161 lines
37 KiB
Plaintext
161 lines
37 KiB
Plaintext
CHAPTER 3
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Understanding Volatility
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Most option strategies involve trading volatility in one way or another. It’s easy to think of trading in terms of direction. But trading volatility? Volatility is an abstract concept; it’s a different animal than the linear trading paradigm used by most conventional market players. As an option trader, it is essential to understand and master volatility.
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Many traders trade without a solid understanding of volatility and its effect on option prices. These traders are often unhappily surprised when volatility moves against them. They mistake the adverse option price movements that result from volatility for getting ripped off by the market makers or some other market voodoo. Or worse, they surrender to the fact that they simply don’t understand why sometimes these unexpected price movements occur in options. They accept that that’s just the way it is.
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Part of what gets in the way of a ready understanding of volatility is context. The term
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volatility
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can have a few different meanings in the options business. There are three different uses of the word
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volatility
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that an option trader must be concerned with: historical volatility, implied volatility, and expected volatility.
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Historical Volatility
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Imagine there are two stocks: Stock A and Stock B. Both are trading at around $100 a share. Over the past month, a typical end-of-day net change in the price of Stock A has been up or down $5 to $7. During that same period, a typical daily move in Stock B has been something more like up or down $1 or $2. Stock A has tended to move more than Stock B as a percentage of its price, without regard to direction. Therefore, Stock A is more volatile—in the common usage of the word—than Stock B. In the options vernacular, Stock A has a higher historical volatility than Stock B. Historical volatility (HV) is the annualized standard deviation of daily returns. Also called
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realized volatility, statistical volatility
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, or
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stock volatility
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, HV is a measure of how volatile the price movement of a security has been during a certain period of time. But exactly how much higher is Stock A’s HV than Stock B’s?
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In order to objectively compare the volatilities of two stocks, historical volatility must be quantified. HV relates this volatility information in an objective numerical form. The volatility of a stock is expressed in terms of standard deviation.
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Standard Deviation
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Although knowing the mathematical formula behind standard deviation is not entirely necessary, understanding the concept is essential. Standard deviation, sometimes represented by the Greek letter sigma (σ), is a mathematical calculation that measures the dispersion of data from a mean value. In this case, the mean is the average stock price over a certain period of time. The farther from the mean the dispersion of occurrences (data) was during the period, the greater the standard deviation.
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Occurrences, in this context, are usually the closing prices of the stock. Some utilizers of volatility data may use other inputs (a weighted average of high, low, and closing prices, for example) in calculating standard deviation. Close-to-close price data are the most commonly used.
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The number of occurrences, a function of the time period, used in calculating standard deviation may vary. Many online purveyors of this data use the closing prices from the last 30 consecutive trading days to calculate HV. Weekends and holidays are not factored into the equation since there is no trading, and therefore no volatility, when the market isn’t open. After each day, the oldest price is taken out of the calculation and replaced by the most recent closing price. Using a shorter or longer period can yield different results and can be useful in studying a stock’s volatility.
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Knowing the number of days used in the calculation is crucial to understanding what the output represents. For example, if the last 5 trading days were extremely volatile, but the 25 days prior to that were comparatively calm, the 5-day standard deviation would be higher than the 30-day standard deviation.
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Standard deviation is stated as a percentage move in the price of the asset. If a $100 stock has a standard deviation of 15 percent, a one-standard-deviation move in the stock would be either $85 or $115—a 15 percent move in either direction. Standard deviation is used for comparison purposes. A stock with a standard deviation of 15 percent has experienced bigger moves—has been more volatile—during the relevant time period than a stock with a standard deviation of 6 percent.
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When the frequency of occurrences are graphed, the result is known as a distribution curve. There are many different shapes that a distribution curve can take, depending on the nature of the data being observed. In general, option-pricing models assume that stock prices adhere to a lognormal distribution.
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The shape of the distribution curve for stock prices has long been the topic of discussion among traders and academics alike. Regardless of what the true shape of the curve is, the concept of standard deviation applies just the same. For the purpose of illustrating standard deviation, a normal distribution is used here.
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When the graph of data adheres to a normal distribution, the result is a symmetrical bell-shaped curve. Standard deviation can be shown on the bell curve to either side of the mean.
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Exhibit 3.1
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represents a typical bell curve with standard deviation.
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EXHIBIT 3.1
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Standard deviation.
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Large moves in a security are typically less frequent than small ones. Events that cause big changes in the price of a stock, like a company’s being acquired by another or discovering its chief financial officer cooking the books, are not a daily occurrence. Comparatively smaller price fluctuations that reflect less extreme changes in the value of the corporation are more typically seen day to day. Statistically, the most probable outcome for a price change is found around the midpoint of the curve. What constitutes a large move or a small move, however, is unique to each individual security. For example, a two percent move in an index like the Standard & Poor’s (S&P) 500 may be considered a big one-day move, while a two percent move in a particularly active tech stock may be a daily occurrence. Standard deviation offers a statistical explanation of what constitutes a typical move.
