The Vocabulary of Options

Because options deal with (1) the underlying security, (2) a strike price, (3) a premium, and (4) a limited time, and because they are often traded in groups (combinations) that are described with special names, the vocabulary of options becomes important. So we start there.


Understanding the Terminology: 12 Key Terms

The following discussion is very basic and certainly not thorough. More complete discussions of option writing are available in many publications, including the pamphlet distributed by the Chicago Board of Options Exchange to everyone who opens an options account with a member firm. Brokers also have access to discussions in their company's procedure manuals. But the following brief summary is all one needs to understand options. It is presented in accordance with my personal views of what the important concepts of option writing are, and how they should be conceptualized. Reading definitions is no fun, but a basic understanding of the vocabulary is essential to further understanding of the concepts.

I classify options into four categories: STOCK CALLS, STOCK PUTS, INDEX CALLS, and INDEX PUTS. Some texts on options that I've seen properly define PUTS and CALLS and then assume that a Put and a Call on an index fits the same definition and a stock Put or a stock Call. Because I think that the risks and strategies involved in Puts and Calls on stocks are very different than those on indices, I recommend thinking about these four kinds of options as if they were four different pieces of paper, like stock certificates, each representing a different kind of investment.

When talking about an option, the option should be designated by the underlying security, its termination month, its strike price, and its type. For example - one Ford Jan 35 CALL is an option to buy 100 shares of Ford Motor Co. At $35 per share until the end of the third trading Friday next January (Figure I.) With that basic information in mind, here is a brief definition of the dozen basic option terms for repeated reference:








Strike Price
















Figure 1: This figure shows an option listing from the Wall Street Journal. The listing is one line of the options on the XYZ Motor Company. The day preceding this listing, XYZ stock closed at $32 per share. The strike price illustrated is $35 per share. Call options with a strike price of $35 for October last traded at 0.125. This means that an XYZ October 35 call would cost 100 times 0.125 or $12.50 plus commission. The November XYZ 35 Call option last traded at 0.25 and the January at 0.625. Note that the November Put is not priced'it is restricted.


One stock Call is a right to buy 100 shares of stock at a particular price until a specified time. We saw the Call in action with our friend the wine producer. He bought a Call to be sure he could acquire his grapes at a maximum of $1,000 per acre.

If I own one Ford January 35 Call, I have the right to buy 100 shares of Ford Motor stock at $35 per share through the close of the business day of the third Friday of the following January. Alternatively I can sell the Call itself. If I own such a Call, someone sold it to me. That person has committed to sell 100 shares of Ford stock to me if I exercise my option. If I exercise my option, the stock is said to be 'called away' from the seller.

The seller of the call is obligating himself to sell the stock at the strike price. This seller might already own Ford stock and have sold a Call against it, or the seller, if called, may have to go into the open market and buy the stock to 'cover' the position. If the stock has moved up significantly above the strike price, this 'uncovered' seller will lose the spread between $35 and the price he has to pay to acquire the stock and deliver it to the holder of the call.

There is no certificate issued to represent the option. It is merely an entry on your broker's books. Only the 'confirm' you receive from your broker, and your broker's credit, guarantee you the option rights.

2. PUT

One stock Put is a right to sell 100 shares of stock at a particular price until a specified time. In our wine story, this would exist if the grower paid the producer $100 per acre for the right to sell the producer the grapes produced for $1,100 per acre. The grower would thus have protected himself from a price decline below $1,000 per acre, and the producer would have collected $100 per acre in exchange for the contingent promise to purchase at a price he can afford to pay.

Similarly, if I own one Ford January 35 PUT, I have a right to sell 100 shares of Ford Motor stock at $35 per share at any time through the expiration date. The person that sold the PUT to me has become obligated to buy the stock. As with the CALL, I can also sell the PUT itself at any time during its life (Figure 1.) I may already own the 100 shares, and have bought the PUT to protect its value. Alternatively, if I do not own the stock and if the stock price goes down during the option period, it will pay me to purchase the stock and then 'put it' (sell the stock by implementing the PUT) to the buyer at the higher ($35) price. The result of the transaction will be that I sold high, then bought low, which never hurts! On the other hand, if I SOLD the put at 35, I guaranteed to buy it at that price. Thus, if the stock goes down during the option period and does not recover, if exercised (and you can bet it will be) I will have to buy the stock at 35 even if the market price is below that figure.


The S&P 100 index is described below. For the moment it is sufficient to understand that an index CALL gives the buyer the right to collect a varying sum of money until a specific time, as the index rises above a specific number. For example, if I buy one index CALL at $300, and the index goes up to $310 before the CALL expires, I instruct my broker to exercise the CALL and my broker will put $1,000, less transaction costs, into my account. This is because one call is equal to 100 shares, the price of each share went up $10, and therefore '10 times 100 shares equals $1000. Alternatively, if the index goes to $290, nothing happens: I bought the CALL, and paid my premium to the seller who took the risk. Since the index did not go up, I just lose the premium that I paid for owning the option. Because it is an index, I do not in fact buy or sell the actual stocks that make up the index. I am only dealing in money.

