Options Pricing: 
Understanding & Using It

Part II of this Guide focuses on the importance OPTION PRICING and how to use it for winning trades.   The concepts we discuss can benefit you, whether you are an option buyer or option seller.  

Inside an Option's Price
Options are great tools for portfolio protection and speculation, particularly because of the great leverage they offer (i.e., a relatively small dollar investment and the potential for high gain).  It's important to remember, though, that options are contracts, and therefore do not trade like stocks.  They have their own valuation mechanism, and, most importantly, they have a finite existence.  Not taking these two factors into account can be costly.  Surprisingly enough, a lot of folks don't.  They'll load up on option contracts because the prices look cheap, or they'll sell options when the conditions least favor it.

Market direction is important in an options trade, but it's still only one factor among others you need to consider.  It does you no good if your analysis of the market was correct, but then didn't apply the right option strategy to benefit from it.  You can still end up with a loser.

So, what are the factors that affect an option's price, and which experienced option traders look for? Well, for starters, let's remember what factors determine an option's VALUE.  An option, of course, is a derivative (i.e., it is derived from the underlying stock, index, or future that it is based on) and it's value is built on two components.  First is it's INTRINSIC VALUE, which will increase or decrease depending on where the underlying is in relation to the option's strike price (i.e., at-the-money, in-the-money, out-of-the-money).    

The second component of the option's value is its TIME VALUE.  Time Value is critical, because of the effects of TIME DECAY, which erodes the dollar value of the option contract with increasing rapidity as it approaches the date of expiration.  The longer the number of days, weeks, months, etc. before expiration, the slower the rate of Time Decay.  It's also important to remember that Time Decay picks up dramatically when the front month (the month closest to expiration) is entered.  

Intrinsic Value and Time Value are factors in determining what an option's worth, but not necessarily what you end up paying for it (i.e., the option premium).  The most important factor that effects premium price  is VOLATILITY.  The better you understand it, the more powerful your trades.

Volatility - Why It's So Important
Simply stated, volatility indicates the range of price movement for a security over a specific time frame.  Readings may be expressed as either a number or a percentage, but the bottom line is the higher the number, the greater the amount of fluctuation in the range (i.e. volatility).  

There are different types of volatility that impact the price of an option.  The most obvious, of course, is the volatility of the underlying.  If the underlying is making rapid moves up or down, volatility rises.  If instead, the underlying is moving within a trading range, volatility is lower.   This activity in the underlying will normally be reflected in the option's volatility.  Beyond this, there are volatility calculations that are specific to the trading of the option itself.  One of these is HISTORICAL VOLATILITY, which is a calculated average of an option contract's volatility over a particular time frame.  Historical Volatility is compared against the most important volatility factor in an option's price - IMPLIED VOLATILITY.  

Implied Volatility is an indication of how market makers at the options exchange expect the volatility of the underlying security to move, and that expectation is built into the option price (that's where the "implied" part comes from).  The significance of using Implied Volatility is that it will tell you whether the option you are looking at is high priced, low priced, or reasonably priced, and whether it serves the objectives of the trade.  Remember that to win in the options game isn't just a matter of correctly analyzing which way the underlying is heading, but in also picking a contract that lets you take the best advantage of the move.  If the contract doesn't do that for you, then either find one that does, or don't make the trade.  

Most option pricing is based on a standard, theoretical price model called Black-Scholes that is used to arrive at Implied Volatility calculations and other pricing factors.  Fortunately, you don't have to calculate Implied Volatility yourself, thanks to software that does it for you, like this freeware below from the Chicago Board of Options Exchange (CBOE).  You simply enter a series of inputs (the key ones are noted below) and these will be used in calculating the option's Implied Volatility.

In using Implied Volatility, here are a few things to keep in mind:

> The higher the percentage of Implied Volatility, the higher the option price.

> The further the strike price is out-of-the-money, the lower the percentage of Implied Volatility.

