic value is deducted from the full option price, the remainder is the time value.

When you buy an option, you are almost always going to be paying for some time value – it is the nature of the beast. Just remember that for your option to make a profit, the stock price must move enough to overcome the loss of some if not all of that time value.

[...] the option with the lowest price is not always the best bargain.

When you buy a call option on a stock, you are taking the view that the stock is going to rise in price. You buy a call option instead of buying the stock to give yourself more leverage for a greater profit.

As you review various choices of call options, think about how much the stock must rise and the time frame during which that rise must occur to produce a profit. Also, if the stock does not make the expected move up, check to see when you can exit the trade to minimize your loss.

General approach: When you consider buying a particular call option, first determine what portion of its total price is time value. Keep in mind that this time value will ultimately be lost as the option expiration date arrives. Then ask yourself, "Can the stock price rise high enough and fast enough to increase the value of this option by an amount that will offset the loss of its time value and provide an acceptable profit?" If you can answer yes to that question, you have a good reason to buy the option.

When you buy a put option on a stock, you are taking the view that the stock is going to fall in price. You buy a put option instead of shorting the stock to give yourself more leverage for a greater profit.

Entering and Exiting Option Trades

Often, the success of an options trade is strongly influenced by how carefully the entry and exit prices are negotiated. The gain or loss of $.10 per share in a stock trade is usually insignificant, whereas in an option trade it can make a huge difference.

Each option exchange will list a bid price (called the bid) and an ask price (called the ask) for every option that is available on a stock or index listed with that exchange. The bid is the highest per-share price that some trader (or market maker) is willing to pay to buy the option. The ask is the lowest per-share price that some trader (or market maker) is willing to accept for the purchase of an option.

The ask is always greater than the bid, and the difference between these is called the bid/ask spread, or more simply the spread. [...] Whenever the spread is wide enough, there is the possibility of negotiating a more favorable price somewhere between the bid and the ask.

There are two main ways to initiate an "opening transaction" for an option. Similar to buying stock, the purchase of an option can be accomplished by means of either (1) a market order or (2) a limit order.

As it is with entering a trade, you can exit an option trade in a closing transaction by means of either (1) a market order or (2) a limit order. There are two additional ways to exit an option trade that are worthy of discussion, namely (3) a stop loss order and (4) a stop limit order.

With [the stop loss] order, you indicate a trigger price at which you want the order to be initiated. The order to sell is then activated when either (1) the option trades at the trigger price or lower, or (2) the ask is at the trigger price or lower. When the order is activated, it becomes a market order to sell the option.

As with a stop loss order, you indicate a trigger price at which you want the [stop limit] order to be initiated. But here you also indicate a limit price at which you want to sell your long option.

Getting filled on a stop limit order can prove tricky. You must carefully select your trigger price and your limit price to give yourself the best opportunity for a fill. If you set the limit price too close to the trigger price, you may not get a fill in circumstances in which you definitely want to be filled.

The Greeks

The "Greeks" [...] are one-word expressions used to describe how the price of an option changes when something else changes.

Delta: The amount that the price of an option changes as compared to a $1 increase in the stock price. This quantity is typically expressed as either a decimal or a percentage.

[...] an at-the-money call [...] typically has a delta of about .50.

[...] an in-the-money call [...] will have a delta greater than .50 but less than 1.0. The deeper-in-the-money, the closer the delta will be to 1.0.

[...] an out-of-the-money call [...] will have a delta less than .50. The further out-of-the-money, the smaller will be the delta.

Near-expiration, all in-the-money options will have a delta close to one, and all out-of-the-money will have a delta close to zero.

When considering an option to buy, make a mental estimate of the delta for that option. You do not necessarily need a precise value. Decide on a realistic increase in the price of the stock you are following. To estimate the new option price, first multiply the change in the stock price by the (approximate) delta of the option to see how much the value of the option would increase. Add that increase to the purchase price of the option, while allowing for some loss of time value in the option. If this estimate of the new price of the option represents an acceptable profit, you have a good reason to buy the option.

The delta of an option is not fixed. When the price of the stock moves significantly, the delta of an option will change.