The index call seller is betting the other way. If the index goes up during the period of the option, this seller is liable for the increase. But if the index declines, he just keeps the premium he acquired in the sale.


An index PUT gives the buyer the right to collect a varying sum of money, until a specified time, as the index falls below a specific number. Thus, if I buy an index 300 PUT, and the index goes up, I lose my premium. If the index goes down, I make $100 for each point it goes down upon exercise or expiration. I can exercise my option at any time until it expires. If I wish, I can 'close out' the position before it expires. If I own the position I can sell it at the market price, and if I have sold the position I can 'buy it back' at market price at any time, unless market liquidity is affected by special events, as happened during the crash of 1987. Then you might not be able to buy or sell for some period of time.

The person on the other side of the trade, the seller of the index put, is in a reverse position (but with more risk, as we'll see below). This seller is liable for $100 for each point that the index declines. If the index goes up, this seller just keeps the premium he collected from the sale.


Figure 2: This figure illustrates at-the-money, in-the-money, and out-of-the-money calls and puts on a $20 stock.



We have talked about the 'strike price' in the previous examples. The 'strike price' is either the dollar value of the stock, or the number of the index, specified in the option. Thus, in the examples above, when we talked about a Ford 35 CALL, the strike price is $50. When we talked about an index option at 300, the strike price is $300.


The 'termination date' is the date on which, at the close of business, the option rights expire unless exercised. Most options expire at the end of the third Friday of the designated month. Note that you can exercise an option (or be put or called, if you are the seller) at any time during the life of the option - not only at the end of the period. Also note that you must initiate some action through your broker, or else the option may expire worthless even if it still has value!


An option is 'at-the-money' when the actual present dollar value or index number is the same as the strike price specified in the option. The option is 'in-the-money' when the stock or index price goes past the strike price in the direction of profit for the holder; and the option is 'out-of-the-money' when the current price is not yet at the strike price, in the direction of the loss for the holder. These terms are illustrated in Figure 2.


A 'combination' is a strategy where more than one set of related option rights is held at the same time. A 'spread' is a particular type of combination. In addition to spreads, one common combination for option traders is to buy or sell an out-of-the-money CALL and an out-of-the-money PUT on the same security at the same time. This combination is described in greater detail in Part IV below.


'Time value premium' is the market value of the option excluding 'intrinsic value' as illustrated in Figure 3. Time value premium is what the conservative option seller is trying to capture. Time value premium is really what the market thinks the underlying option rights for the future are worth. Thus, when an option is 'out-of-the-money' the market price is 100% time value premium. This is covered in more detail below.


Figure 3: This figure illustrates a Time Value Premium (T.V.P) for an out-of-the-money call with a strike price of $30. The Time Value Premium goes up as the price of the stock gets closer to the strike price ($30), but declines with time.


'Intrinsic value' is the amount of money, excluding 'time value premium,' which could be realized from the sale of an option at a specific point in time as illustrated in Figure 4. Another way to look at intrinsic value is that it is the value than can be realized today, before any additional value is added for the possible profits in the future.

For example, if Ford Motor stock is at 35, and the 34 call is selling at $3, the intrinsic value is $1 and the time value premium is $2. This is because the owner of the call has a right to buy the stock at $1 below market value, but the option value is $2 higher than this price differential. If there is no other change in the market price, on the last day of the option, when there is no more 'time value premium' because time has run out, the option will have a value of $1.


We speak of a holding as 'long' when we own the position. To own a position means that you have purchased it, whether voluntarily or involuntarily. Accordingly, if you buy a Call you are long that Call. If you sell a Call, you are short that position., If I say 'I am long the Ford 55's and short the Ford 50's,' that means that I bought the Ford Calls at a strike price of 55, and sold the Ford calls with a strike price of $50. I would then have to specify the termination date to fully describe my position. If I also own the Ford stock, I can be described as 'long Ford.' If I own 1,000 shares I might describe it as 'long 1,000 shares of Ford.'

When you sell calls, such as the Ford 50's, we say that you are 'short the Ford 50's.' When you sell an option it is sometimes referred to as 'writing' the option and the seller is referred to as an 'option writer.'



In 45 Days

In 90 Days

Intrinsic Value

20 (40 20)

30 (50 ' 20)

15 (35 ' 20)





Total Price




Figure 4: Intrinsic Value and Time Value Premium for an in-the-money call with a strike price of $20. The Time Value Premium shrinks with time while the intrinsic value changes with the stock price. If the option were not so far in-the-money, the Time Value Premium would fluctuate more as the stock price approached the option strike price.


