Chapter 15 Option Volatility "The market can remain irrational longer than you can remain solvent" The word volatility, particularly to newcomers, conjures up images of wild price swings in stocks (most often to the downside.) If a stock moves sideways in a trading range, these same newcomers might say that the market isn t volatile. This definition of volatility is accurate, but options traders need to be able to quantify the price swings in the market in order to place a value on an option. Volatility is simply a mathematical computation of the magnitude of movement in an option. This is based on the activity in the underlying security. Of the market is making a rapid move up or down, volatility will rise; in a quiet market volatility will be low. Getting back to the basics, it s important to remember that option premiums are manufactured from two main ingredients: intrinsic value and time value. Intrinsic value is an option s inherent value, or in other words, an option s equity. If you own a $50 call option on a stock that is trading at $60, this means the intrinsic value or equity of this option is $10 (60 50 = 10). The only factor that influences an option s intrinsic value is the underlying stock s price in relation to the option s strike price. No other factor can influence an option s intrinsic value. Using the same example, let s say this option is priced at $14. This means the option premium is priced $4 more than its intrinsic value. This is where time value (extrinsic value) comes into play. Time value is the additional premium that is priced into an option, representing the amount of time left until expiration. The price of time is influenced by various factors, such as time until expiration, stock price, strike price and interest rates, but none as significant as implied volatility. Implied volatility represents the expected volatility of a stock over the life of the option. As expectations change, option premiums react appropriately. Implied volatility is directly influenced by supply and demand of the underlying options and by the market s expectation of the share price s direction. As expectations rise, or as the demand for an option increases, implied volatility will rise. Options that consist of high implied volatility levels will result in high-priced option premiums. Conversely, as the market s expectation decreases, or demand for an option diminishes, implied volatility will decrease. Options containing lower levels of implied volatility will result in cheaper option prices. This is an important because the rise and fall of implied volatility will determine how expensive or cheap time value is to the option. There are a variety of mathematical models that attempt to value options. The most common is the Black-Sholes model, named after the two University of Chicago professors who designed it in 1973 and later won a Nobel prizes for its creation. No matter what option model is used, the value of an option depends on five variables: 1) the underlying stock price, 2) the option s strike price, 3) the time left until expiration, 4) current risk free interest rate, and 5) volatility as measured by the annual standard deviation. Of these five components of option value, volatility and time left until expiration are the two most important variables in options trading, even more important than the underlying price. There are two types of volatility: historical and implied. Historical volatility is a mathematical calculation of the magnitude of changes in stock price on an annualized basis. Implied volatility, on the other hand, is the market s expectation for the magnitude of changes in stock price on an annualized basis from today until the option expires; it is the common denominator of option prices. Stated another way, implied volatility is the market s forecast for where historical volatility will be tomorrow. Option Volatility Page 1
Figure 1 A Graph of Implied Volatility on NDX The chart above plots daily readings for both historical volatility and implied volatility for the past 12 months for at-the-money Nasdaq composite index options. The blue line is historical volatility and the gold line is implied volatility. There are two things to notice on this chart right away. One, implied volatility is usually higher than historical volatility. Two, both measures of volatility have declined steadily in the past year. Why? Uncertainty was taken out of the stock market as the economy improved and a quick military victory in Iraq became likely. Due to high implied volatility levels, buying options between December and March would have been discouraged because high implied volatility made stock options expensive. In the June to November period, however, implied volatility fell to low enough levels to be cheap. Buying options or net long premium positions in that period would be an appropriate strategy. Just as prices/earnings ratios allow comparisons of stock prices, implied volatility enables comparison of options on different underlying instruments and comparison of the same option at different times. In trading options you must learn to be flexible, using whatever the market gives you to your best advantage. Using only your favorite strategy may not be appropriate for the current market conditions. Changes in volatility levels require the use of different strategies, depending on the levels of both implied and historical volatility. The formula for calculating historical volatility would be familiar to anyone with a statistics background because it is the calculation for the variance of a sample. There is a wide array of options software that will calculate volatility on a real-time basis, which make it easier for the trader. However, it is good mental exercise to know how this number is derived, and webbased resources such as ivolatility.com are also excellent sources of volatility for free or at reasonable subscription levels. Calculating Historical Volatility The following table shows the calculation for 10-day historical volatility (variance of a 10-day sample.) To calculate a 10-day historical volatility, take the closing price of today and divide by the closing price of yesterday and place that number in the Option Volatility Page 2