The distinction between the delta for a call and the delta for a put is that the delta of a long put is always negative. This is because an increase in the stock price results in a decrease in the price of a put.

Theta: The amount that the price of an option changes as compared to the passage of a unit of time (typically one day).

The value of theta is always a negative number, because the value of an option diminishes over time. In the terminology of options, the loss of time value is referred to as theta decay.

Gamma: The amount that the delta changes as compared to a $1 increase in the price of the stock.

The gamma becomes important in situations where the delta of an option becomes especially sensitive to changes in the price of the stock. Such situations are said to have gamma risk. One such scenario in which gamma becomes important occurs as an option approaches its expiration date.

The "vega" of an option provides a measure of its volatility.

Vega: The amount that the price of an option changes compared to a unit increase in the volatility of the stock.

Rho: The amount that the price of an option changes as compared to a unit increase in the risk-free interest rate (that is, the rate for a U.S. treasury bill).

Risk Graphs

To follow the price movement of a specific option, the two factors of primary importance are the price of the underlying stock and the time remaining until expiration. The risk graph provides the visual means to comprehend how the profit or loss in an options trade is affected by changes in stock price as well as changes in time.

LEAPS

Some stocks and indexes have options with expiration dates that occur two to three years into the future. These options are called LEAPS, which is an acronym for Long-term Equity AnticiPation Securities. Most LEAPS expire in January of their designated expiration year.

One of the more popular uses of LEAPS is as a substitute for a buy-and-hold stock. In fact, LEAPS are sometimes referred to as the poor man's stock. This is because they can be purchased for a fraction of the cost of stock and then held for a long period of time.

[...] a LEAPS call performs much differently than stock. If the stock performs well, the LEAPS call will provide a greatly enhanced return. On the other hand, if the stock price gains little or experiences a small drop during the first quarter or first half of the LEAPS lifetime, the call option will perform poorly. The option may even suffer a loss while the stock makes a small gain, and it can suffer a substantial loss even if the stock has only a small drop in price.

For the same cost as owning 100 shares of a single stock, it is possible to participate in the price movement of 100 shares of several stocks by buying LEAPS calls, thereby spreading risk across a diversified portfolio.

Unlike owning the stock, the owner of a LEAPS call does not receive any dividend distributed by the company. You must take this into account when comparing the performance of the option with the stock.

Assignment Anxiety

If the short option is out-of-the-money, you will (essentially) never receive an assignment.

If the option is in-the-money, there is not going to be an early assignment as long as there is sufficient time value included in the price of the option.

When the expiration date of a short option is close and the time value of an in-the-money option has almost disappeared, the possibility of an early assignment becomes much more likely.

[...] the early assignment of the put option happens more often than the early assignment of the call option. Someone who wants to get rid of his stock via an assignment is usually in a rush to get the cash from the sale and move on to a new investment. Someone who is considering buying the stock via an assignment is more likely to postpone the purchase as long as possible so as to avoid committing the cash until absolutely necessary.

The possibility of an early assignment can sometimes depend on a dividend payment. You may be more susceptible to the early assignment of a short call from someone who wants to collect an upcoming dividend. You may be less susceptible to an early assignment of a short put from someone who wants to wait for the dividend payment before selling his stock.

Whenever your short option becomes deep-in-the-money, there will be very little time value in the bid price of the option, even if the expiration date is far into the future. This situation makes early assignment a definite possibility.

Broker Selection

If you are going to trade options on a regular basis, you should be concerned about commissions. Because commissions on options trades are always higher than on similar stock trades, it is worthwhile to pick a broker who offers a reasonable rate.

The most important feature is that you have real-time stock and option quotes. In today's market, things move way too fast for you to be making decisions based on delayed quotes.

Miscellaneous Tips

If you own an option, time is your enemy. You must keep in mind that the time value of your option will diminish, particularly during the last two to three weeks before expiration. If your option is out-of-the-money, you are especially vulnerable to a total loss of investment in the trade. Never hold an out-of-the-money option until the very end with only the faint hope that unforeseen circumstances will cause the stock to move favorably for you.