These are three terms that are related, and are easier to learn if learned at the same time. Naked is easy if you know the other two terms: it means that the position is not covered or hedged. For example, if you just sell a call, and you don't have any protection against the unlimited potential loss of an increase in the underlying stock (just as owning the stock), you hold that call 'naked.' Hedged is a very broad term that includes the condition of being covered. Hedged just means 'protected.' Covering is one way to protect. If you sell a call, and you own 100 shares of the underlying stock, you are covered by the stock. That cover is a type of hedge. Another way to hedge your potential loss might be by buying a different call, creating a 'spread''something we will discuss below. Hedging is a very broad term, and includes some very imperfect hedging devices, such as holding stock in a different company but which is in the same industry group.


Option Glossary

by Harvey S. Frey


To browse, start with Option

American-Style Option
An American-Style option is one which can be exercised at any time before its Expiration Date. All of the options we will deal with are American style. The alternative is European style options which can only be exercised on the expiration date.
An asset, for our purposes, is something of value which is publicly traded on an exchange, such as shares of stock, exchange traded funds (ETFs), commodities, etc. These are usually traded as 'lots' of 100 shares., though prices are quoted for only one share.
I'll often just call it a 'stock', since there's minimal substantive difference.
Bid/Ask Spread
This has nothing to do with the spread which is a hedge.

Option tables typically show 3 prices for an option: The lowest price you'd have to pay for it, the "Ask" price; the highest amount you could sell it for, the "Bid" price; and the "Last" price at which a transaction was actually completed. Normally the Ask price is higher than the Last price, and the Bid price is the lowest. The difference between the Bid and the Ask is the Bid/Ask Spread, and is the loss you would experience if you bought and then immediately sold the option. (Of course, you'd also have to pay fees and commissions.)

However, you don't have to deal at those prices (unless you have a margin call). You could have your broker put out a bid to buy for less than the listed ask price, and wait for the market to drop to your price, and similarly, if you owned the stock, you could offer to sell it at higher than the listed bid. If the price doesn't come to your bid or asked price, there is no transaction.

The Bid/Ask Spread also means that as soon as we take a hedge position, we show a loss when we consider the Liquidation Value, even when there is a big Intrinsic Value because we lose the spread on every leg of the hedge. It may be 2 or 3 weeks before the decline in Time Value allows the Liquidation Value to approach the profitable Intrinsic Value.

Sometimes the bid, last, and ask prices are not in the proper order. This usually occurs when the options aren't actively traded, so that there may have been no option trades while the underlying asset may have moved, and the bid and asked moved with the asset price, while the Last trade reflects a previous asset price.

Bulls, Bears, and Hedgehogs
These are terms referring to the psychologic state of the investor, as shown by how he invests.

A Bull is someone who expects the market or an asset to go up, so he buys stock, buys calls, or sells puts.
A Bear is some one who expects the market or an asset to go down, so he shorts stock, buys puts, or sells calls.
A bull spread or other hedge is one which makes a profit if the asset goes up in price.
A bear spread or other hedge is one which makes a profit if the asset goes down in price.

I suggest the term Hedgehog for some one who admits he doesn't know which way the market or asset is going to go, so he hunkers down defensively and sells neutral hedges, which make a profit whether the asset goes up or down..

A Call is an option in which the buyer pays a premium to the seller, thereby gaining the right to require that the seller sell him the asset at the strike price on or before the expiration date.

Ignoring transaction costs:
The call buyer loses the full amount of the premium if the asset price is below the strike price at expiration. He cannot lose more than the premium.
He breaks even if he exercises the call at a stock price equal to the strike price plus the premium.
He makes a $100 profit for every $1 the stock price is above the break even point at exercise.

The call seller keeps the premium as profit if the call expires with the asset price below the strike price
Above the break even point, he loses $100 for every $1 the asset price goes up.
He can limit his loss by buying back the call before the expiration date.

If a person wants to sell a stock he owns, he can sell it at a higher price by selling an OTM (higher) call instead. He gets a premium for the sale, and he sells the stock only if it moves up to his strike price. If the stock doesn't go up to his strike price, he still gets to keep the premium. He may do this several times before he sells the stock, each premium increasing the effective sale price of the stock.

Another common use for a call is to sell OTM calls on a stock you own to increase your income. If the call is exercised you merely tender the stock you already own, so risk is very limited. This is called a "Covered Call".
If you do this, it is important to check for Ex-Div Dates.

Profit at Expiration for Calls

Buy a CallSell a Call

Say you have a stock you want to keep, say because of its dividend, but you are worried about losing money through price drops. You could protect yourself from price drops by buying a nearby OTM put, but that might be a significant regular outlay. You can offset that cost by selling a nearby OTM call on the other side, thus constructing what is called a "collar", at minimal cost. Of course, you limit your potential profit as well as your loss, but we already assumed that you were holding the stock for its dividend or some other purpose. (You would still profit from stock splits, as the options will be adjusted in that case.) If you buy a call and sell a put at the same strike price, you can create a Virtual Stock at a fraction of the cost of a real one.

Ex-Div Dates
Stocks that pay dividends usually do so quarterly on a schedule of their own choosing. They pick one day of every 3d month, and whoever owns the stock on that date gets the last 3 months worth of dividends, even if he bought the stock just the day before. That is called the "ex-div" date, and the stock price often falls by the amount of the dividend the next day.