third column below. This column houses the values of X. Take the natural log of X and place it in column four. Average all observations in the column four. Now square the difference between Ln(X) and the average Ln(X) and place that number in column five. Sum column five and divide it by the number of days in the calculation, minus 1 (in this case 10-1=9). The formula gives us 0.00051 at this point. The next step is to take the square root of 0.00051. The result is the raw variance. Now the raw volatility number must be annualized. To do so, take the square root of 260 trading days and multiply it by the raw volatility number. The final result is 36.40% for the 10-day historical volatility. Day Stock Price X = Ptoday/Pyest Ln(X) (Ln(X) Avg) Squared 1 $26.74 2 $27.03 1.0108 0.010742 0.000005 3 $26.81 0.9919-0.00813 0.000066 4 $27.92 1.0414 0.040566 0.001646 5 $28.05 1.0047 0.004689 0.000022 6 $27.21 0.9701-0.03036 0.000921 7 $28.13 1.0338 0.033241 0.001105 8 $28.88 1.0267 0.02635 0.000694 9 $29.17 1.0100 0.00995 0.000099 10 $29.04 0.9955-0.00451 0.000020 11 $29.12 1.0028 0.002796 0.000008 Average= 0.008534 Sum 0.004587 For 10 day Volatility Sum / 10-1 0.00051 Raw Volatility Sq Root 0.022575 Annualize to 260 Days Sq Root of 260 16.12452 0.02257 Multiplied by 16.124515 0.364007 Annual Historical 10-Day Vol 36.40% Using this formula, a trader can calculate historical volatility for other time frames, such as 20-day or 50-day historical volatilities. It is much easier and faster to use one of the myriad of option software packages or information services (such as ivolatility.com) for calculations of implied and historical volatilities. Differences between Historical and Implied Volatilities Every trading market is built upon expectations, and the options market is no different. Let s assume that an earnings report for Cisco Systems (CSCO) is due tomorrow and forecasts for its earnings are positive. The day before the earnings release a trader calculates both historical volatility and implied volatility on CSCO. Historical volatility has no mechanism for quantifying market expectations, so historical volatility is already expecting positive news for CSCO tomorrow, the market will make a trader pay more to buy a call option today. When traders talk about volatility, it s usually implied volatility that they are talking about. Implied volatility is associated with an option, and should be the basis for almost all trading decisions! Normally, you would want to buy premium when volatility is low and sell premium when volatility is high. In theory, all calls and puts for a given underlying security should have the same implied volatility, because they are all based on the same underlying security. In practice, however, each call and put has its own implied volatility and therefore will be valued at slightly different levels. Implied volatility is derived from the closing price of the option, whereas historical volatility is calculated based on the closing price of the underlying security. Intraday fluctuations in the underlying will create option volatility that is much higher than the Option Volatility Page 3
volatility based on the closing price. These intraday fluctuations can temporarily distort option value, and can often provide good trading opportunities. It will become clear later in this text just how important volatility is in trading options. In fact, it is possible that a trader can be wrong in the market direction and still make money, and be right the market direction yet lose money! A famous example of just such a circumstance occurred during the 2008 stock market crash. A trader bought OEX calls at a normal volatility rate of 25% prior to the stock market crash (in the 2008 break, most major stock indices lost half their value in a series of a few days). In the aftermath of the crash, while prices were stabilizing, this trader checked the quote for the OEX calls on a strike price 50% higher than where the market is today. Because implied volatility soared to 150%, the trader was able to offset his call positions at a profit. This example, while unusual, illustrates why trader talk about buying 12 percent volatility and selling 40 percent volatility. If you are buying an option, you must buy when implied volatility is lower than normal or sell an option when it is significantly higher than normal. In this sense, it would not be an unfair characterization to view the implied volatility as something very similar to a price/earnings ratio for a stock. How Implied Volatility Affects Options The success of an option trade can be significantly enhanced by being on the right side of implied volatility changes. For example, if you own options when implied volatility increases, the prices of these options climb higher. However, a change in implied volatility for the worse can create losses, even when you are right about the stock s direction! Each listed option has a unique sensitivity to implied volatility changes. For example, short-dated options will be less sensitive to implied volatility, as opposed to long-dated options. This is simply based on the fact that long-dated options have more time value priced into them, while short-dated options have less. Also consider that each strike price will respond differently to implied volatility changes. Options with strike prices that are near the money are most sensitive to implied volatility changes, while options that are further in the money or out the money will be less sensitive to implied volatility changes. An option s sensitivity to implied volatility changes can be determined by vega an option greek. Keep in mind that as the stock s price fluctuates and time until expiration passes, vega values increase or decrease, depending on these changes. This means an option can become more or less sensitive to implied volatility changes. How to Use Implied Volatility to Your Advantage One effective way to analyze implied volatility is to examine a chart. Many charting platforms provide ways to chart an underlying option s average implied volatility, meaning multiple implied volatility values are tallied up and averaged together. For example, the Volatility Index (VIX) is calculated in a similar fashion. Implied volatility values of near-dated, near-the-money S&P 500 Index options are averaged to determine the VIX s value. The same can be accomplished on any stock that offers options. Option Volatility Page 4
