Options Primer

[Alchemist]

I am enclosing an options primer for your convenience.

OPTIONS PRIMER

We must clearly understand what an OPTION is. An American style option is the right to buy (a Call option) or sell (a Put option) an underlying asset at an agreed price (a strike price) at or before a given time (the expiry date). It is a right, and only that. It is not an obligation. You do not have to exercise that right; obviously if it is in your favour you would and if not in your favour you would not. European styled options can only be exercised at expiry. We will keep our discussion to American style options.

When buying options you pay a premium for the right to exercise that option at the agreed price and time. Option prices are related primarily to risk (volatility), time and interest rates. Should the contract not go in your favour you may let the option expire worthless: so your losses, even though they are total for that transaction, are fixed. You cannot lose more than you paid for the option and this you can determine before you enter into the contract. For this privilege and guarantee you pay handsomely, premiums are not cheap and indeed should not be. When writing or selling an option you are making a commitment, an obligation, similar to that of a futures contract. This commitment to make good on the option if it is exercised exposes you to large even unlimited loss.

When you write or sell an option you will receive the premium payed for that option but you will have to leave this premium on deposit with your broker until the option has expired as well as a margin with your broker. The Exchange has a minimum margin requirement and brokerages often demand more than this minimum requirement. This margin is not as in buying stocks with margin from your broker, it is not a loan. Margin is a down payment on the commitment you have made, it is a bond, a security, for if you maintain the contract you will have to deliver on the promise in full, either to take delivery of the underlying asset at the agreed price if you were a buyer, or to deliver the underlying asset at the agreed price if you were a seller of the contract at the agreed delivery time. Of course you do not have to keep that commitment until expiry, you can close your position by selling your commitment to someone who is prepared to buy it from you. In liquid markets this no more difficult than buying an option.

Once you are of the opinion, for whatever reason, that a certain investment asset is likely to make a significant market move and could be the profitable subject of an option strategy you are only at the beginning of the exercise. Once you have made this conceptual decision you are faced with an apparently bewildering array of choices to execute that concept; which strike price, which expiry month, should you buy Puts or Calls, should you write Puts or Calls, should you trade spreads or combinations and on and on it goes. The purpose of this resource is to bring rational order to this plethora of choice and make the decision or choice a simple, step wise, rational and reproducible exercise.

The appropriate choice is arrived at by evaluation of seven interrelated factors and these are:

l. Asset or share price
2. Option strike price
3. Option premium
4. Volatility
5. Dividends
6. Interest rates
7. Time to expiration.

The interrelationship of the first six items leads us to recognize that there may be an intrinsic value to an option. The seventh item suggests that an opportunity cost may not be out of line. Relating these items will indicate that there is a decaying time value associated with any option. It is fundamental when choosing an option to understand and be able to assign value to these derived entities - intrinsic value and time value.

Intrinsic value

Intrinsic value is the profit realized if you simultaneously close out a position in the option and the underlying financial asset.
Intrinsic value of a Call = asset price - strike price
Intrinsic value of a Put = strike price - asset price

One can readily see then that as asset prices increase the intrinsic value of a Call increases and conversely the intrinsic value of a Put increases with a decline in asset price.

It follows from this that when a call option strike price is equal to or more than the asset price then the option has zero or no intrinsic value, similarly a Put option has no intrinsic value if the asset price is equal to or more than the strike price.

The use of position diagrams illustrate the concept of intrinsic value. (Figs.1 and 2)

Some further definitions to be understood are:

Options that are IN-THE-MONEY are priced lower than the asset price for a Call and priced higher than the asset for a Put and have an intrinsic value greater than zero.
Options that are AT-THE-MONEY are when they are priced (their strike price) the same as the current asset price and have zero intrinsic value.
Options that are OUT-OF THE-MONEY have a strike price higher than the current asset price for a Call and lower than the current asset price for a Put and have no zero intrinsic value.
For example, if the OEX is trading at 410.00 on June 1, 93 then:
The OEX June 415 Call is Out-of the-Money and has no intrinsic value.
The OEX June 415 Put is In-the-Money and has an intrinsic value of 415.00 - 410.00 = 5
The OEX June 410 Call is At-the-Money and has an intrinsic value of 410.00 - 410.00 = 0
The OEX June 410 Put is At-the-Money and has an intrinsic value of 410.00 - 410.00 = 0
The OEX June 405 Call is In-the-Money and has an intrinsic value of 410.00 - 405.00 = 5
The OEX June 405 Put is Out-of the-Money and has an no intrinsic value.