> Generally speaking, Implied Volatility tends to decline over time as the option approaches expiration.  The rate of decline is greater for out-of-the-money options.

> Implied Volatility tends to level off for deep in-the-money options.

Other factors to consider with respect to volatility and option pricing include:

Historical Volatility: Historical Volatilities for most U.S. stocks can be downloaded for free from the CBOE website for various months.  Historical Volatility is an averaging of past option prices for a security, and it can vary based on such factors as seasonality or the historical time frame that is being looked at.  Implied Volatility is normally measured against Historical Volatility to determine how much of a premium one is paying for a contract.  What I find to be a useful rule of thumb is to avoid buying an option contract where Implied Volatility is significantly higher than Historical Volatility for the same security.  There is, though, one exception.

Volatility of the Underlying:  Having just given my rule of thumb above, there is one exception that I may make with respect to a stock option.  There are occasions when Implied Volatility can be as much as double Historical Volatility, and the trade is still worth it.  In this case, it's because the Implied Volatility of the option is being driven by high volatility in the underlying.  So, a modified rule of thumb here is that Implied Volatility should be less than or equal to the underlying's volatility.  A number of chart programs calculate the volatility of the underlying.  Big Charts.com, a free service, also lets you add a parameter to measure volatility in their Interactive charts.

Open Interest (OI):  Open Interest represents the number of option contracts outstanding at various strike prices.  For strikes where there are high levels of OI, the premiums tend to fetch a higher price because of demand.  Implied Volatility may therefore rise, but it is reflecting the demand for the particular contract, and not necessarily a rise in the volatility of the underlying.   If you decide to trade a contract where the OI is especially high relative to other strikes, be aware that you may be truly buying that contract at a premium.  In these cases, it's particularly important to look at the option's "Delta" (more on that below).  

Index Options v.s. Stock Options: If you plan to buy and trade index options, there are a few things you need to remember.  Options on indices are a little trickier with respect to Implied Volatility and pricing, especially since they are frequently used by large investors for hedging.  Consequently, Put prices tend to be higher.  Implied Volatility for index options is also normally higher than the volatility of the underlying index.   Bid and Ask prices are also generally higher and wider for index options than for stock options.  In both cases, you want to pay close attention to the "spread" (i.e., the difference between the Bid and Ask prices) in helping to determine how expensively the premium may be priced.   I elaborate more on this a little later. 

This leads us to the next important part of our discussion, which is to have an idea going in of how much we can expect the option to appreciate (or depreciate) as it reaches expiration.  For this, we look to OPTION SENSITIVITY to guide us.  To measure option sensitivity, we need to understand the "GREEKS." 

Using the Greeks
Greeks are absolutely important in helping you pick the right option.  Amazingly, they are frequently overlooked by novice option traders, probably because the terms sound more complicated than they really are.  Quite simply, the Greeks are terms that are used to distinguish different types of sensitivities that affect an option's price.  Since an option's price is affected by different factors, as we saw earlier, the Greeks tell us how sensitive the option is to a change in any of these factors.  Again, an options calculator program like the one above computes the Greeks for you, along with Implied Volatility.  

There are six Greeks:  Delta, Gamma, Theta, Vega, Rho and Psi.  Of the six Greeks, most option traders are mainly concerned with the first four.  (Rho is related to a change in interest rates, and Psi is related to a change in dividend rates.)  Of the first four, Delta is at the top of the list.  

DELTA measures the rate that the option price changes when the price of the underlying changes. Therefore, let's say the price of an option is $5, it has a Delta of .40, and the current price of the underlying is $50.  If the underlying rises 2 dollars to $52, the option price will rise to $5.80 (i.e. .40 x $2 = .80 + $5 = $5.80).  If instead the same option had a Delta of .60, the option price would have risen to $6.20 (i.e. .60 x $2 = 1.20 + $5 = $6.20).  

Based on these examples, look at the options calculator below, and calculate what the option price would be for the Call if the underlying rises 5 dollars, from $60 to $65.

