## 07 May 2008

In the previous article, I received a question with regards to comparing implied volatility (IV) and historical volatility, so I’ll talk a bit about that.

Firstly I want to concentrate on HV. As I’ve pointed out in previous articles, HV looks backwards. A period of time is selected, that is, the most recent x days of data is used to calculate the historical volatility mathematically as per my previous article on volatility.

This begs the question, how many days should we look back over: 10 days, 20 days, 30, 100, 250? The general rule of thumb is either 20 or 30 days, roughly one month. But depending on the look-back period, we can get vastly differing figures for HV.

Consider the following chart where 10, 20, 30 and 100 day HV is plotted: click to enlarge

This shows the vastly differing values that can be derived, depending on the look-back period.

And below, the IV mean compared against 30 day HV for the same chart:

The thing to remember here is that IV is trying to predict future realized volatility. As this chart is of near expiry IVs, it is trying to predict actual volatility about 20 – 30 days ahead, so to truly make a comparison; IV should be compared with HV about a month into the future.

Three things to note here:

1) The market does a reasonably good job of it at times, but drastically wrong at other times.

2) It is not possible to do in real time as we cannot see into the future.

3) Volatility is mean reverting; it tends to oscillate up and down around the mean.

We can use this information to make a “guess” as to what volatility (not direction) will do next. It is suggested in many texts to buy options when IVs are low and to sell options when IVs are high. It is also suggested that options are overpriced when IV is higher than HV, and under priced when IV is lower than HV.

That may be the case at times, but at other times it is absolutely false. It is then clear that assumptions such as these can get you into trouble if applied indiscriminately. But it is a good starting point; just don’t treat it as gospel.

How can the trader tell when options are overpriced or under priced? You can’t! You can only do it in retrospect.

However as traders, we get paid for taking risk. The options trader must make a volatility bet along with a bet on direction (or no direction). So if IVs are high, the question is whether the underlier is about to get very volatile for some reason, or whether option traders have just got a bit carried away and realized volatility does not increase, or falls; and visa-versa.

## 05 May 2008

### Implied Volatility

We have now gone through the six inputs into the Black Scholes Option Pricing Model (as proxy for any model in use). The sixth input, volatility, is problematic as a forward guestimation of volatility is used, it is equivocal; different traders will have different ideas of what this input should be.

For instance, I may believe a particular option’s fair value is \$2.65 using my own volatility projection, but when I go into the market it may be \$3.75, for the sake of example. What is going on?

What is happening here is that the “market” believes that the future volatility of the underlier is going to be a lot more volatile than you do. How does the market do that? Simply by the bids and asks in the market depth and by arbitrage. Depending on your data supplier or broker, there may be a figure supplied called “Implied Volatility”.

This is worked out by algebra, using the first five unequivocal inputs into the option pricing model and the tradable price, which is also unequivocal at that point in time, to derive a volatility figure. So what we are saying here, is that the volatility “implied” by the option’s price is x; Hence “Implied Volatility”.

Let’s look at an example:

* The underlier (XYZ) is trading at 52.75 with no dividend payable.
* I’m looking the XYZ \$55.00 call option, which expires in 63 days, which I can buy for \$2.45.
* Risk free interest rates are 5%

By plugging those known values into our option pricing model, (in this case I’m using the Cox, Ross & Rubinstein Binomial Model) we can calculate an implied volatility of 36.7%.

So how does that help us?

Quite simply, it is from this figure that you can determine whether the option is fair value or not.

Often in various textbooks and spots around the Internet, the suggestion is to compare Implied Volatility (IV) to Historical Volatility (HV) to determine whether an option is over, or under priced. This is a gross oversimplification. Historical volatility should be studied to get an idea of the volatility characteristics of the underlier, but says very little about what volatility will be going forward.

Remember Implied Volatility looks forward, while Historical Volatility looks backward. For instance, IV can rise before an earnings announcement, sometimes quite dramatically, even though the underlying stock has become very non-volatile as the market waits for the announcement. The market is therefore making a judgment on the volatility once earnings are released. IV invariable drops equally dramatically once the earnings are actually released, as the market discounts the move from the announcement.

The history of Implied Volatility can be plotted on a chart, just like Historical Volatility, again to see the characteristics of IV and how it changes under various circumstances. There are various vendors of IV data, but there is a free source from www. cboe.com from where I sourced the following chart:

The IV plotted in the above is an average of near expiry, implied volatilities across several strikes, so the IV of the particular option you’re interested in may vary somewhat from what is represented here. It does however give the trader an idea of the ebb and flow of volatility over time. You can use this information to make volatility projections and to bet on future volatility fluctuations with a suitable strategy.

The standard wisdom is to buy low volatility and sell high volatility. While this may make sense on the face of it, it isn’t always the wisest thing to do, but more on that later.

Next - More On Volatility

## 02 May 2008

### VIX Doldrums

A few thoughts on the situation on the VIX.

From VIX And More:

Dissecting views on VIX technical analysis

VIX Numbers and Overbought Signals

Ten Things Everyone Should Know About the VIX

And from The Daily Options Report:

On VIX @ < 20

Tommorow Cancelled

It certainly has gone a bit quiet and the market seems to be anticipating a repeat of last summer's relentless upward grind.

Sans the end of the world happening, I think that about sizes things up until next earnings season... unless of course the sky does fall down.