Volatility

Volatility is just another name for fluctuation or variance. It is a relative term and as such there are several types of volatility depending on the context. There are four commonly defined volatilities

Historic Volatility

This is simply the percentage range of movement of the price of the asset over the past period of observation. For a stock the 52 week high and low is recorded in the daily newspaper stock quotes. E.g. If Motorola had a 52 week high of $55.00 and a 52 week low of $35.00 then the range for the year would be $20.00. The one year historic volatility is calculated thus:
2 x (high - low) = 2 x (55 - 35) = 2 x 20 = 0.44



(high + low) (55 + 35) 90
Historical volatility of Motorola can be stated to be 44%, i.e. over the course of a year one can expect Motorola stock to vary 44% from high to low.

Based on this one year historic volatility you can extrapolate the volatility for varying time periods by multiplying this calculated historic volatility by the square root of the ratio of the times involved.

e.g. If you want to compute the likely volatility of Motorola over a 2 year period based on its recent annual historic volatility of 44% then:
Historic 2 year volatility = historical volatility x ˆ1/2 = 44 x 1.414 = 62%
That is over a 2 year period based on recent annual volatility we can expect Motorola prices to vary 62%.

Most professional traders have a six month historic volatility factored into their Block-Scholes (or equivalent) valuation computer models. Six month volatility for Motorola would be:
Historic volatility x ˆ1/2 = 4480.7 = 31%
Historic volatility can also be calculated using weighted and unweighted averages.

Forecast Volatility

This is prediction or assumption of future volatility for a given period. These are often extrapolations of statistical variance. As with all extrapolations, it ain't necessarily so; or, probability does not preclude the possible.

Individual Volatility

This is simply a calculated volatility from the option pricing formula (Block-Scholes or other). The volatility calculation is computed using the current price of the option with all the other known inputs (except the volatility number), i.e. this computation informs us what the volatility should be to justify the current price of the option.

Implied Volatility

This is exactly the same process as calculating the individual volatility but instead of using the one option price, we use all the available options' prices of the underlying asset of the same expiry. Some traders do not include the far out-of-the money options or underweight their importance. This implied volatility calculation gives an idea of the most appropriate volatility applicable over the range of the options available.

These assessments of volatility are useful not only in the calculation of the price of options but also if you recognize that current asset price is at or near a 52 week extreme it gives you some idea of the possible counter move should the stock fail to breakout and go on to new highs or lows. This alerts one to possible candidates whose options may be particularly profitable to trade.

Dividends

The dividend or more correctly the anticipated dividend has to be factored into the valuation of an option. Stocks associated with high dividends tend to have lower Call values and higher Put values than you would otherwise expect. Option holders do not participate in dividend payments. Stocks trade lower immediately ex-dividend usually by an amount equal to the dividend. This ex-dividend depreciation of the stock makes its Call also worth less and its Put worth more. This ex-dividend asset-option valuation phenomenon will effect even low dividend paying stocks if it is close to the day of record for dividend payment purposes. Other dividend related effects on option valuation are:

High dividend paying stocks tend to be bought and held for yield and are, therefore, less volatile. Consequently with lower volatility their option valuation is lower.

An unexpected change in dividends (e.g. an increase or omission) will have a sudden and appropriate impact on asset and option price.

Interest Rates

In recent years interest rates have become increasingly volatile. The risk free interest rate is an integral part of option valuation in theory and practice. In the normal course of trading options (short term options) it is a minor input. However when trading LEAPS it is a very important factor. Changes in interest rate could cause increased profits (losses) over and above that anticipated at the outset of a trade. During the 2-3 year life of a LEAP interest rates could change several percentage points, e.g. a 1% increase in interest rates could increase a LEAP call price from $5.00 to $6.00, i.e. 20%.