This is important for someone writing covered calls, since if the call is executed just before the ex-div date, he will lose 3 months of dividend income. If he sells a call during a month with an ex-dive date he must make sure that he makes a profit even if the dividend is lost.

There are 2 ways to do this:
1. make sure that the premium received is greater than the potentially lost quarterly dividend payment, or
2. select a strike price high enough that if the stock is called, the profit on selling will exceed the lost dividend.

Short-sellers also may be surprised to find that they are responsible for paying the dividend to the party from whom they borrowed the stock to short. So it is not a good idea to short dividend -paying stocks.

On the expiration date an option expires worthless if it is OTM.
If it is ITM, the buyer will exercise (or 'execute') it at the exercise price or strike price, either 'calling' the asset from, or 'putting' the asset to the seller. The seller may actually deliver or buy the asset at the strike price, or he may simply pay the buyer his expected profit, called 'settling for cash'.

A buyer need not wait till the expiration date, but may exercise an option at any time before the expiration date when he feels he has made an adequate profit.

A third way of terminating an option is called 'Covering'. The seller of the option may buy it back in the market at the current market price, and thus transfer his responsibilites to the new seller.
Similarly, a buyer may take his profit by selling the option in the market, rather than by exercising it.

Expected Profit
The expected profit at expiration for a hedge is estimated by integrating the probability density of predicted stock prices at expiration using the observed 3 year probability distribution (see volatility by the sum of the intrinsic value for each option in the hedge for that stock price.

Expiration Date
All monthly options of interest expire on the Saturday following the 3d Friday of each month. The Friday is the last trading date. All options which are not worthless, must be executed or covered by that date.

Some stocks and ETFs also have weekly options, expiring on Friday. Yahoo intersperses them in its option tables, so it is important to check the symbols for the date.

A hedge is a combination of options designed to minimize risk. Risk can never be eliminated, but it can be limited to desired areas of the price/profit plane.

Common hedge types are spreads, straddles, and strangles.
Three types of hedges, which are used in the HedgeHog strategies, have been given idiosyncratic names by me, known only by Our broker.
They are, in increasing order of complexity, mesas, skillets, and homburgs.

There are 2 disadvantages to the skillet hedge.
One is that, outside of the range of the mesa, the loss can be many times the amount of money invested. Of course, we have stop loss orders in place, but in a market panic it may be impossible to get out at the stop loss point. Though the limited liability of the LLC company is designed to protect us from losses greater than our investment, the losses may still be painful.
The second disadvantage of the skillet is that maintenance margin requirement increases as the asset price approaches the limits of the profitable range, and this may result in margin calls which might force us to liquidate the skillet at a loss, even though if we were able to hold it, there would have been a significant profit.

The homburg is designed to ameliorate the first disadvantage, and eliminate the second. It does this by buying a strangle slightly wider than the short strangle of the skillet, which we call the "brim". Those 2 strangles together are equivalent to 2 OTM credit spreads, and are treated as such for margin purposes. At the low strikes, we have a bull put spread, and at the high strikes we have a bear call spread. These combine to give us a profit in the center.

Since the margin on a spread depends only on its width, and is independent of the price of the underlying asset, the margin requirement is constant, and we can never get a margin call.
And, we have also limited our maximum possible loss to that same amount, no matter how far the price of the asset moves in either direction. It is still a big loss, but not unbounded.
Another benefit of the homburg, is that the margin is generally lower than on a skillet, so we get a better return on margin.

Unfortunately, it is not always possible to find a suitable strangle for the brim, because the options may not exist that far out, so we have to be satisfied with the skillet, but we use the homburg wherever possible.

The name 'homburg' comes from the resemblance of the price/profit curve to the hat of the same name - with a central crease and a wide brim.

Intrinsic Value
This is the difference between the strike price of an option and the last price of the underlying asset. I.e, it is the value of the option if it were to expire immediately, stripped of all time value, bid/ask spread, and psychologic effects. If the value is negative, it is considered zero.

For a call, the IV is the larger of 0 or stock price - strike price.
For a put, the IV is the larger of 0 or strike price - stock price.

Eg: If a call has a strike of 50, and the asset is selling at 55, at expiration the buyer could call the stock at 50 and immediately sell it at 55, for an immediate profit of $5/share ($500/contract), so the IV is 5.
If the stock was at 45 and he did the same thing he'd have a $5 loss, so he wouldn't do it, so the IV would be 0.

For a put, with the stock at 45, the buyer would buy the stock at 45 and make the seller pay him 50 for it, so the situation is the mirror image of the call.

Generally no stock is actually bought or sold, the parties just settle in cash and avoid paying the transaction costs.