### Volatility

The sixth and final input into the Option Pricing Model is volatility.

It is my observation that there is often a bit of confusion about this term. If you listen to any of the financial media, volatility is only ever mentioned when the market is going down. To be sure, a 400-point down day on the Dow is a volatile move, but a 400-point up day is never described as volatile, yet it is equally so.

In the simplest terms, volatility is the relative rate at which the price of a security moves up and down. Market technicians have various methods of measuring volatility, using a variety of formulae, but our option pricing model requires a particular measure of volatility; the annualized standard deviation of logarithmic daily change in price.

Now that’s a mouthful, and most option traders view volatility in relative terms without understanding the calculation, but I think it helps to actually understand the mathematics behind it. We can do this with Excel or charting software, which I will give an example of, but let’s do it in English first

We start of by calculating for each day’s data, today’s closing price divided by yesterday’s closing price. This will return a number that is today’s price as a proportion of yesterday’s price. If there is no change, the number will be 1.0, if it is up 2% it will return 1.02, if it is down 5% it will return 0.95 and so on.

The next stage is to find the natural logarithm of the above. This is to reflect the lognormal distribution of stock market returns. Next, multiply this by 100 to express it as a percentage. We can plot this as a scatter chart, which will show the lognormal daily move as a percentage

The next step is to calculate the standard deviation of the above. Normally this is calculated over the last 20 or 30 days of data; it can be any length, but for this example we will use 20 days. This gives us the standard deviation of logarithmic daily change in price, which can be plotted on a chart to see changes in volatility as time goes by. However, Option Pricing Models require that volatility is expressed as an annualized percentage and we do this by multiplying by the square root of the total number of trading days in a year, which is the square root of 252.

This is now the finished volatility calculation, which is called “Historical” or “Statistical” volatility, plotted in the chart below”

This equation can be plotted in charting software to show current and past historical volatility. In Metastock or Amibroker language, (the two platforms I am familiar with) it can be plotted by using the following formula:

(StDev(log(C/Ref(C,-1)),20)*sqrt(252))*100

The above formula calculates historical volatility based on he last 20 days, the figure in red. Any look-back period can be used and some option traders use various length.

So now we can enter this volatility figure into our Option Pricing Model to get an accurate option price; or can we?

The historical volatility number, depending on the look-back period can vary enormously, and as the name implies, looks at past data, whereas what we really want to know as option traders is what volatility will be in the time left until the option expires. As this cannot be known, this forces the option trader to make a volatility forecast, or at least an idea of where volatility might be relative to the present in order to calculate his or her idea of fair value. This where historical volatility can be used as a tool, but the trader must look forward.

Often the market will disagree with you, which I will discuss in the next section.

Next - Implied Volatility

### Effect Of Dividends Payable

The fifth input into the Option Pricing Model is dividends. If the underlying pays no dividend, then there is no effect on option prices. However if the stock does have an upcoming cash dividend payable, it will have an effect on option prices. It is very important to be aware of this, as many a neophyte option trader has been caught out by thinking an arbitrage opportunity existed with mis-priced options, when in fact the pricing anomaly was due to an upcoming dividend; hence not an anomaly at all.

The reason for this is that option holders are not entitled to participate in cash dividends, so option prices must compensate.

It is a general rule of thumb that the underlying stock will drop by the dividend amount when the stock goes ex-dividend, all things being equal. As far as the stockholder is concerned, he/she ends up squits; what is lost on the stock, is gained in cash.

Option Pricing Formulae account for this by considering the move in the underlying due to going ex-dividend.

When the stock is cum-dividend, call option prices will be cheaper than they would be if there were no dividend payable, reverting to “no-dividend” pricing on the ex dividend date. This has the effect of shielding the call option holder from an unwarranted loss due to the drop in the underlying.

The reverse is true for put options. When the stock is cum-dividend, put prices will be more expensive than they would be if there were no dividend payable, reverting to “no-dividend” pricing on the ex dividend date. This has the effect of ensuring that the put holder doesn’t receive an unwarranted windfall profit.

### In a Nutshell

When a dividend is payable:

• Call option prices will be cheaper.
• Put option prices will be more expensive.
Next - Volatility

### Effect Of Interest Rates

The fourth input into the Option Pricing Model is “risk free interest rate”.

Firstly, what are risk free interest rates? The risk free interest rate is the theoretical interest rate that would be returned on an investment completely free of risk, generally taken to be the yield on 3 month Treasury Bills.

At first glance it is a bit hard to imagine why this would affect option prices. However, it is in the presumption that one side of the trade may be holding stock for no possible return and that the stockholder is due a risk free return for having their capital tied up and not earning interest.

Firstly, let’s have a look at call options. As we know, call options give the owner of the option the right to buy the underlying stock at the strike price. And we know that the writer of the option is obligated to sell shares to the holder of the option at the strike price. The option-pricing model therefore assumes that the option writer is actually holding the stock to be able to sell it to the buyer, if the buyer exercises.

This means the stockholder is incurring carrying costs in the form of loss of risk free interest income on cash and is due some compensation in the option price. The option buyer is in effect, paying the option writer risk free interest rates, in advance, for the life of the option. The effect however, is incremental according to the moneyness of the option. The risk free rate is fully priced in for deep ITM call options, whereas it is not priced in at all in far OTM call options.

The fact that you are paying the risk free rate “up front” means that the longer to option expiry, the higher the interest rate component of the call option premium.