When you are considering an option to buy, make sure that you allow enough time to be proven right in your judgment about the stock. It may be tempting to select that cheap front-month option on a stock that you expect to soon move up, but three to four weeks can pass very quickly.

Before initiating an option trade, check the current trend of your stock as well as the overall trend in the market. Because option trades are time limited, make sure that the trend is working with you.

After you have decided on an amount that you feel comfortable using for high-risk trading, commit only about 15 percent of that amount to any single options trade.

It is important to keep abreast of any upcoming events that concern the stock associated with your option trade. Any event that might have a significant influence on the stock price has the potential to produce a huge change in the price of a related option.

Trading Strategies

Vertical Spreads

In the simplest spread trade, you buy one option and sell another in order to reduce the cost of the trade.

A vertical spread can be one of two basic types: a debit vertical spread or a credit vertical spread. Furthermore, each of these basic types can be structured as either a bullish or bearish trade. A debit spread is typically used when you expect the stock movement to occur over an intermediate to long-term period of time, whereas a credit spread is typically used when you want to take advantage of a short-term situation.

The bull call spread and the bear put spread are debit spreads. For these trades to pay off, the stock needs to have enough time to move to the targeted level. For this reason, you want to use options with expiration months that allow enough time for this move to occur. To achieve the maximum profit, the stock price needs to have reached (or exceeded) the strike price of the short option at expiration. The maximum possible profit is always the difference between the strike prices of the long and short options less the original cost of the spread.

Typically, you need to wait until near expiration to get the best payoff from a debit spread. This allows the short option to lose all of its time value.

In the case of credit trades, the return is calculated from comparing the profit achieved to the maximum risk [...].

The bull put spread and the bear call spread are credit spreads. These trades bring money into your account, which ultimately becomes a profit if the stock price reaches (or exceeds) the targeted level at expiration. These trades are typically short-term trades that seek to capture the credit as soon as reasonably possible.

As in the case of debit spreads, the maximum profit is achieved if the stock price reaches (or exceeds) the strike price of the short option at expiration. The maximum profit is the amount of the original credit.

Credit spreads enjoy an advantage over debit spreads in that, when their target is reached, no action is required at expiration. Both options expire worthless.

Event-Producing Credit Spreads

[...] the three major elements that typically characterize a good vertical credit spread:

1. A credit spread works best when extra premium has been pumped into the price of the option being sold.
2. A good credit spread is structured so that the underlying stock price needs little or no movement to achieve maximum profit.
3. Conditions are such that 1 and 2 can be realized using front-month options.

A good goal on these credit spreads is to receive a credit that nearly equals or possibly even exceeds the max risk. This kind of opportunity often presents itself following a special event that produces a dramatic price move accompanied by high volume.

As with most credit spreads, time is your friend, which suggests the use of near-term options.

Finding opportunities for these credit spreads does not require hearing about the special event as it is happening. In fact, you should wait a day or two (perhaps even longer) for the price burst associated with the public awareness of the event to exhaust itself. On the other hand, you cannot wait too long, because the extra premium pumped into the option prices will soon dissipate.

It is important to research the background of the special event that caused the dramatic move in the stock price. Make sure it is the type of event that is unlikely to have further repercussions in the near future. The event can be either a good-news or a bad-news situation, as long as it is all of the story.

Calendar Spreads

In a basic calendar spread, you buy a distant month option and sell a closer month option. Both options have the same strike price, which is typically selected to be the one nearest the price of the stock at the time the trade is initiated. When things progress well in a calendar spread, the short option ultimately expires worthless while the stock price remains essentially unchanged. This leaves the long option with a reduced cost basis, which can be either sold for profit or used for further trading.

[...] a primary feature of the calendar spread is the ability to continue establishing a new calendar spread each month. In the ideal scenario [...] the front-month option is allowed to expire worthless, thereby leaving the long-term option with a reduced cost basis. Then the next-month option with the same strike can be sold to establish the new calendar spread.

The process of converting the old calendar spread into a new calendar spread does not necessarily require waiting until the expiration date arrives. Frequently, the conversion is best accomplished by buying back the front-month option before expiration while simultaneously selling the next-month option. This maneuver is called the rollout.