If you calculated $7.33, you were correct (5 x .0565 = 2.83 + 4.506 = 7.331, or $7.33). 

You should know that the Delta for a Put option is normally accompanied by a minus (-) sign, as in the above example, but don't be thrown by this, as it is not intended to suggest that the Delta for the Put option is negative.  There are reasons for this that have to do with the theoretical pricing model, but the more practical and significant point is that the same principles for Delta apply, whether for a Put or a Call:

Delta is one of the reasons why buying a "cheap" out-of-money option can lose you money in the end.  Normally, if you add the Delta for a Call and a Put for the same strike price, it should equal 1.0.  If, say, you bought a Put expecting the market to drop, but it rose instead, the Delta on the Call is going to rise, while the Delta for the Put is going to drop.  If the Call Delta hit .80. the Put Delta would be -.20 (remember, ignore the minus sign).  

You can see why Delta is at the top of the list of Greeks.  When I'm an option buyer, my preference is normally to stick with at-the-money options, or no more than one strike price out-of-the-money, in order to take good advantage of Delta.  As a good rule of thumb, try to look for options where the Delta is .45 to .47 if the option is out-of-the-money.

Since Delta is such a significant factor in options pricing, it's also useful to know how much the Delta itself moves.  That leads us to our next Greek.

GAMMA measures the rate that the Delta changes when the price of the underlying changes. 

Using the earlier calculator example, let's see what would happen to the Delta based on the Gamma rate, which is 0.037.  We know from the previous example that, based on the Delta, the Call option price would be $7.33 with a $5 rise in the underlying.  The Gamma tells us how much the Delta should increase too:  

0.037 x 5 = 0.185 + 0.565 = 0.75.  

Therefore, based on the Gamma for this Call option, a $5 rise in the underlying from $60 to $65 would also increase the Delta from 0.565 to 0.75.  Of course, stocks and indices are always moving, and so is the Delta.  If you had bought a Put expecting the stock to drop, and it fell from $60 to $55, the Put Delta would have increased at about the same rate (.76) based on a Gamma of  0.038 (as noted in the calculator).  Keep in mind, of course, that the calculator is computing theoretical values, though in the real world they are fairly accurate.

The next two Greeks measure the sensitivity of the two other key factors in an option's price that we spoke of earlier: Time Value and Implied Volatility.

THETA measures the rate of Time Decay for an option.  

Remember, we said that part of an option's value is determined by it's time to expiration.  The longer its time before expiration, the greater its Time Value.  Conversely, the closer it is to expiration, the faster it's Time Value erodes.  That erosion is called Time Decay, and the rate of decay is measured by Theta.  

Basically, when trading options, time is as much a consideration as market direction.  Another way to look at it is that time is the friend of the option seller, and the enemy of the options buyer.  So, when trading options, you always want to have an eye on where the Theta value is at.  

In the calculator example above, the Call option has a Theta of -0.027.  The option is 90 days away from expiration.  Unlike Delta, the minus (-) sign for Theta is exactly that.  What this means is that the Call's price will drop overnight by its Theta value (as well as the Put, of course).  Therefore, the Call option price will fall to $4.48 (i.e., $4.506 - 0.027 = 4.479, or $4.48).  Big deal, you might say, that's only a couple of cents.  Let's see what happens when the option gets closer to expiring.

In the above examples you can see how the Theta has increased over 30 to 10 to 5 days before expiration.  Note how much the option prices have fallen as well for the Call and the Put.  That's why it's important to remember how critical a factor time is when you decide to enter an options trade.  

A couple of other points on Time Decay and Theta.  These examples were all for an at-the-money option.  If you had bought a Call and it was in-the-money, Theta would normally be lower.  If it was out-of-the-money, it would be even lower, perhaps as low as zero -- but that's because the option has lost it's Time Value.  If you are buying an option well into the front month, and it has a Theta of zero, then it means the option has no Time Value at all.  