Of course it also means that higher risk free interest rates mean higher call option prices, all things being equal.

The effect is quite obvious on our risk graph of call options. Below is an image for comparison of the same option at differing risk free rates. Both graphs are of a \$50 ATM call option with 145 days to expiry. To make the comparison visually obvious, I have used radically different risk free rates. It is most obvious in the deep ITM side of the graph, as marked. The top ATM call option at 1% has a premium of \$3.85, whereas the bottom image at 12% has a premium of \$4.95.

With put options the story is somewhat different. It is not the option writer who is presumed to be holding stock, as is with the case with call options; it is the option holder who is presumed to be holding the stock. The holder of a put option has the right to sell the underlying to the writer, so it is the put option holder who is compensated for loss of interest income on cash before putting to the option writer.

Therefore the rule of thumb for put options is that higher risk free rates mean cheaper put prices, all things being equal.

With put options it is not so graphically obvious, but we can see it in the option premium. Both graphs are of a \$50 ATM put option with 145 days to expiry. The top ATM put option at 1% has a premium of \$3.65, whereas the bottom image at 12% has a premium of \$2.87.

It should be noted that the above only applies where there is real cost of carry considerations, i.e. when the stockholder is required to finance the stockholding with cash and/or interest paid on margin. With options on futures, the cost of carry is prices into the price of the futures contract; therefore risk free rates have no significant effect on option prices.

### Time & Time Decay

The third input into Option Pricing Models is time until expiry. The key to understanding this principle is understanding that the option buyer is paying the option writer to take on risk. The buyer has the right to transact shares, but the writer is obligated to transact shares if the buyer exercises that right.

The call writer stands to lose a substantial amount of money if the stock rises past the strike price. Likewise, the put writer can lose a substantial amount of money if the stock drops below the strike price.

The general principle is very similar to insurance premiums. The more insurance you buy in terms of time, the more expensive it is. So it is with options, the more time you buy, the more premium you pay.

On the option writer’s side of the equation, the more time the option writer sells, the higher the chance of the option moving ITM, therefore the more you get paid for taking on this higher risk.

Therefore the general rule of thumb is, all things being equal, more time equals higher option premium, less time means lower option premiums.

This has implications for option holders. Options are a depreciating asset, often described as like holding melting ice in your hand. As the life of an option is finite and fixed, the option loses time value the closer to expiry it gets. This is known as “time decay”.

The graph below is of a call option with 30 days until expiry plotted as the uppermost line in red, with the other colored lines at six-day intervals with the black line at expiry. This clearly shows the time decay in long options.

On the other hand, this is to the benefit of option writers, who in return for assuming the bulk of the risk, get to profit from time decay.

For options that are ATM, time decay accelerates as expiry approaches. Have a look at the graph below. It is a graph of the extrinsic value only of the call option in the above graph.

It is very clear from this graph the accelerating nature of time decay. At 30 days from expiry, the ATM option has \$295 (in this example) of extrinsic value, yet according to our model, at 6 days from expiry, the option still retains \$130, with approximately \$90 at 3 days.

It is often graphically represented as follows with time elapsed on the x axis:

But what not many option resourses will tell you though, is that this is a representation of time decay ATM or quite close to it. As the option gets further ITM or OTM, this characteristic changes. Time decay, depending how far away from the money it is, will actually decelerate into expiry, as shown in the graph below:

This is useful knowledge when considering strategies where deep ITM or deep OTM options are used.

Next - Effect Of Interest Rates

### More On Options Pricing

In an earlier section, I outlined the six inputs into the option pricing model that are required to calculate an option premium:

1/ The price of the underlying
2/ The strike price
3/ The time till expiry
4/ Risk free interest rates
5/ Dividends, if any
6/ Volatility

Note that “premium” is not a term I’ve used before, but is interchangeable with “price”.

In this section I want to cover in more detail the first two inputs, the price of the underlying asset and strike price as it is important how these to relate to each other.

Both of these inputs are unequivocally known at any point is time, the strike price of course is constant, whereas the price of the underlying will fluctuate from day to day and minute to minute.

It is in the relationship of these two inputs that we derive 3 new terms, which I will introduce now:

• Intrinsic value
• Extrinsic value
• Moneyness

Moneyness is further divided into three terms of relevance:

• At the money
• In the money
• Out of the money

Let’s cover the moneyness terminology first. An option is said to be “at the money” (ATM), if the underlying stock is trading at or near the option strike price. This is fairly self-explanatory and is the same for both call options and put options. For example, if we have a \$50 call or put option where the underlying is trading at \$50.00, that option is trading ATM.

A call option where the underlying is trading higher than the strike price is said to be “in the money” (ITM). For example, if we have a \$20 call option where the underlying is trading at \$22.30, that call option is ITM.

It therefore stands to reason that a call option where the underlying is trading lower than the strike price is said to be “out of the money” (OTM). For example, if we have a \$30 call option where the underlying is trading at \$27.90, that call option is OTM.

Put options on the other hand are precisely the opposite to call options.

A put option where the underlying is trading lower than the strike price is said to be “in the money” (ITM). For example, if we have a \$50 put option where the underlying is trading at \$46.70, that put option is ITM.

It therefore stands to reason that a put option where the underlying is trading higher than the strike price is said to be “out of the money” (OTM). For example, if we have an \$80 put option where the underlying is trading at \$83.90, that call option is OTM.