Liquidation Value
This is the amount that would be brought in or paid out by covering all the legs of a hedge at market price before expiration.
This usually involves a loss, since you are on the wrong side of the Bid/Ask Spread for every leg. Even if there is a profit, it is much less than the intrinsic value.
The long options that were bought at the high ask price, will now be sold at the low bid price, and vice versa.
Usually a little money can be saved by not buying back the shorts at the other side of the hedge from the current stock price.
Liquidation is usually involuntary, because of a margin call, or hitting a stop loss point.

This is a measure of how easy it is to buy and sell the options.
If an option has a very low daily trading volume or open interest, it may be difficult for the broker to fill the orders, which may be especially troublesome in a Liquidation situation.
So it is best to avoid illiquid options.

When you sell options you don't own, your broker wants to be sure you have the assets to buy it back if necessary.
Those assets don't need to be cash, but they need to be instantly convertible into cash, like stocks and bonds in your account. These are your collateral, but no interest is charged for using it as such.
You can also borrow money from the broker to buy stocks and options 'on margin', and pay interest, but that's not what we're talking about here.

The amount of margin for uncovered short options generally depends on the price of the underlying asset and the distance of the stock from the strike price. When you sell the options initially, the margin is calculated based on the stock price at that time. However, the maintenance margin requirement will increase if and when the stock price moves closer to the strike price. If it exceeds the amount of your collateral, you will get a Margin Call.

However, the margin requirement on a spread depends only on the difference in strike prices between the 2 legs of the spread, so it is independent of the price of the underlying stock. This means that you can never get a margin call on a spread.

Margin Call
When, because of a change in the price of the underlying asset, the maintenance margin requirement on a short position exceeds the amount of collateral provided by your marginable securities, the brokerage will make a Margin Call.

This is a demand that you immediately either deposit more money into your account, sell some collateral, or buy back the offending short position. If you don't do it promptly enough, the brokerage will sell some of your collateral, of their choosing. to get enough money to satisfy the margin call. This is not a good thing!

Even if the intrinsic value of your hedge would show a profit, the margin call usually comes when the liquidation value shows a considerable loss, so you will lose money even though the you're in profitable territory and would probably have made a profit if allowed to continue to hold the position. Bummer!

One of the major advantages of the homburg strategy over the skillet is that it cannot incur margin calls, so you can never be forced to liquidate it prematurely..

Mesa is the name I give to a wide, symmetric, short strangle. A Mesa is the foundation for all the hedges used in the HedgeHog strategy, the skillet and the homburg. It is the part that brings in the money, but it is rarely used in isolation.

It has 2 parts, a short put with a strike price well below the current stock price, and a short call, with a strike price an equal distance above the current stock price. This results in a flat profit line at expiration for all final prices between the 2 strike prices, dropping off to losses beyond. Thus the name, "Mesa".

The distance between the strikes should be chosen to minimize the chance that the stock price will go outside of that range during the life of the hedge. To estimate that chance, we look at the price changes over a similar period for that past 3 years. We can then pick a Mesa width which would have had less than any desired probability of ending in a losing position in the last 3 years.

However, the wider the mesa, the further OTM the put and call are, and therefore the less premium they bring in, so one must sell more of them to reach one's desired minimum profit. These counteracting criteria require a computer program to find the width which yield the optimum expected profit.

There are several problems with this approach. Stock prices are chaotic, and this month may be quite different from any month in the past 3 years in volatility, trends, etc. Unfortunately, there is no way of predicting the future accurately.

Another problem is that until the expiration date, because of the time premium and the bid ask spread, the liquidation profit curve is not the nice flat line. Rather it is a somewhat parabolic curve, well below the Mesa line. Especially toward the edges of the range, it may show a significant loss. This may trigger a margin call, forcing us to cover and take the loss.

Thus, the actual probability of loss is significantly greater than predicted by the 3 year data. This makes it important to make the width of the Mesa as wide as possible, and to add the improvements leading to the other types of hedges we use.

When the Intrinsic Value of an option is greater than zero, it is said to be "In The Money" (ITM). That would be when the asset price is greater than the strike price of a call, or less than the strike price of a put, and the option could therefore be exercised at a profit for the buyer.

When the asset is trading exactly at the strike price of an option, the option is said to be "At The Money" (ATM).

Otherwise, when the Intrinsic Value of an option is zero, it is said to be "Out of The Money" (OTM). That would be when the asset price is less than the strike price of a call, or greater than the strike price of a put. Therefore exercise would result in a loss for the buyer, so he would not do it. It would be cheaper for him to just let it expire.

An option is a contract between a buyer and a seller, arranged through their stock brokers.

The option buyer pays a premium to the seller, thereby buying the right to require the seller to buy or sell some asset at a defined strike price at any time before a defined expiration date.
Each option contract is for an even lot of the underlying asset consisting of 100 shares, but the prices are quoted for a single share. so if you buy one option at a premium of $3, your actual cost is $300 + fees and commissions.

There are 2 kinds of options, puts and calls. In a put, the buyer can require the seller to Buy the asset from him; in a call he can require the seller to Sell the asset to him.