Further, the interest rate changes will have an impact on volatility, particularly with interest rate sensitive stocks. A change of volatility from that used at the outset when pricing the option can have a dramatic impact on the price of the option, e.g. if at the issuance of a LEAP the historic volatility was 35% and after an interest rate change the implied volatility is 45% one could expect a LEAP call to increase from say $6.00 to $8.00, i.e. 33.3%. So if you intended trading LEAPS keep your finger on the pulse of
the Fed..

Time Value

It is readily apparent that at-the-money and out-of the-money options still cost money even though they have zero intrinsic value. This cost is the time value or time premium of the option. It is the premium demanded by an asset holder for the risk he undertakes in allowing you the time to buy or sell his asset from or to him; it is the cost you pay for the time opportunity you require for the anticipated successful outcome of your option strategy.
Time value then can be easily seen to reflect two risk factors for the writer (seller) of the option - one is interest rate (he could receive Treasury Bill rate interest at no risk) and the other is the price volatility of the optioned asset, a highly volatile asset price would substantially increase his risk and so that risk has to be paid for. It is this volatility risk that accounts for the variance of premiums between different assets in a similar asset class.

However, we can now easily calculate the total time premium of any given option. The cost of at-the-money and out-of-the money options have zero or no intrinsic value, it is all time premium.

Time premium = total option premium - intrinsic value
As the time premium is related to current short term interest rates and the historic volatility of an asset (which is assumed unchanged), it can be easily appreciated that as time runs out the time value decreases. For periods up to a couple of months before expiry the rate of decay of time premium is small, but in the final weeks the decay of premium accelerates exponentially and becomes zero at expiry. This decay of time premium is the same for Puts and Calls. Fig. 3 illustrates the exponential nature of the decay of time premium of an option (Put or Call) and illustrates the deadly effect of time on option trading. In the latter days the rate of decay is such that relatively large price moves in the underlying asset are needed, in the direction of the trade executed, just to maintain value let alone be profitable.

So it can be intuitively deduced that the most expensive options to buy are the deepest in-the -money with the longest time to expiry and the cheapest are the most out-of the-money with the shortest time to expiry. The reason for most options players ending up broke is because of greed and scrooge instincts which leads them to buy the least expensive options - that places them in a position of holding an option with no intrinsic worth with the most rapid decay of premium - a sure combination for failure.
Legions are the ex-option players who disgruntling complain of the market makers, "My expectations of the market were correct and I still lost money, it is a rigged game". Sure it is rigged, in the sense that risk has a price put on it, but the price of that risk is apparent to all who take the trouble to decipher it; one can hardly blame the market makers if you opt to be a dumb scrooge; you invite your own undoing. It doesn't take a rocket scientist to look at Fig.3 and recognize that one should initiate one's option trade as far out in time as to keep you on the relatively flat part of the time decay curve, so that the anticipated asset value change in price has time to profitably occur. If you expect an asset value to change over the ensuing months it is stupid to buy options expiring in the next few weeks.

The correlation between asset price and option price

Generally speaking options with an intrinsic value move in lock step with changes in value of the underlying asset, i.e. an in-the-money Call or Put will move one unit up or down for each unit up or down in the movement in the price of the underlying asset respectively. Out-of the-money options will not show any such correlation for they have zero intrinsic worth and only a time premium. At-the-money options have no intrinsic value either, but if asset prices move favorably they will become in-the-money and then have appropriate unit price moves from that point on. Consequently, at-the-market options often move at approximately a 50% rate of a favorable move of the underlying asset until it becomes in-the-money when it will then move uniformly with favorable asset price change.

Theoretically just as asset prices are determined by supply and demand so are option prices. Theoretically demand for Calls for example could be even greater than that for the underlying asset even though asset demand was sufficiently high to cause an increase in underlying asset price. Theoretically this would cause a relative over valuation of the option, i.e. its intrinsic value would increase relative to the underlying stock, or if the option was in less demand than the underlying asset its intrinsic value would decline compared to the underlying asset. Except for those few assets with poor liquidity such distortions do not exist for long. The professional traders with zero commissions are continuously monitoring the relationship between option price and underlying asset price to capitalize on any valuation inefficiencies, i.e. any inefficiencies of option valuation are seized on immediately so that the arbitrage profit is immediately locked in. Rarely will a valuation with a quarter or half a point inefficiency exist more than momentarily.