VEGA measures how much an option's price will change with a change in Implied Volatility.  

We discussed before how important Implied Volatility is in measuring whether an option is fairly priced or overpriced, and gave some ways to determine if it is especially high for a particular option.  Vega tells us how much the option price is likely to increase, based on the current price of the option and a change in Implied Volatility.  

In this example, Implied Volatility is 35%, with a Vega of 0.117.   If Implied Volatility increases to 37% (an increase of 2%) the Call price will increase to $4.74 (i.e., 0.117 x 2 = .234 + 4.506 = 4.74).  Note in the calculation that even though we are talking about a 2% rise in Implied Volatility, we multiply the Vega by a whole number.   

Vega normally decreases as the option moves closer to expiration.  This is because, as we mentioned earlier, Implied Volatility also tends to decline, and at a faster rate for out-of-the-money options.  Vega will also decrease the deeper the option is in-the-money, since Implied Volatility tends to level off.  

Taking the Short View
Up to now, we've looked at all this primarily from the perspective of the option buyer.  So, how can you effectively use this knowledge to benefit you as an option seller?  And, what should option buyers be aware of from the seller's side of the equation? 

Because an option buyer has the right of exercise, the option seller's position is always more tenuous, and can result in susbstantial losses if forced to cover a sale.   Given this situation, your goal, of course, is the exact opposite of the option buyer's.  You want to sell the option at the highest possible price, and then have it expire worthless, so you can keep all the premium you made on the sale.   Far out-of-the-money options are normally best for this purpose.  The nominal price of the contracts is lower for these options, frequently below $1.  But, it could be fatal to turn your nose up at this and be lured by contracts at higher strikes just because they have a higher asking price.  You also need to look at the value and pricing factors we mentioned earlier, but from a different perspective.  With that in mind, here are some things to consider:

>  Time Decay:  Remember I said earlier that time was the friend of the option seller?  Well, time gets even friendlier as expiration approaches, since it's helping to erode the value of the option.  Take a look at our earlier discussion of the effects of Theta as an option approaches expiration.   This will give you a good idea of how much Time Value the option is losing, or if it indeed has already lost it.

>  Implied Volatility:  Generally, a period of high volatility in the underlying market normally means high volatility in the options market.  This is reflected by Implied Volatility, and such a climate is most favorable to an option seller.  You get to walk away with more premium from the sale than in a lower volatility environment.  I said earlier Implied Volatility tends to decrease the farther out-of-the-money the option is;  however, the percentage could still be high relative to those that are closer to the money, meaning it is overpriced.   One way to help determine this is by analyzing the "spread."

>  The Spread:  Something that both option buyers and sellers should always look at is the spread, which is the difference between the Bid and Ask price of the option.  Market makers at the options exchange make their money on the spread as they process buy and sell orders.  In the end, they're the ones who set the price, using the various factors we've discussed.  While the nominal price of an option might suggest it is "cheap," it's relative price may be higher than it appears on the surface.  Options expert Bernie Schaeffer recommends using the spread to determine the price percentage being applied at different strikes.  Let's say, for instance, that the spread for an out-of-the-money strike is 15 cents at the Bid, and 20 cents at the Ask.  Let's also say, the next higher strike has a Bid of 80 cents, and an Ask of 85 cents.   The spread for both is 5 cents.  So, which option is more expensive?  The nominal price might lead you to think that the one closer to the money is more expensive (i.e., 85 cents v.s. 20 cents).  However, if you divide the spread by the Bid price, a whole other picture emerges:  5 cents/15 cents = .33;  5 cents/80 cents = .06.  What this comes down to is that the premium for the so-called "cheaper" option is 33% higher at this strike price, compared to 6% at the next higher strike.  This is a benefit to an options seller, and a big red flag for an options buyer, because the Delta will normally be low at this strike, and therefore price appreciation will also be poor.