It is not necessary for the seller to own the asset he has promised to deliver. It is only necessary that he has the funds or liquid assets so that he can buy it when demand is made, so he can deliver to the buyer as agreed.
Usually, he doesn't even do that - he just gives the buyer the profit the buyer would have made if he got the asset at the strike price and sold it at the market price at the time. This is called a 'cash settlement'.

The brokers act like escrow agents, holding the stakes to assure that the seller can perform upon the buyer's demand. For this they require that the sellers must put up a certain amount of collateral, called margin.

Options are combined into hedges to reduce risk.

Most options are traded on the Chicago Board Options Exchange (CBOE), and are identified by a unique Option Symbol.

This is the situation where the stock, or the entire market, has made a major move, and people fearful of losses if the move continues, all rush to liquidate their positions at once, creating a positive feedback, which causes the move to accelerate. This is like people getting trampled in the theater doorway when someone yells 'Fire'. In such a situation, the volume of orders may make it impossible to execute stop orders. They then get executed later at at worse prices, so that losses much larger than anticipated can occur. This is the main danger afflicting the HedgeHog strategies.

Because of the boom and bust nature of markets, such events must be expected to cause major losses every few years, and every strategy must attempt to minimize their worst effects.

The premium is the price paid for an option. For the buyer this is a debit to their cash account. For the seller it is a credit.

There are 5 terms that make up the premium:
1. Intrinsic Value: What the option would be worth if it expired with the asset at its current market price.
2. Time Premium: A bet that the option will be worth more at expiration than it is now.
3. Bid/Ask Spread: The difference between what you'd have to pay to buy or to sell the option.
4. Irrational Exuberance: Hopes and fears, ie: the difference between what theory says the premium should be, and what it actually is.
5. Time mismatch: Where trading is slow, it may happen that the last trade of the asset and of the option occurred at different times, so they don't match up. There can also be a time mismatch between the price of the last trade of the option and the last bid and ask prices.

Premiums for ATM 1-month options are typically between 1-10% of the asset price, depending on the volatility and price trend of the asset and the market.

Premiums are generally higher for options with more time to run, the ATM premium typically going up approximately as the square root of time remaining.

A Put is an option in which the buyer pays a premium to the seller, thereby gaining the right to require that the seller buy the asset from him at the strike price on or before the expiration date.

Ignoring transaction costs:
The put buyer loses the full amount of the premium if the asset price is above the strike price at expiration. He cannot lose more than the premium.
He breaks even if he exercises the call at a stock price equal to the strike price less the premium.
He makes a $100 profit for every $1 the stock price is below the break even point at exercise.

The put seller keeps the premium as profit if the call expires with the asset price above the strike price
Below the break even point, he loses $100 for every $1 the asset price goes down.
He can limit his loss by buying back the put before the expiration date.

If a person wants to buy a stock, he can buy it more cheaply by selling an OTM (lower) put instead. He gets a premium for the sale, and he buys the stock only if it drops to his strike price. If the stock doesn't drop to his strike price, he still gets to keep the premium. He may do this several times before he gets the stock, each premium decreasing the effective cost of the stock.

Profit at Expiration for Puts

Buy a PutSell a Put
Risk has many definitions, which we need to distinguish:
1. the probability of loss, with size of loss undefined. Let's call it "probability of any loss".
2. the maximum possible loss, with probability undefined. Let's call it "Max Loss".
3. Max Loss compared to investment. Let's call Max Loss / Investment "Max Loss Ratio".
4. the loss at a particular price of the underlying asset. Let's call it the "Point Loss".
5. the Expected Loss, given an expected distribution of prices of the underlying asset.
Let's define it as the sum over all asset prices of the product of the probability of the asset price times the Point Loss at that price.
This is the number we try to minimize when deciding which hedge position to implement from among the many possiblities.

The basic risk in the market is that an asset you own will drop in value, or one that you are short will rise in value.

Many people consider options to be "riskier" than stocks, which is odd since each type of option position decreases some portion of the risk associated with simply trading the underlying asset.
In addition, many people contain their risk by planning on taking some action at some pre-defined point, ie: a stop loss order. But, in a high volume panic situation, the stop loss may not be able to be executed, and the loss may be much greater than planned.
An appropriate option position is a fail-safe mechanism, invulnerable to panics, for limiting loss to a pre-defined amount. This is taken advantage of in the homburg strategy.

If you buy a stock, your Max Loss is the cost of the stock. The stock could fall to zero.
If instead, you buy a call on the stock, your Max Loss is the premium you paid, which is a small proportion (usually between 1% and 10%) of the cost of the stock, and you have the same possibility of upside profit, though only if the stock makes its move within the time span of the option.

If you short a stock, the stock could conceivably go arbitrarily high, so your Max Loss could similarly be arbitrarily high, but, of course, stocks never rise to infinity, so the commonly claimed 'infinite risk' is an absurdity. Still, there is significant risk.
If you sold a put instead, you'd have the same Max Loss if the stock rose, and the same profit if it dropped, plus the amount of the premium you took in, so the short put is superior.
The danger is in leverage. Since you're only paying, say 5% as much, for the option as for the stock, you might be tempted to sell 20 times as much for 20x the profit as with the stock. But now your Max Loss is also 20x as great. An up-move could then prove disastrous.
The risk is not in the option, but in the temptation to use excessive leverage.