In practice, the nearest strike to the price of the underlying is often referred to as ATM, even though it may be a little bit ITM or OTM.

### Intrinsic and Extrinsic Value

If an option is ITM, is has intrinsic value. Why? Let’s look at an example. Let’s say we own a \$50 call option with the underlying trading a \$55.00. That option is \$5.00 ITM.

A \$50 call option gives you the right to buy those shares at \$50, so if you exercise the option you can buy the stock for \$50 and immediately sell for \$55.00, a \$5.00 profit. Therefore that option is worth at least \$5.00.

So “intrinsic value” is simply the amount by which an option is ITM.

Remember that put options are the reverse. A put option is ITM if the underlying is trading below the exercise price, because you can exercise to sell stock and buy back with an immediate profit.

ATM and OTM options have no intrinsic value at all. Yet in most cases, they still have value; it costs money to buy them. Also in most cases, ITM options have value in excess of their intrinsic value. This is referred to as “extrinsic value” or “time value”.

I prefer the term extrinsic value over time value, because extrinsic value also considers volatility, not just time until expiry.

Have a look at the diagram below of the value of an ATM call option some time before expiry. (All of the following diagrams are for ATM options) The purple area represents intrinsic value and the light blue area represents extrinsic value.

Put options have intrinsic value below the strike price. (See below)

You will note that extrinsic value is greatest when ATM. If we plot the extrinsic value only without intrinsic value, this concept becomes very obvious, an important point for when we get into the Greeks. (See below).

This is the graph of extrinsic value for a call option, but has a similar shape for calls and puts . Note that in this instance the extrinsic value is greater when underlying prices are higher, than when they are lower. This applies to stock options and won’t be seen on futures options. This relates to “cost of carry” because a stock is an actual tangible and will be discussed later in the section on risk free rates.

Next - Time & Time Decay

### Buying, Selling And Open Interest

Buying and selling options is just like buying and selling stock - almost.

They are traded via a broker, have bid and ask prices and market depth, just like stocks do. As a matter of fact with some electronic platforms, you won’t notice any difference.

If you want to buy or sell common stock, you just go into the market and place your order. There is a set number of shares outstanding, issued by the company that never changes unless by corporate action.

Options are different in that the company the option pertains to do not issue them; traders create them out of thin air. This is where the term “Open Interest” is applicable, which I mentioned in the last section, more on that in a moment.

When placing a trade, it is important to tell the broker whether the order is to open or close a trade. If for instance you want to buy 10 INTC May \$20 call options that you do not yet own, you would say “buy to open 10 x INTC May \$20 call options at x price”. If you wanted to sell those options before expiry, you would tell the broker “sell to close 10 x INTC May \$20 call options at x price”.

Similarly if you were going the write the above options, you would say, “Sell to open 10 x INTC May \$20 call options at x price”. If you wanted to buy back those options before expiry, you would tell the broker “buy to close 10 x INTC May \$20 call options at x price”.

Some electronic platforms will know whether the order is to open a position or to close a position automatically.

This brings me at last to open interest. Open interest is simply the number of open contracts in existence at that point in time. If an option has 0 open interest there are no open contracts. For there to be an increase in the open interest, there must be opening orders on each side of the trade.

For instance in the example above where we bought to open 10 INTC call options, the person selling you those options would have to be selling to open for there to be an increase by 10 in the open interest. That means that there are 10 new call option contracts that have been created in that series.

Likewise, for the open interest to decrease, both sides must be closing orders. For instance in the example above where we sold to close 10 INTC call options, the person buying those options would have to be buying to close for there to be decrease by 10 in the open interest. That means that there are 10 call option contracts that have been closed out in that series.

If however one side of the trade were an opening transaction and the other side of the trade a closing transaction, there would be no effect on open interest.

Open interest is an effective indicator on the likely liquidity of a particular option series. The higher the open interest, obviously the higher the number of traders involved in that contract. This generally results in tighter bid/ask spreads.

By the process known as novation, the person you traded with when you opened a position does not have to be the person with which you close the position. It can be anybody who is in the market at that time. This ensures that you can readily trade out of any position that you may have open; you are not obliged to wait until expiry.

Next - More On Options Pricing

### Option Chains & Symbology

We discussed earlier that options were standardized contracts with various striking prices and expiries available. This is where the options trader needs to make a choice as to which strike and expiry to use. The options available to be traded are viewed via what is known as an option chain, which is simply a list of options.

It is from the option chain that you will choose which option contracts you want to trade. Option chains are available on a number of financial sites, or from your options broker. Public sites may display delayed data so it is better to rely on quotes from your broker.

Below, courtesy Yahoo Finance is an example of an option chain for INTC options that expire in May 2008. Click to enlarge.

You will notice each Option has it’s own unique symbol (N.B. Yahoo adds the .x suffix and is not part of the official symbol). It is important to know this symbol if you are using a full service broker to avoid errors. You can just use the description of the option, but I think it’s better to use both the symbol and the description. That way the chance of a mistake is minimal.

There is a logic behind option symbols and generally the symbol contain letters representing the following: Root symbol + Month code + Strike price code. For a further explanation of option symbols for US options go to http://biz.yahoo.com/opt/symbol.html or the exchange where you will be trading.