Figure 2 A Graph of Implied Volatility Using INTC Options Figure 1 illustrates how implied volatility is applied to a chart. As you examine it, you ll see it fluctuates the same way prices do. Implied volatility is expressed in percentage terms and is relative to the underlying stock and how volatile it is. For example, General Electric (GE) stock will have lower volatility values than Apple Computer (AAPL) because Apple s stock is much more volatile than General Electric s. AAPL s volatility range will be much higher than GE s. What might be considered a low percentage value for AAPL might be considered relatively high for GE. Because each stock has a unique implied volatility range, these values should not be compared to another stock s volatility range. Implied volatility should be analyzed on a relative basis. Meaning, after you have determined the implied volatility range for the option you are trading, you will not want to compare it against another. What is considered a relatively high value for one company might be considered low for another. Figure 3 Determine an Implied Volatility Range Using Relative Values Figure 2 is an example of how to determine a relative implied volatility range. Look at the peaks to determine when implied volatility is relatively high, and examine the troughs to conclude when implied volatility is relatively low. By doing this, you determine when the underlying options are relatively cheap or expensive. If you can see where the relative highs are (highlighted in red), you might forecast a future drop in implied volatility, or at least a reversion to the mean. Conversely, if you determine where implied volatility is relatively low, you might forecast a possible rise in implied volatility or a reversion to its mean. Implied volatility, like everything else, moves in cycles. High volatility periods are followed by low volatility periods, and vice versa. Using relative implied volatility ranges, combined with forecasting techniques, helps investors select the best possible trade. When determining a suitable strategy, these concepts are critical in finding a strategy with a high probability of success, helping you maximize returns and minimize risk. Using Implied Volatility to Determine Strategy Option Volatility Page 5
You ve probably heard the phrase, Buy undervalued options and sell overvalued options. While this process is not as easy as it sounds, it is a great methodology to follow when selecting an appropriate option strategy. Your ability to properly evaluate and forecast implied volatility will make the process of buying cheap options and selling expensive options that much easier. When forecasting implied volatility, there are four things to consider. Make sure you can determine if implied volatility is high or low and whether it is rising or falling. Remember, as implied volatility increases, option premiums become more expensive. As implied volatility decreases, options become less expensive. Because volatility is mean reverting, don t forget that as implied volatility reaches extreme highs or lows, it is likely to revert back to its mean. If you come across options that yield expensive premiums due to high implied volatility, understand that there is a reason. Check the news to see what caused such high company expectations and high demand for the options. It is not uncommon to see implied volatility plateau ahead of earnings announcements, merger and acquisition rumors, product approvals, and other various news events. Because this is when a lot of price movement takes place, naturally the demand to participate in such events will drive the option s price higher. Keep in mind that after the market-anticipated event occurs, implied volatility will collapse and revert back to its mean. When you see options trading with high implied volatility levels, consider selling strategies. As option premiums become relatively expensive, they are less attractive to purchase and more desirable to sell. Such strategies include covered calls, naked puts, short straddles and credit spreads. On the contrary, there will be times when you discover relatively cheap options, such as when implied volatility is trading at or near relative to historical lows. Many option investors use this opportunity to purchase long-dated options and look to hold them through a forecasted volatility increase. When you discover options that are trading with low implied volatility levels, consider buying strategies. With relatively cheap time premiums, options are more attractive to purchase and less desirable to sell. Such strategies include buying calls, puts, long straddles and debit spreads. Conclusion This modules purpose is to give you a better understanding of what implied volatility is, how it works and how it can affect an option premium. In the process of selecting strategies, expiration month or strike price, you should now gauge the impact that implied volatility has on these trading decisions, and therefore, make better choices. You should also better understand a few simple volatility forecasting concepts. This knowledge can help you avoid buying overpriced options and avoid selling underpriced ones. As mentioned earlier, one motto that option investors live by is to buy undervalued options and sell overvalued options. As you apply the concepts discussed today, it will drastically improve your abilities to trade with the trend of implied volatility. Option Volatility Page 6