A few corollaries arise from this arbitrage activity of inefficient option valuation

l. Don't bother to look for valuation inefficiencies for even if you should fleetingly recognize one you cannot capitalize on it because the costs of commission exceed the arbitrage profitability.
2. Assume option valuations and, therefore, option prices are appropriate and efficient.
3. Efficient option valuation maintains the relative value of Calls and Puts - i.e. if a Call is expensive to buy then a Call is appropriately valuable to write.
The underlying rationale for arbitragers lies in the relationship of stock price, interest rates, stock dividends, the strike price and the price of options, Puts and Calls. The relationship between these entities is expressed in the following equivalence formula:

Stock price + Put price + interest = strike price + Call price + dividends
These are the equivalence parameters that the computers of the professional traders are continually monitoring. Once this goes out of balance because of supply and demand and the Call price say becomes half a point overvalued then the arbitrageurs immediately move in and lock in the overvalued profit by writing the overvalued Calls, increasing their supply and, therefore, bring the elements of valuation back into balance, they could also buy in the stock and drive its price up and buy Puts. Conversely if the price of Calls fell they would bring about balance and lock in profits by shorting the stock, writing Puts and buying Calls to bring about appropriate balance of the value of the elements of valuation. These arbitrage manoeuvres described are known as conversions and reconversions (or reverse conversions) respectively and will be pursued on another resource board.

Which option to choose

If we are to assume that at any given time option valuations are efficiently priced how do we choose which option? This question has different answers for different strategies. Primarily one is either going to be long (buy) Puts or Calls or short (sellers of or writers of) Puts and Calls. These two strategies have opposing criteria. Buyers of options ideally need time, intrinsic value and volatility. Sellers want to reduce risk to their positions by reducing time, volatility and intrinsic value. So we will look at option choices for both strategies.

A. Option choices for buyers
l. Time
Well we have already seen from the time premium decay curves that we should seek options far enough away in time that the anticipated underlying asset price move should occur during the relatively flat part of that curve. Therefore, expiry is determined by your reasonable expectations of time.
2. Strike price
Valuation of offered options can be calculated with the complex Black-Scholes formula and favorable inefficiencies of valuation (undervaluation) can be the object of selection. However, with professional traders constantly monitoring option valuation to capitalize on arbitrage opportunities it is unlikely that this method will reveal undervalued options in liquid markets. The best way to look at the problem is to look at risk reward characteristics of the options offered and to select those with the lowest risk for the highest reward or, put another way, seek out the highest percentage point gain per unit cost of the option.

In any option buying strategy the maximum risk is the full cost of the option expiring worthless at the expiry date. The potential profit of an option if it reaches its target price can, theoretically, be calculated, assuming efficient option pricing in liquid markets, so we can calculate risk-reward and cost- per-percentage point gained.

Consider OEX June Calls and you believe the OEX will reach 415 before expiry. You could choose from:
l) OEX June 405 Calls at $4.25
2) OEX June 410 Calls at $1.95
3) OEX June 415 Calls at $0.80
The percentage profitability would be:
l) OEX June 405 (in-the-money) would have intrinsic value of 415 - 405 = 10
Therefore, Profit = 10 - 4.25 = 5.75

therefore percentage gain = 5.75 x 100 = 135%



4.25

2) OEX June 410 would have intrinsic value of 415 - 410 = 5
Therefore, Profit = 5 - 1.95 = 3.05

therefore percentage gain = 3.05 x 100 = 156%



1.95
3) OEX June 415 would have zero intrinsic value and so would be a 100% loss situation at expiry.

So an easy calculation reveals that of the choices available the most profitable on a percentage basis was the June 410 Calls.
Consider OEX June Puts anticipating a fall of the index to 400 by expiry:
l) OEX June 410 Puts at $4.25
2) OEX June 405 Puts at $1.95
3) OEX June 400 Puts at $0.80
The percentage profitability when the OEX reached 400 would be:
l) OEX June 410 Puts would have an intrinsic value of 410 - 400 = 10
Therefore, Profit = 10 - 4.25 = 5.75

therefore percentage gain = 5.75 x 100 = 135%



4.25
2) OEX June 405 Puts would have an intrinsic value of 405 - 400 = 5
Therefore, Profit = 5 - 1.95 = 3.05

therefore percentage gain = 3.05 x 100 = 156%



1.95
3) OEX June 400 Puts would have no intrinsic value at expiry and so would incur a 100% loss on the trade.
So we can again see that on a profitability basis the OEX June 405 Puts are the ones to buy.
The profitability of Calls and Puts can be formulated as:
% Profitability of Call = intrinsic value - Call price x 100