The rollout maneuver is a necessity when the short option is in-the-money as expiration nears. In this situation, the short option must be bought back to avoid an assignment.

The objective of a calendar spread trade is to capture the time value in a front-month option, which will decay faster than the time value in a more distant month option.

A calendar spread is only profitable if the stock price at the options expiration date is within a fairly narrow range.

Often the decision as to whether to use calls or puts for a calendar spread depends upon a more likely direction of drift in the stock price. Generally speaking, a call spread is used when the expected drift is toward a higher stock price, whereas a put spread is used when a downward drift in the stock price is considered more likely.

A reasonable criterion is to exit a calendar spread when the loss reaches 50 percent of the amount paid to establish the trade.

Anytime you can realize at least 50 percent of the maximum possible profit in a calendar spread, consider closing the trade for a profit.

Advanced Calendar Spreads

Implied volatility (IV) is one of the most important pieces of options data used in finding a good calendar spread. The primary use of IV is to determine whether an option is comparatively overpriced or underpriced.

In the case of calendar spreads, the IV data is used to make a comparison between the long and short legs of the spread. To increase our chance for success with a calendar spread, we want the short leg of the spread to be overpriced as compared with the long leg. This volatility skew is observed when the IV of the short option is larger than the IV of the long option.

A useful modification of the classic calendar spread trade is the ratio calendar spread trade. The ratio concept simply means that fewer contracts are sold than are bought. The purpose of having more long contracts than short ones is to remove the constraint on one end of the profitability range, thereby allowing for unlimited profit if the stock price makes a large move in the appropriate direction.

Another version of the calendar spread is the diagonal spread, which uses a different strike price in the front-month option than in the back month. The basic idea is to select the long option to have a strike price that is out-of-the-money compared to the strike price of the short option. This reduces the cost of the calendar and in some cases even creates an initial credit.

Covered Calls

In its simplest form, the covered call trade requires that you own 100 shares of stock and then sell 1 out-of-the-money call contract. In this trade, the short call is described as covered because it is secured by your long stock. If the option is exercised, you possess the stock required for sale at the strike price.

The month-by-month management of covered call trades can be tricky. Some months are going to require a tough decision as the expiration date arrives.

Because almost all your risk is in what you paid for the stock, keep your eyes on the stock price and to a much lesser extent on the option price. Decide on an appropriate stop loss price for the stock, and if it falls to that level, protect the major portion of your investment by selling the stock and buying back the call.

When deciding on the strike price of the call that you are going to sell, make sure it is a price you will comfortable about giving up your stock if that becomes necessary. If your primary goal is to keep your stock, select a higher strike price. If you are willing to sell your stock at a price closer to its current value, pick a nearby strike price to bring in more cash.

Do not go too far out in time. Those juicy premiums in the longer-term options are tempting, but you will generally do better by selling either the front-month call or the next month out. In today's volatile market, the price of a stock can move significantly (up or down) in four to eight weeks. By selling near-month options, you will be better placed to make an adjustment when the expiration date arrives.

If the stock price is above the strike price at expiration, avoid buying back the option for a loss unless you have a good reason to do so. [...] Avoid the situation in which you buy back the option for a loss to keep your stock, and then have the stock price collapse.

Straddles and Strangles

The straddle trade and the strangle trade are intended to take advantage of stock movement in either direction. They use a combination of a call option and a put option to benefit from a significant move up or down in the stock price.

The basic idea of a straddle trade is to buy a call and buy a put with the same strike price. These options should also have the same expiration month, usually about two to three months in the future. The reason given for doing this type of trade is that if the stock price goes up, the call will show a profit; and if the stock price goes down, the put will show a profit. The catch here is that when one option shows a profit, the other option will show a loss.

For the straddle to become profitable, the stock price must move far enough so that the profit in one option more than offsets the loss in the other. If the stock price manages only a modest move in either direction before the options expire, the trade will lose money.

