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9 Weeks to Better Options Trading: An Options Pricing Primer


Veteran options trader Steve Smith breaks down the concepts of implied volatility and time decay.

Editor's note: To help investors profitably navigate the options market, Minyanville has launched "9 Weeks to Better Options Trading," an educational series aimed at increasing trader understanding of the nuts and bolts of options, with an emphasis on real-world applications. In this series, veteran options trader and author of OptionSmith, Steve Smith will demystify a range of topics from options pricing to trading strategies to special situations like earnings reports and takeovers.

For the first article in the series, click here.

We are now on the second week of our nine-week journey into the world of options, and now that we've got some of the basics out of the way, it's time to jump into options pricing.

So what do former NBA star Allen Iverson and implied volatility have in common? They have both been labeled "The Answer." While Iverson has been more of a question lately (how exactly did he spend that $100 million+?), implied volatility remains the key to answering the number-one question on an option trader's mind: Is this option "cheap" or "expensive"?

The most commonly used apparatus for valuing options is the Black-Scholes model, which considers five factors in calculating a particular option's theoretical fair value:

1. The price of the underlying security

2. The strike price

3. The time, or expiration date of the option

4. Interest rates

5. Implied volatility

The first four inputs are known variables. To get number five, we plug those four inputs into the Black-Scholes model. This would give us "theoretical" implied volatility, which helps us answer our big question above. But given that options trade regularly, there is already an "actual" implied volatility assigned to each option based on its price, which is constantly updating in real-time. Therefore, our mission, should we choose to accept it, is to determine whether an option's current price looks cheap or expensive based on its volatility level.

Let's go over exactly what implied volatility is. Implied volatility is a measure of the probability of a certain percentage price move occurring within a given time frame. It is typically anchored to the underlying's historical volatility, which measures recent price action.

A notable exception would be in biotechs such as Dendreon (DNDN) or Biogen (BIIB). Shares of these names can trade rather benignly for months on end, while the prospect of volatility-inducing events, like FDA rulings, keeps implied volatility at elevated levels. And more related to our current events, options on banks like JPMorgan (JPM) and Bank of America (BAC) have implied volatilities that are premiums to historic levels because of ongoing worries over exposure to Europe and other issues.

Let's look at the April at-the-money calls in two very different types of stocks. (CRM), a high-octane momentum stock which regularly makes massive price swings, has a current 30-day historical implied volatility (HV) of 38%. On the other hand, the relatively staid and less-exciting utility Consolidated Edison (ED) currently has a 30-day HV of 11%. But which one's options are cheaper? is the obvious answer, but to be sure, let's look under the hood at implied volatility readings.'s April $135 call has an implied volatility of 35%, carrying a three-percentage-point, or 5.7% discount to HV. On the other hand, Con Ed's April $57.50 calls carry a 12.5% implied volatility, which is a 1.5-percentage-point, or 14% premium to HV. So at this point, I would say's options, which trade at a discount, are cheaper than Con Ed's, which trade at a premium.

Reverting to the Mean

Now let's look at how historical volatility can be used to avoid the "options don't work" argument put forth by naysayers who get frustrated when they make an options bet, are correct on the direction of the underlying, yet don't make money.

Keeping with, ahead of its February 24 earnings report, implied volatility climbed up to 50%, which was well above the then 32% rate at which the 30-day historical was running. This was because the options market was pricing in the 7% price move that the shares had averaged over the past four earnings reports.

The down-and-dirty way to gauge what the options market is pricing is to look at the straddle and revert the IV back to the mean. (I will elaborate further on this in an upcoming piece on trading earnings and other special situations.) An increase in implied volatility ahead of an event is simply the expression of a higher probability of a larger-than-usual price move within a given time frame. In this sense, an increase in implied volatility is an artificial expansion of time. In other words, what could happen over a long period of time is now being priced into a shorter period of time.

Understanding where IV stands relative to HV, and why it is at the current level is crucial to valuing current option prices and anticipating future moves. If a volatility-inducing event is anticipated -- like with an earnings report -- implied volatility will revert back to the mean after the event. But if there is unanticipated news -- like a surprise FDA ruling on a drug -- IV will spike. So regardless of what happened, one should expect that IV on options would revert toward the mean of around 35% following the report. This means one would need at least a 6% price move to break even. (Note: This is not 7% because the options would still retain some time value. This is part of an extended discussion beyond the scope of this article.)

As it turned out, blew away expectations and jumped some 10% following earnings, so an owner of calls enjoyed a nice profit. However, if shares rose just 3% after earnings, an owner of calls would have actually lost money since the increase in the stock price wasn't sufficient enough to offset the expected decline in implied volatility.

A great free site that offers an option calculator, and historical and implied volatility readings over various time periods can be found here.

Time Is Square, Man

There's a basic math formula used in the Black-Scholes model which is a good starting point for understanding the rate of decline in an option's value due to the passage of time, also knows as time decay or theta. Basically, we use the square root of time to calculate and plot time decay. The math involved in the nitty-gritty of evaluating theta can be extremely complex, so focus on this: Time decay accelerates as expiration approaches.

For example, if a 30-day option is valued at $1.00, then the 60-day option would be calculated as $1 times the square root of 2 (2 because there is twice as much time remaining). So all else being equal, the value of the 60-day option is $1.41, or $1 times 1.41 (1.41 is the square root of 2). A 90-day option would be $1 times the square root of 3 (3 because there is three times as much time remaining) for an option value of $1.73. (1.71 is the square root of 3).

If you notice, the premium of the 60 day over the 90 day ($0.32) is less than that of the 60 day over the 30 day ($0.41). So again, the important takeaway is to realize that the closer an option gets to expiration, the rate at which time value decays gets faster.

Here are some other basic concepts you need to know about theta:
  • An options theta can be calculated as follows: If a particular option's theta is -10, and 0.01 of a year passes, the predicted decay in the option's price is about $0.10 (-10 times 0.01 is 0.10).
  • At-the-money options have the highest theta. Theta decreases as the strike moves further into the money or further out of the money. In-the-money options are mostly composed of intrinsic value (the difference between the strike price of the option and the market price of the underlying), while out-of-the-money options have a larger implied volatility component.
  • Theta is higher when implied volatility is lower. This is because a high implied volatility suggests that the underlying stock is likely to have a significant change in price within a given time period. A high IV artificially expands the time remaining in the life of the option, helping it retain value.
Next week, when we discuss calendar spreads, I'll drill down into isolating theta or decay, and how to transform it from a drag on performance to a tailwind.

For complete access to Steve Smith's OptionSmith portfolio, which returned 28% in 2011, click here.

Here is a complete schedule for "9 Weeks to Better Options Trading":

Week 1: 5 Rookie Mistakes Options Traders Make

Week 2: Option Pricing Basics: Understanding Implied Volatility and Time Decay

Week 3: Trading Strategy: Calendar Spreads

Week 4: Trading Strategy: Butterfly Spreads

Week 5: Trading Strategy: Iron Condors

Week 6: Trading Strategy: Risk/Reversals

Week 7: Trading Strategy: Back Spreads

Week 8: Managing Risk

Week 9: Special Situations: Earnings Reports, Takeovers, and Extreme Market Moves
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No positions in stocks mentioned.

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