Market Risk cannot be eliminated by hedges, it can only be moved around. The intent of the mesa, skillet and homburg hedges is to move the risk to places the stock price is very unlikely to go.

To 'short' an asset or option is to sell it when you don't own it, hoping to be able to buy it back later at a lower price. The rule is still 'buy low, sell high', but in the reverse order from what is normally done.
In theory, you borrow the asset from someone who owns it, and to whom you'll ultimately return it, or else give him the money he'll need to buy it at that time. In actuality, you just get it from the broker and whether he really borrows it, or just makes an entry in a ledger is immaterial. You will settle in cash at any rate.
Where the "borrowing" theory still makes a difference is if you are short a dividend paying stock on its ex-div date, you will have to pay the amount of the dividend to whoever you borrowed the stock from.

Even though money comes in when you short an asset, the broker will require that you have enough margin equity available to cover reasonably possible losses, typically 50%, and you may get margin calls if the stock goes too far up.
Typically when that happens, all the people with short positions rush to cover their shorts, driving the stock even higher. This is known as a "short squeeze", and the owners are said to be "caught short", as they all try to cover at once.

However, shorting an OTM put is a superior way to buy a stock you want to own.
Say you want to buy a stock which is selling at $10, but want to get a better deal. You might sell a naked (ie: uncovered) put with a strike price of $9 and bring in, say, a premium of 50 cents (ie: $50 for the contract). If the stock drops below $9, buyer forces you to buy it at $9, so your effective cost is $8.50, instead of the $10 you would have paid if you just bought the stock outright. And if the stock goes up, you don't have to put out additional money, but you get to keep the $50 commission. You have, however lost out on any profit from the rise in price of the stock.

Skillet is my name for a hedge consisting of a mesa plus 1 or 2 long ATM strangles. Originally I was using wide (i.e. strike prices far apart) strangles, so the profit curve looked like a skillet with a flat bottom with sides sloping up on either end, hence the name. Subsequently, I found that expected return was always better with narrower strangles, even a straddle, but I kept the name. The profit curve now looks like a capital "M".

The purpose of the central strangle is two-fold. First is to allow the investor to profit from up or down moves in the stock, instead of the flat profit curve of the mesa. Second is to decrease the loss toward the edges of the hedge, should the user be forced to liquidate by a margin call, or by reaching the stop loss point.

To get rid of the threat of margin calls, and unlimited loss, we can add an outer long strangle to a skillet to create a homburg hedge.

A spread is a hedge consisting of a long and a short option of the same type and expiration date, but with different strike prices.
Its profit profile shows a constant loss on one side, a constant profit on the other side, and a sloping section between the 2 strike prices.

There are 8 kinds of spreads:
They can be constructed of puts or calls
They can be Credit (ie; they bring in money) or Debit (ie: they cost money). They are Credit when you sell the one with the higher premium (ie, less OTM) &vv.
They can be Bull (ie: they profit on the upside) or Bear (ie: they profit on the downside.) They are Bull when you sell the one with the higher strike &vv.
(well actually 16 types, they can be ITM or OTM, but we never use ITM spreads.)
(well actually 32 types, they can be overlapping or not, but we never use overlapping spreads.)

Profit and loss are thus totally constrained outside of the region between the strikes. Thus the margin requirement is totally independent of the price of the underlying asset, but depends only on the width of the spread. This eliminates the possibility of margin calls.

A straddle is a strangle where both the put and the call have the same strike price.

A strangle is a hedge consisting of a low-strike put and a high-strike call. If they are both bought, it is a long strangle. If they are both sold, it is a short strangle. If the strikes are the same it is called a straddle.
A strangle ATM is thus a neutral hedge, being agnostic as to which way the stock will move over the life of the hedge.
A long strangle is a bet that the stock will move a lot, and a short strangle is a bet that the stock will not move a lot, "a lot" being defined as the width of the strangle between the strikes plus the sum of the premiums.

A long strangle will cost money to place, and make a profit if the stock price goes either up or down further than the sum of the premiums paid. A short strangle will bring in money which you can keep if the stock doesn't go further in either direction than the respective strike prices.

All the HedgeHog hedges are based on strangles centered on the current stock price. The mesa is simply a number of wide, short OTM strangles. The skillet is a mesa plus a smaller number of long strangles ATM. The homburg is a skillet plus a number of long strangles further OTM than the mesa.

Strike Price
The Strike price or Exercise price is the pre-determined price at which the buyer of an option can require the seller of the option to buy (if a put) or sell (if a call) the underlying asset to him. Obviously, the stock will only be put or called if it results in a profit for the option buyer, ie: if he can make the option seller sell the stock below market price (if a call), or buy above market price (if a put).