Call price where intrinsic value = share price - Call strike price.
or, % Profitability of Call = (share price - Call strike price) - Call price x 100



Call price % profitability of Put = intrinsic value - Put price x 100

Put price where intrinsic value = Put strike price - share price


or, percentage profitability = (Put strike price - share price) - Put price x 100


Put price
The other measure of selecting which option is the risk-reward ratio. This you should do to decide if you are going to buy any of the options offered.
Assuming you are likely to be correct in your market predictions a little over 50% of the time, you need to have your gains to be twice as big as your losses, better in fact if you are to accommodate the cost of commissions. So your intended trade should, if successful, yield over 100% gain, if it doesn't then you should seriously consider not taking the trade.

One should only go for those low risk, high reward opportunities. In any option buying trade your maximum loss is the cost of the options expiring worthless. The profit is the intrinsic value minus the cost of the option.
Therefore, Reward/risk = profit = intrinsic value - price of the option
cost price of the option

if this is less than 1.0 you should not take the trade.
B. Option choices for sellers (writers)
The position of the seller of options is quite different from that of the buyer of the option. The most important differences should be noted:
l. Time is to the advantage of the buyer, not the seller.
2. The outcome of the option (exercised or not and when) is in the hands of the buyer.
3. The maximum profit to the seller is limited to the price received for the option.
4. The liability to the seller can be substantial and is not necessarily limited.
5. The buyer benefits at the expense of the seller if the option acquires intrinsic worth.
Therefore, ideally the seller wishes to sell only those options that have a short time to expiry, without intrinsic value and with the highest premium. Can these criteria be quantified and rational rules created for successful option writing? Within limits yes.

General rules would include:

1. Sell options at-the-money or out-of the-money as close to being at-the-money as possible.
2. Write only those options with 2 - 4 months to expiry.
3. Write only those options whose price is at least 10% of the strike price.
4. When writing options use stop loss orders. Place them at the price of the underlying asset at the time plus (for a Call) or minus (for a Put) the price of the option.
5. When you have made 75% profit close out your position.
6. Do not sell options for more money than you are prepared to lose, i.e. 10% of your trading capital.
7. Never answer a margin call; close out your position.
8. Avoid takeover target companies.

Quantifying the criteria to select which options to sell

To make rational choices we need to be able to quantify the associated risk-reward with each offered option one can sell. We know that the maximum profitability is the price received for the option. For selling uncovered Calls the risk is infinite as the stock can rise indefinitely, for selling uncovered Puts the risk is finite but huge as the underlying stock could go to zero. The option writer is passive once the sale is made, the buyer determines the fate of the option and so it is through the eyes of the buyer that we must evaluate future possible scenarios of the value of the option. Even so some relative quantification of risk and reward can be made.

If we consider the percentage profitability of each of the option choices available, through the yes of the buyer, it follows that the least profitable choice for the buyer must be the most advantageous to the seller of the options.

Evaluating Time Premium

Options priced out-of the-money have no intrinsic value and, therefore, represent time value. If we break down the time value over the intervening time we can at least assess relative time values of the options available. So in February if we were considering writing OEX June Calls, i.e. 5 months hence, we could tabulate them as follows:
Premium return/month
OEX June 405 at 4.25 4.25 / 5 = 0.85
OEX June 410 at 1.95 1.95 / 5 = 0.39
OEX June 415 at 0.8 0.80 / 5 = 0.016
On this basis the best Call option to sell is the OEX June 405.
The important relationships between underlying assets and their options, their appropriate valuation and the concept of asset equivalence and synthetic derivatives made up of equivalences have been outlined on this resource board. It also outlines rational, quantitative ways to evaluate the options available for both the buyer and the seller. The concept of percentage profitability is a particularly good way to choose which, if any, option should be traded.

The above excerpt was taken from http://www.tradertalk.com/tutorial/opprim.html