Most important, any event that you are expecting to move the stock price must be significant enough to cause a large increase in the price of the appropriate option. Also, the event must occur relatively soon after initiating the straddle to avoid the loss of too much time value. With a straddle, the ongoing loss of time value is doubly harmful because it is occurring in both options of the trade.

The stock price should be within the range of $20 to $50. If the stock is cheaper than $20, it may not have enough room for the price to fall. If the stock price is above $50, the options may be too expensive to create a straddle with a good potential for profit.

Do not stay in the straddle too long after the event has taken place. If the event does cause a significant move in the stock price, it will temporarily pump extra time value into the price of the profitable option. Sell the profitable option before that extra time value shrinks.

A strangle trade is similar to a straddle trade, except that the call and put options have different strike prices. The idea is to lower the cost of the trade by using out-of-the-money options. Essentially, this is a more aggressive version of the straddle trade.

Stock Repair and Stock Enhancement

For this strategy to work, it is necessary for your fallen stock to make at least a partial recovery. The stock repair strategy uses options to expand that partial recovery into a full recovery of your original investment, with little or no additional expense. If the stock price remains unchanged or continues to fall, this strategy offers no help.

The basic plan is to buy one at-the-money call for each 100 shares of stock that you own. You are going to pay for this one long call by selling two out-of-the-money calls with the same expiration date. The idea is to use the cash received from the two short calls to pay for the one long call.

To do the stock repair strategy for little or no cost, it typically requires options with at least two months until expiration. The more time allowed, the more likely a credit will be generated.

Married Puts

The basic idea of the married put strategy is to buy an appropriate put option at the same time you purchase stock. Typically, a put is selected that will provide several weeks of protection against a downside move in the stock price, while you comfortably wait for the expected uptrend to begin.

Collars

The collar trade is intended for use with stocks that are worthy of being held for at least 10 to 12 months. To do a collar trade, the stock needs to have LEAPS options associated with it.

It is often possible to arrange the collar trade so that it is completely without risk. Usually, this will mean giving up some of the potential profit.

Advanced Collars

The key to understanding the collar trade is the realization that long-term calls have more time value than comparable long-term puts. And the more distant the expiration date, the larger is this difference.

The maximum potential loss on a collar trade is reduced by moving the strike prices of the call and put options closer together. Unfortunately, this adjustment also reduces the maximum potential profit. The strike price of the short call must always exceed that of the long put for a profit to be possible.

Naked Option Writing

When you sell either a call or a put without any compensating position to "cover" the short option, you are said to be "naked". By having a short naked call or naked put position in your brokerage account, you are exposed to substantial risk. So, it is important to be prepared to manage this type of trade if the underlying stock begins to move against you.

Stock Substitutes

When held as a unit, the combination of a long call and a short put, with the same at-the-money strike price, has a delta of 1.0. Because long stock has a delta of 1.0, this combination of options is known as synthetic stock.

There are some drawbacks to synthetic stock. If the real stock pays dividends, this surrogate does not get a penny. And if the stock price were to fall so far that the naked put becomes deep-in-the-money, there is the possibility of an early assignment.

A synthetic position that is equivalent to a short stock position is created by buying a put and selling a call with the same strike price.

Backspreads

The backspread trade is used to take advantage of large moves (up or down) in the price of a stock or index. A backspread trade consists of more long options than short options with the strike prices selected so that the cost of the spread is small and even sometimes can be initiated for a credit.

The main drawback to a backspread trade is that it returns a significant profit only for large moves in the underlying stock or index. In fact, the spread incurs its maximum loss when the stock or index has achieved only a modest move in price at the option's expiration date.

The basic concept of the backspread trade is to finance a long option by combining it with a credit spread. The standard version of the trade uses a ratio of two long options versus one short option [...].

Butterfly Spreads

The butterfly spread trade is typically a cheap trade with low risk and lots of leverage. The drawback of the butterfly trade is that it focuses on a narrow range of profitability.

Options traders often refer to the price that maximizes the return from the butterfly spread as the sweet spot.

The positive features are that (1) it is typically an inexpensive trade, and (2) its maximum return provides plenty of leverage. The negative features are that (1) the price range for a profit is rather narrow, and (2) to achieve the maximum return, the timing is critical because the stock price needs to be exactly at the sweet spot on the expiration date.