Those using electronic platforms might rarely actually use the option symbol, but it is still useful knowledge for statement reconciliation etc. If you are familiar with option symbology, you will know at a glance whether an option is a put or call, the expiry month and strike price. There is other information on the option chain that you will recognize from stock quotes; lets have a look at an individual contract to show what the information is telling us.

• Symbol - The symbol for that particular contract.
• Last - The last traded price. Please note that the last traded price may have taken place some time ago, perhaps days in some cases and may not reflect the current tradable price.
• Change - If there has been any trades today, this will be the difference between the last trade and the previous trade, but as before, the previous trade may have taken place some time ago.
• Bid - The current highest price someone is willing to pay for that option.
• Ask - The current lowest price someone is willing to sell the option for.
• Volume - The number of contracts transacted today.

There is an additional column there titled “Open Interest”, which we will discuss in the next section.

### Short Or Long?

Now that we know how to read risk graphs, we can clear up another area that is often confusing to the neophyte options trader, the principle of “long” and “short”.

For this purpose I’d like to separate out two concepts.

1/ Being long or short an instrument (share, future, option etc)
2/ Being long or short the market

This is going to seem blindingly obvious at first, but stick with me on this.

Share traders have uncomplicated mechanics with regards to being long or short. We’re all pretty comfortable with the concept of going long stock. When we are bullish on a market, we want to go long that market. We do this by going long, or buying stock. We are long the market and long the instrument (the stock).

Likewise, if we are bearish on a market, we want to go short on the market, we do this by short selling stock. So we are short the market and short the instrument.

Easy.

The picture with options can become a bit more complicated. Ignoring two, and multi-legged positions, which we will be covering later, it is possible to be long and short at the same time and here is where our risk graphs can help us.

If you buy an option, you are long the instrument. Likewise if you write an option, you are short the instrument. But our market bias will be affected by whether the option is a put or call.

This is the same sentiment as being long stock. As you can see we need the underlying market to rise in order to profit. You are long the call option and also long on the market.

2/ Buy a \$50 put with the underlying trading at \$50. (Assuming no accompanying stock position)

This is the same market sentiment as being short stock, we are bearish and short the market because we need the market to go down in order to profit. Yet we are long the instrument because we bought the put. So in this case, we are long the instrument, but short on the market.

3/ Write a \$50 call with the underlying trading at \$50.

Here is a case where we are short the instrument, because we have written, or sold the option. We are bearish because we really want the stock to go down so we are short the market as well. But if you look at the risk graph, the stock can actually go up a little bit to just under \$52.50 and there will still be a profit at expiry. So in the case of a written call, we can be said to be short the call and short to neutral on the market.

4/ Write a \$50 put with the underlying trading at \$50.

Finally, the written put, a short the instrument position in the above risk graph is long to neutral on the market.

It’s important to get this concept firmly in your mind as confusion here can lead to execution errors, particularly if using an electronic platform.

In conclusion:

Next - Option Chains & Symbology

### Understanding Risk Graphs

A risk graph is a diagram of the potential profit or loss of an option strategy. I actually prefer the term “payoff diagram”, but “risk graph” seems to have taken a firm hold in options trading vernacular.Many people avoid the use of risk graphs for one of two reasons. They either find them confusing, or they somehow equate the use of a risk graph to charting or technical analysis.

A risk graph is definitely not technical analysis. There is no prediction or analysis of share prices implied by the use of them. They simply make the calculation of potential profit and loss easier for those of us who are more visually oriented, or as a visual estimation tool to shortcut the need for a mathematical spreadsheet.

What I want to do here is to address the confusion factor in understanding risk graphs, by building some risk graphs from scratch.

I believe the confusion factor stems from what the x and y axes represent. Most of us have at least a basic grasp of a price chart, even if not chartists. Most people are aware of what the axes on a price chart represent. The x axis represents the passage of time and the y axis represents price.

However a risk graph does not have time represented on any axis, rather, it is a snapshot at a moment in time, usually at expiry of the option. The x axis, rather than representing time, represents price. The y axis, rather than representing price, represents profit or loss. Below is the risk graph of 100 common stock bought at \$50.00, which is represented by the blue line.

I have annotated the risk graph at 3 points. Point A represents the profit of the stock when trading at \$50. Because we bought the stock at \$50, of course there is no profit or loss. At \$56, because we bought 100 stock at \$50, there is \$600 of profit, which is plotted at point B. At \$46, there is a \$400 loss, plotted at point C.

Because we know there is a linear relationship between price and profit/loss, we can connect the dots and show the entire risk graph of the common by the blue line. “Passage of Time” is not involved here.

So we can now see what the “hockey stick” shaped risk graph of an option is portraying. Below is the risk graph, at expiry, of 1 x \$50 call option (expiry date etc is not important for this example) bought for \$2.50.

We can quickly ascertain, that if the option expires with the stock trading at anywhere from \$50.00 or less, our loss would be a maximum of \$250. We can also see that the stock is required to be trading at \$52.50 in order to break even as well as determining the exact profit at any point higher than \$52.50.

What about a risk graph of option values before expiry? We can, and should do that too. Below is the same option at the time of purchase, with the common trading at \$50.

This presents a somewhat different picture and demonstrates very clearly that the profit and loss picture of an option changes as time goes by. This demonstrates the time decay of long options. With the software I mentioned in an earlier section, we can view the risk graph at expiry, at analysis date and at any point in between, very handy.