In all options we are discussing the option can be executed at any time up to its Expiration Date. This is called American Style.

Stop Loss
This is an order to sell (or buy) a stock at a loss to avoid a possibly worse loss. It is placed with the brokerage house and executed automatically. When the stock price hits the stop loss price it is converted to a market order, and executed as soon as possible. If there happens to ba a fast-moving panic market, it may be executed far from the ordered price, resulting in a much greater loss than expected.

Unfortunately one can't place a simple automatic stop loss order for a complicated hedge. One can only give the order to the broker, but he will need to personally monitor the market and cover the various legs of the hedge by orders to the traders at the appropriate time. It is thus important to have an attentive cooperative broker.

The new OCC option symbol, as used on Yahoo, consists of 4 parts
1. the symbol of the underlying stock or ETF
2. the expiration date, 6 digits in the format yymmdd
3. option type, either P or C, for put or call
4. strike price, as the price x 1000, front padded with 0s to 8 digits
example: IOC130518P00075000 is put on IOC, with a strike price of $75, expiring on May 18, 2013

The pristine beauty of this scheme has recently been marred by the optional addition of a character between the stock symbol and the expiration date for a small number of expensive stocks or ETFs, including SPY and AAPL.

These can be:
'7' to signify a "Mini" contract for only 10 options
'8' or '9' to signify "Corporate Action", not further defined, or
'J' to signify a "Jumbo" contract for 1000 options.

Time Premium
The major part of an option premium beyond the intrinsic value.
It is the bet that the stock price will change enough before expiration that the expiration price will be higher than it is now. For an OTM option, where the intrinsic value is zero, that is essentially the probability that the option will be ITM by the expiration date.

To a first approximation, stock prices are a "random walk", a well-defined statistical concept. In random walk theory, the probability that the price will move a given distance in a given time is proportional to the square root of the distance and the time., and actual option prices follow this rule fairly closely, though distorted by the other factors mentioned in the premium definition. Time premium thus falls most rapidly toward the end of an option's life, so to maximize annualized yield, we always sell the option closest to expiration. Distance is measured in units of average step size, which is related to volatility, so that time premium also varies as the square root of the volatility of the stock.

Virtual Stock
If you buy a call and sell a put at the strike price nearest to the current stock price, your profit graph will be almost precisely the same as if you had bought the stock. And vice versa for a short position. This is called a Virtual (or synthetic) long or short stock position.
The difference, aside from the limited duration, is that you have put up far less money than if you bought the stock - just the difference between the option prices.
The danger is in being swept away by the low price and using it to increase your leverage, instead of to decrease your risk.

If you leave an offset between the strike prices, you can create a Collar around an existing stock position to protect you from large moves in either direction.

This is a measure of how much the stock price varies day to day. It is usually measured by the standard deviation over the mean of daily price changes, sometimes after any trend has been removed.
That is not to imply that these changes follow a standard Normal Distribution curve. They do not. The distribution is typically 'kurtotic', ie: they are more likely to have very small and very large changes, and fewer middle-sized changes than a Normal curve would predict, ie: they are more sharply peaked and have fatter tails. They are chaotic, as characterized by rare big leaps.

Therefore, we make no attempt to fit them with theoretical curves, but use the actual observed distribution for a reasonable period of time, typically the most recent 3 year period.

Graphs of Profit vs. Stock Price for Options and Simple Combinations

Explanation of the Graphs
The above illustration shows 6 graphs in a circle, and one on either side. For each graph:
The x-axis represents the possible prices of a stock
The y-axis represents the profit at expiration for each possible closing stock price
The origin is at stock price=strike price, profit=0
The offset on the y-axis represents the Premium, either paid or received.
For the 2 graphs at the top and bottom, representing stock transactions, the origin of the x-axis is the price at which the stock was bought or shorted, and of course there is no premium.

The 6 graphs in the circle represent the profit profiles of the 6 possible basic strategies: to buy or to sell a stock, a put or a call.
The double arrows indicate that any of those strategies can be simulated by the sum of the 2 adjacent strategies on the circle.
EG: selling a put and buying a call will result in the same profit profile as buying the stock.
The graph at the upper right represents buying a call. It shows a fixed loss of the cost of the premium for all final stock prices less than the strike price, and a dollar for dollar increase above the strike price, breaking even when the stock price is greater than the strike price by the amouint of the premium.
A similar analysis applies to the other graphs. Note the symmetries.
Note that a covered call (buy stock, sell call) has the identical profit profile as selling a naked put.

The outer 2 graphs demonstrate how a put and a call at the same strike price can be combined to form a straddle.
Spreads aren't shown, as they don't fit neatly into the schema.

Note that these graphs ignore transaction costs.

DISCLAIMER: This is an educational site. The trades suggested on this site are examples to help the readers understand the principals of option trading. They are not intended as "tips" for actual trading and are suggested so that the reader can enter and follow hypothetical trades in the portfolio manager.

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