Iron Condors and Double Diagonals

[The iron condor trade and the double diagonal trade] are designed for a stock or index whose price is expected to remain within a reasonably narrow range during a one-to-two-month time period. Both of these trades are credit trades.

The basic setup of the iron condor is to sell one out-of-the-money call and one out-of-the-money put with strike prices that are about equally placed from the middle of the price range of the stock. To hedge these short positions, buy one call and one put that are even further out-of-the-money. All of these options have the same expiration date. Because the purchase prices of the long options are less than the sale prices of the short options, the iron condor creates a net credit.

The goal of the iron condor is to have both short options expire worthless and hence retain all of the initial credit received when the trade was initiated. By using options that will expire in one to two months, the expectation is that the price of the stock will not have time to drift outside of its normal trading range.

The basic setup of the double diagonal is to sell one out-of-the-money call and one out-of-the-money put with strike prices that are about equally placed from the middle of the price range of the stock. These two short options have the same expiration date, usually one to two months until expiration. To hedge these short positions, buy one call and one put that are even further out-of-the-money, and with at least one additional month until expiration.

The main advantage of the iron condor is its simplicity at expiration if the stock price is between the strike prices of the short options. All options expire worthless and the trade is automatically closed without the need for any action. No commissions are incurred.

An End-of-Year Tax Strategy

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Special Topics

Day Trading an Index with Options

A large number of indexes have options. For day trading purposes, you want an index with highly liquid options, and you want an index with a range of daily price movement that is sufficient to create opportunities for profit.

The most conservative way to day trade [...] is simply to buy a call or a put, depending on which way you anticipate the index price to move. The recommended option is the front-month, slightly out-of-the-money call or put. [...] The magnitude of the delta of this option typically is about 0.40 to 0.50. Keep in mind that as the index price moves in the desired direction, the magnitude of the delta of the option will increase, thereby improving your potential for profit.

Delta-Neutral Trading

The definition of a delta-neutral portfolio is that the net delta of all the components of the portfolio is zero. Why is this significant? The significance of a delta-neutral portfolio is that a small change in the price of the underlying stock will have essentially no effect on the net value of the portfolio.

Theory of Maximum Pain

Briefly, max pain refers to the situation in which the price of a stock seems to lock in on an option strike price as expiration nears. During the last few days, the stock price will vacillate around the strike price as if tethered by an elastic cord. The targeted strike price is typically the one that has the largest amount of open interest in the about-to-expire options.

There has yet to be found a reliable theory that can consistently predict when the max pain effect will be observed and what price will be targeted.

Implied Volatility and the Black-Scholes Formula

To calculate the current price of a call option, the Black-Scholes formula requires the input of five pieces of information, namely (1) the current price of the stock, (2) the strike price of the option, (3) the amount of time remaining until the option expires, (4) the current interest rate, and (5) the value of the volatility parameter for the stock [...]. Each of the required pieces of information is readily available, except for the value of the volatility parameter. [...] One possible choice for the value of the volatility parameter is the "historical volatility" associated with the stock.

Rather than trying to guess what value to use for the volatility parameter, the modern approach is to insert the actual option price from the marketplace into the Black-Scholes formula, and then let the formula tell us what the volatility should be. The value of the volatility parameter determined in this manner is called the implied volatility, or IV for short.

Checking the IV of an option is also a good way to avoid a trap, which is known in options trading as the volatility crush. Buying an option with an extremely high IV can be a costly mistake. High IV is often associated with some intense excitement about the underlying stock, such as the rumor of a buyout, FDA drug approval, settlement of a court case, and so on. As soon as the excitement is over, the IV falls back to some more normal level, and the value of the option is "crushed".

The Put-Call Parity Relationship

[...] the price of the call is always greater than that of the put. The difference would be small in the front-month options, but becomes significantly larger as you go out to more distant expiration dates. The most pronounced difference in price is seen in the LEAPS options. This price difference between puts and calls is known in option pricing theory as put-call parity, even though it might seem more appropriately titled as put-call disparity.