The Hoadley software plots both the risk graph at analysis date and at expiry as default, and will perform an animation of the decay process up until expiry. This is very useful for if/then analysis without having to be a mathematics major.

Next - Short Or Long?

### Basic Options Pricing

As we noted earlier, options are derivatives, and are so called because they derive their value from their underlying instrument. Determining the value of options had always been problematic up until the point when in the early 70’s, Fischer Black and Myron Scholes developed the “Black Scholes Option Pricing Model”. The model has been refined and improved over time with alternative equations such as the “Cox, Ross & Rubinstein Binomial Model” being the more usual model used for American style stock options these days.

I shall use the generic term of “Option Pricing Model”, or OPM as proxy unless specifically mentioned otherwise.

I submit that only mathematicians would be interested in the actual formula, and by the miracle of technology we have software to compute this for us non-mathematicians. There is much available on the web on the topic if you’re so inclined.

At this point I would like to introduce a piece of software to you, that I use for pricing and producing payoff diagrams (or risk graphs as they are sometimes known) and will be used extensively throughout this course. It is free for the evaluation version and at less than \$100 for the full version it is very inexpensive. I have no financial interest in the product and there are other modelers that are equally useful.

It is the Hoadley Options Strategy Modeler and is available for download at http://hoadley.net/options/strategymodel.htm. All instructions in how to use the software are at the site. I consider it an essential tool for analyzing trades, particularly for those who learn more visually-spatially than by pure abstract. Its real value becomes apparent in analyzing multi-legged spread trades.

The OPM considers six variables or “inputs” in order to generate a price for an option. They are:

1. The price of the underlying
2. The strike price
3. The time till expiry
4. Risk free interest rates
5. Dividends, if any
6. Volatility

At any point in time, the first five inputs are known unequivocally. However for the sixth input, volatility, it is the future volatility of the underlying that must be known. This of course is impossible, so a volatility projection must be made. I will be discussing volatility in depth in a later section.

But here are some general rules of thumb that you can use as a guide, before we get to more in-depth pricing principles:

• Higher prices mean higher call prices.
• Higher prices mean lower put prices
• Lower prices mean lower call prices
• Lower prices mean higher put prices
• More time till expiry means higher option prices
• Higher volatility means higher option prices

Please not that these are general principles and there are several dynamics that can effect the above and I would like to cover some other principles before continuing on with option pricing.

### Two Sides To An Options Contract

We’ve learned that an option is a contract, and we’ve learned what your rights are if you own an options contract. But there are two sides to every contract, right? So if you buy an option contract, somebody has to sell it to you.

The person selling an option contract can be any market participant, market makers, other traders, whoever. It can also be you. This is often called “writing” options and the option seller often referred to as the “writer”.

We’ve learned that the option buyer has the right to buy or sell, so what does that mean for the option writer? That logically translates into obligations for the writer.

Thus, if the buyer of a call option has the right to buy, then the writer of the call option has the obligation sell, if the call owner exercises his/her right. The full statement therefore, is that the call writer has the obligation to sell a certain amount of shares, if called, at a certain price, on or before a certain date.

This is where the term “call” comes from; the option buyer has the right to “call” shares away from the option writer.

Looking at the put side of the equation, if the buyer of a put option has the right to sell, then the writer of the put option has the obligation to buy, if the put owner exercises his/her right. The full statement therefore, is that the put writer has the obligation to buy a certain amount of shares, if put to, at a certain price, on or before a certain date.

This is where the term “put” comes from; the option buyer has the right to “put” shares to the option writer.

### In a Nutshell:

• The call option writer has the obligation to sell.
• The put option buyer has the right to sell.
• The put option writer has the obligation to buy.
Next - Basic Options Pricing

### Options Are Standardized Contracts

There are two types of option, call options and put options.

The owner of a call option has the right, but not the obligation, to buy a certain amount of shares, at a certain price, on or before a certain date.

The owner of a put option has the right, but not the obligation, to sell a certain amount of shares, at a certain price, on or before a certain date.

In a nutshell, the owner of a call has the right to buy, and the owner of a put has the right to sell.

Options have been traded on all sorts of things for centuries, and on stocks for several decades. But these were non-standard contracts, the terms of which were individually negotiated by the parties involved.

In the US in the early seventies, to expedite the efficient trading of options contracts, the Options Clearing Corporation (OCC) was formed to facilitate the trading of options between stock market participants. The mechanics of how the OCC operates does not concern us in this section and I suggest you find out the activities of the options clearing house in the country in which you live. For the sake of international neutrality, I’ll use the term options clearing house (OCH) as a generic term. Suffice to know that they are operating in the background with the following benefits to option traders:

1. Options contracts are standardized.
2. Options exchanges were formed for the trading of these contracts
3. Market Makers were enlisted to guarantee liquidity
4. Facilitated the process known as “novation”.

N.B. Novation is the process whereby the person who you entered the contract with, does not have to be the person whom you conclude the contract with. This is another mechanism that ensures liquidity.

Let’s look at the standardization of option contracts. Each option contract will have the following features as set by the OCH

1. The underlying instrument (e.g. the share the option is on)
2. Whether the option is a put or call.
3. The size of the contact. That is the number of shares contained in one contact. The standard contract size of US stock options is 100 shares, but please note that this may vary due to corporate actions during the lifespan of the option. (E.g. share splits etc.)
4. The exercise price (or strike price as it is sometimes called): This is the price you have the right to buy or sell at, no matter what the market price is.
5. The expiry date: This is the date up until which you have the right to buy or sell. After this date the option ceases to exist.