> Open Interest:  OI tends to be high at three different strikes: those that are at-the-money, those that are one strike price out-of-the money, and those that are farthest out-of-the-money.  It's the last category you're most interested in as an option seller.  Given the spread pricing I just mentioned above, you can see why.

> Put/Call Ratio of Open Interest:  Another way I use OI is to calculate a ratio of OI Put v.s. OI Call positions at various strikes (i.e., Put OI/Call OI).  Then I calculate the total OI positions of both to arrive at an overall ratio for comparison.  It helps to use a spreadsheet for this, which can usually be downloaded from the CBOE for numerous stocks and indices.  Besides being a good read on trader sentiment towards a particular security (i.e., the percentage of bulls v.s. bears), it gives a good idea of which way the pricing bias is skewed.  And the bias can change from one strike price to another.  For stocks, a ratio of 0.80 or higher indicates the bias is leaning bearish, and that Puts are likely pricier; below 0.50, sentiment is more strongly bullish, and Calls are likely pricier.  For indices, I use 1.00 as the threshold, since large investors frequently use indices for hedging.

> Delta: Of course, as an option seller, Delta is another important factor you want to look at.  As we stated earlier, Delta decreases the farther an option is out-of-the-money.  For an option seller, the lower the Delta, the better.  

Timing Your Options Trades
Finally, we want to make a few points about when, and when not, to enter option trades.  Assuming you've done your analysis of the underlying, and taken the foregoing pricing factors into consideration, then obviously you want to pick the most auspicious time to trade.  The following are more guides than rules, and, as with trading in general, timing is always more of an art than a science.  But they've generally helped keep me out of trouble.

> Front Months:  If you're an option buyer, and unless you are really adept at options trading, front months are very risky.  Time is always working against you.   If you decide to trade a front month, it's best not to be greedy, and if you've realized a percentage gain, I recommend you take your money off the table quick, rather than try to squeeze out the last percentage point.   For an option seller, however, a front month can be very rewarding.  Look for the out-of-the-money options, particularly where there is heavy Open Interest, and apply the pricing factors we mention above.  

> Stops:  Applying stops for options is tricky.  Each of the exchanges that trade options have their own policies regarding stops.  In highly volatile markets, stops on options can also knock you out of a position prematurely.  If you are an options buyer, however, you can use time to your benefit.  Bernie Schaeffer recommends using a "time stop," meaning that you should buy your option at least 2-3 months before expiration, and exit the position before it enters the front month.  Remember, once the front month is reached, Time Value rapidly declines, along with the price of the option.

> Expiration & Witching Days:  The last day for trading front month contracts is the third Friday of the month.  A "witching day" is a term used by traders to describe those Fridays that option and futures contracts expire.  Normally, these days are accompanied by high volatility, and are generally the worst days for option buying.  I've seen cases where the option price significantly dropped in the days following an expiration or witching day -- even though the underlying made a favorable move.  This is particularly true when entering a front month.  For an option seller, however, the high volatility climate is exactly what you're looking for.

> The First & Last Hour of Trading:  These are generally the two most volatile periods in the trading day.  As a buyer, you want to avoid them and wait for a quieter period.  Usually, the lunchtime hours have less volume, and pricing is less affected by volatility.  On the other hand, if you're looking to sell an option, then these two hours can be a good time to pounce.

* * * *

Hopefully, this guide has been useful to you, and will help set you on a path to profitable option trades.   We've only scratched the surface, and I recommend you continue your study of how to make options work for you.  

Finally, we believe you can never know too much about options trading, and recommend visiting the CBOE website, which offers an excellent and extensive options tutorial that you can download for free. 

For an extensive study and descriptions of money-making options strategies, we also highly recommend the book Option Volatility & Pricing, widely used and praised by options traders.  Click here fore more details about the book.


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ęCopyright 2003 Tony Carrion.  All content presented is the exclusive property of Market Harmonics. com, which is owned & operated by T. Carrion & Co., LLC, and may not be duplicated or distributed without the express written consent of the author.