### American or European

One further distinction, options contracts are classified as either American style, or European style, and refers to when it is possible to exercise your right to buy or sell.

An American style option can be exercised at any time up until the expiry day. Generally options on individual stocks and futures are American style.

A European style option is only able to be exercised upon expiry and cannot be done so beforehand. Some options on broad based indices are European style.

### A Couple of Quick Examples

First a call option: The “MA April 18, 2008 220 call option”, an American style option, gives the owner the right, but not the obligation, to buy 100 shares in MasterCard Corporation, on or before April 18 2008, for \$220.00 per share.

If MasterCard is trading at, lets say \$250 at expiry, you are sure going to exercise your right to buy, if however it is trading at \$170 at expiry, you’re sure not going to pay \$220 for it and you will let it expire without exercising your right to buy.

Next the put option: The “FSLR May 16, 2008 195 put option” an American style option gives the owner the right, but not the obligation, to sell 100 shares in First Solar Inc. on or before May 16, 2008, for \$ 195.00 per share.

If I own FSLR shares which are trading at \$160 and I also own the above put option, it makes sense that I might exercise that right and get \$195 for shares trading at \$160, but if it’s trading at \$210, I am not going to sell at \$195.

Note that waiting till expiry and either exercising or not, is not your only alternative. You can trade out of the option if that suits your trading plan, but more on that later.

### What Are Options

OK let’s take a few steps back to the very beginning.

Most investors know that buying common stock entitles them to a part ownership in the company issuing those shares. This means that you have entered into an “equity” participation in the company and in most cases gives the owner of stock the right to dividends paid by the company from time to time and entitles you to a vote in company affairs.

On many companies listed on the world’s stock exchanges, you are also able to trade options. So what is an option?

An option is actually a contract, which gives the owner of the option, the right to buy or sell parcels of shares in a particular company. In this case, these are often referred to as “stock options”, however options can also be traded on ETFs, futures contracts and a number of other instruments. Within the context of this course, I will generally be referring to stock options unless otherwise stated.

It should be noted that options issued by the company to its executives as incentives (and sometimes the subject of controversy) or non-standardized company options traded on some stock exchanges are also called stock options, but these are not included within the context of this course. We are learning specifically about “exchange traded options”
An option does not convey any ownership in the underlying security at all, merely the right to buy or sell a particular security. An option is termed as a “derivative” security, as any value it may have is derived from the value of the underlying security.

Next - Options Are Standardized Contracts

### A Quick Word On Risk

Out there in options land there are various, and sometimes-conflicting statements on the risk involved in options trading. They limit risk, they’re very risky, naked options have unlimited risk, etc. etc. etc.

I want to take this opportunity to dispel any notions you may have about risk in options trading. I’m jumping ahead just a little bit, but now is a good time to get this particular point across. Once again, if you’re a beginner some of the terminology might be foreign, but don’t worry about that right now. As you go through the course, you’ll hark back to this section and it will begin to take on more and more significance; trust me on that.

In any market where options exist on an underlying instrument, whether that is common stock, a futures contract or anything else, there are six possible single leg positions.

1. Long stock
2. Short stock
3. Long call
4. Long put
5. Short call
6. Short put

Let’s say we have the common stock XYZ trading at \$50 per share with the ATM options trading at \$2.50 apiece (both puts and calls to make it easy) and six traders who each take on one of the above positions.

Important: The presumption is that all the option trades are the same strike price and same expiry.

1. The first buys 100 shares @ \$50.
2. The second 2 shorts sells 100 shares @ \$50.
3. The third trader buys one \$50 call contract (representing 100 shares) @ \$2.50.
5. The fifth trader writes (short sells) 1 \$50 call contract @ \$2.50.
6. The sixth trader writes 1 \$50 put contract @ \$2.50.

What happens to the profit or loss of each of these traders if the stock is trading at \$40 at the option expiry? I won’t go into the mathematics or the mechanics right now, because we’ll be going into that in depth in the course, so you’ll have to trust me on the figures. Brokerage and spread will make a small difference, but for the sake of simplicity we’ll ignore that right now.

1. The trader who bought loses \$1,000.
2. The trader who short sold makes \$1,000.
3. The trader who bought the call loses \$250.
4. The trader who bought the put makes \$750.
5. The trader who wrote the call makes \$250.
6. The trader who wrote the put loses \$750.

There is a lot of analysis that can be gleaned from the above, but what want you to notice in this instance, is the risk of each position. It turns out that the long stockholder has lost the most money. So does that mean that common stock is the most risky? Note also the stock short seller made the most money.

Now I want you to add up all the profits and losses above. Notice it comes to zero.

Again, lets look at what happens if at option expiry the common is trading at \$51.00:

1. The trader who bought stock makes \$100.
2. The trader who short sold stock loses \$100.
3. The trader who bought the call loses \$150.
4. The trader who bought the put loses \$250.
5. The trader who wrote the call makes \$150.
6. The trader who wrote the put makes \$250.

In the above example it is the long put trader who has lost the most money, in fact both the long put trader and the long call trader have lost more than the trader who shorted stock, but both the option writers made more than the long stock trader. Does this mean that long options are the most risky position?

Note once again the results all add up to zero.

What I’m hoping you see from this little exercise is that options are not more or less risky than common stock, but that options “transfer” risk. This is apparent in the way that all the sum of all the above position’s profit and loss result in zero. I hope you see that the assertions that you hear about unlimited risk in naked options and that long options reduce risk is largely nonsense.

In fact the person that gravely cautions you about the risk in naked puts, yet will quite happily go long the common, is cognitively dissonant. We’ve shown that in the first scenario, where the long stockholder carries the most downside risk.

Likewise, the person who will indiscriminately buy options to “limit his or her risk” is due a few shocks.

With options, it is not less or more risk that the trader accepts, but they do alter their risk profile. The fantastic thing about options is that you get to select exactly where you want your risk to be and exactly where you don’t want your risk to be.

Now I don’t want to play down the fact that you can lose money trading options. The fact is that you can leverage yourself to ludicrous proportions, and many option traders do just that

This is the really important thing to learn about options trading; understanding exactly where your risks are, how big they are, the face value of your position, what you’ve accepted in order to achieve the particular goal you had in mind, and being aware of how your position may hurt you.

Next - What Are Options

### Why You Should Trade Options

Probably the most common reason people get involved with options is because of the leverage options afford to the retail trader. We've all heard the stories of huge leveraged profits - 100%, 500% 1000%. It is true that these gains are possible on long option strategies, but the reality is a bit more complicated than the big wins. Leverage as we should know, is a double edged sword. Often it is this leverage that prompts people to select inappropriate strategies for their account and risk profile.

If you have started trading options or considering trading options for this reason alone, I suggest it is a very bad reason for doing so because of the nuances of option pricing. You can of course use options for the massive leverage they offer and a few people will “get rich quick”. That is the law of large numbers. But most traders attracted by gargantuan gains and willing to take on the risk, will “get poor quick”, but you don't often get to hear about those. Like any gambler, they only tell you about the wins.

This is not to criticize options trading at all, but there are a number of "good" reasons to trade options.

Let’s look at some good reasons why you should trade them:

* To speculate on the direction of stock with limited risk.
* The hedge a stock or portfolio.
* To reduce capital usage.
* To make extra income from long term stock holdings
* To take advantage of large moves in the market, no matter which way.
* To profit from range-bound stocks.
* To construct specific risk/reward profiles that suit your forward view, even if that view is unclear.
* And yes, leverage, if intelligently applied and providing risk is controlled.

The reason is flexibility. You can create a multitude of risk/reward profiles, rather that “if it goes up you win, if it goes down you lose”. You can use ALL the strategies according to the varying situations you’re faced with, you can use a select few, or you can choose one single strategy and look for opportunities to suit.

I recommend being conversant and proficient with as many strategies as possible, because market conditions can change very quickly and one type of strategy may no longer be suitable for the new conditions.

There are of course, risks in trading options, just like any endeavor where there is reward, and I’ll be comprehensively detailing those risks as we get into the meat of the course.

It is a sad fact that many option traders quit the game after sustaining a few losses where they did not understand the reason for the loss. If I could achieve one thing with this course, it would be to help traders understand exactly where their risks are.

I’ll have a quick word about risk in the next section, before we start into the main course.

Next - A Quick Word On Risk

### Introduction To The Options Trading Guide

The purpose of this site is to build, over time, a free industry standard course on options. A no-cost resource for options traders, or those considering becoming an options trader, to use at will, for however long you like and without having to sign up to any email marketing to clog up your inbox.

Furthermore, it is to be a collaborative process. All sections of the course are open for specific questions on the current topic, constructive criticism, requests for clarification, inclusion of oversights and omissions, etc. I want this to be the best it can be for retail options traders, so your comments are all welcome.

I think there is an unfilled niche for a serious, no BS options guide tuned specifically retail options traders whether they are just starting out, or have a little bit of experience, to take them to the next level. A course written by someone who has come up through the retail trader ranks and knows exactly how you’re all thinking at different stages, and how to progress without having to be super intelligent and overly mathematical.

The goal is to get you to a level of proficiency and long-term profitability.

This will take shape in four stages.

1. The Basics. Just in case you don’t already know.
2. Options Pricing, Volatility & The Greeks. This is an area that is skimmed over or completely ignored by many resources, or it is covered in a highly abstract and technical fashion. This area is extremely important to understand for long-term success and in fact, understanding here opens up a whole myriad of new trading possibilities.
3. The Strategies & Synthetic Relationships. More than a ready reckoner like most strategy lists, the trader needs to be able to think creatively to construct trades to suit his/her view and to achieve the particular goal in mind.
4. Trading in the Real World. In most books and courses, everything is structured in black or white, win, lose or draw. It is all nicely constructed with hand chosen scenarios. But we all know that trading in the real world doesn’t happen that way, don’t we. Stuff happens all the time, so the options traders need to know what to do when things go wrong when and how to defend and adjust positions, how to protect your capital.

Welcome to the journey. I can attest that going to the trouble of learning this properly IS definitely worthwhile.

It is a journey, an apprenticeship if you will, so take your time with this. Learn in small bite sized chunks, absorbing and mastering one concept at a time, take small breaks of a few days and come back to review and move on to the next concept.

To quote an old horseman’s saying: “If you take the time it takes, it takes less time.”

Next - Why You Should Trade Options