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In
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Exhibit 3.1
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, the lines to either side of the mean represent one standard deviation. About 68 percent of all occurrences will take place between up one standard deviation and down one standard deviation. Two- and three-standard-deviation values could be shown on the curve as well. About 95 percent of data occur between up and down two standard deviations and about 99.7 percent between up and down three standard deviations. One standard deviation is the relevant figure in determining historical volatility.
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Standard Deviation and Historical Volatility
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When standard deviation is used in the context of historical volatility, it is annualized to state what the one-year volatility would be. Historical volatility is the annualized standard deviation of daily returns. This means that if a stock is trading at $100 a share and its historical volatility is 10 percent, then about 68 percent of the occurrences (closing prices) are expected to fall between $90 and $110 during a one-year period (based on recent past performance).
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Simply put, historical volatility shows how volatile a stock has been based on price movements that have occurred in the past. Although option traders may study HV to make informed decisions as to the value of options traded on a stock, it is not a direct function of option prices. For this, we must look to implied volatility.
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Implied Volatility
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Volatility is one of the six inputs of an option-pricing model. Some of the other inputs—strike price, stock price, the number of days until expiration, and the current interest rate—are easily observable. Past dividend policy allows an educated guess as to what the dividend input should be. But where can volatility be found?
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As discussed in Chapter 2, the output of the pricing model—the option’s theoretical value—in practice is not necessarily an output at all. When option traders use the pricing model, they commonly substitute the actual price at which the option is trading for the theoretical value. A value in the middle of the bid-ask spread is often used. The pricing model can be considered to be a complex algebra equation in which any variable can be solved for. If the theoretical value is known—which it is—it along with the five known inputs can be combined to solve for the unknown volatility.
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Implied volatility (IV) is the volatility input in a pricing model that, in conjunction with the other inputs, returns the theoretical value of an option matching the market price.
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For a specific stock price, a given implied volatility will yield a unique option value. Take a stock trading at $44.22 that has the 60-day 45-strike call at a theoretical value of $1.10 with an 18 percent implied volatility level. If the stock price remains constant, but IV rises to 19 percent, the value of the call will rise by its vega, which in this case is about 0.07. The new value of the call will be $1.17. Raising IV another point, to 20 percent, raises the theoretical value by another $0.07, to $1.24. The question is: What would cause implied volatility to change?
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Supply and Demand: Not Just a Good Idea, It’s the Law!
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Options are an excellent vehicle for speculation. However, the existence of the options market is better justified by the primary economic purpose of options: as a risk management tool. Hedgers use options to protect their assets from adverse price movements, and when the perception of risk increases, so does demand for this protection. In this context, risk means volatility—the potential for larger moves to the upside and downside. The relative prices of options are driven higher by increased demand for protective options when the market anticipates greater volatility. And option prices are driven lower by greater supply—that is, selling of options—when the market expects lower volatility. Like those of all assets, option prices are subject to the law of supply and demand.
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When volatility is expected to rise, demand for options is not limited to hedgers. Speculative traders would arguably be more inclined to buy a call than to buy the stock if they are bullish but expect future volatility to be high. Calls require a lower cash outlay. If the stock moves adversely, there is less capital at risk, but still similar profit potential.
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When volatility is expected to be low, hedging investors are less inclined to pay for protection. They are more likely to sell back the options they may have bought previously to recoup some of the expense. Options are a decaying asset. Investors are more likely to write calls against stagnant stocks to generate income in anticipated low-volatility environments. Speculative traders will implement option-selling strategies, such as short strangles or iron condors, in an attempt to capitalize on stocks they believe won’t move much. The rising supply of options puts downward pressure on option prices.
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Many traders sum up IV in two words:
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fear
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and
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greed
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. When option prices rise and fall, not because of changes in the stock price, time to expiration, interest rates, or dividends, but because of pure supply and demand, it is implied volatility that is the varying factor. There are many contributing factors to traders’ willingness to demand or supply options. Anticipation of events such as earnings reports, Federal Reserve announcements, or the release of other news particular to an individual stock can cause anxiety, or fear, in traders and consequently increase demand for options that causes IV to rise. IV can fall when there is complacency in the market or when the anticipated news has been announced and anxiety wanes. “Buy the rumor, sell the news” is often reflected in option implied volatility. When there is little fear of market movement, traders use options to squeeze out more profits—greed.
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Arbitrageurs, such as market makers who trade delta neutral—a strategy that will be discussed further in Chapters 12 and 13—must be relentlessly conscious of implied volatility. When immediate directional risk is eliminated from a position, IV becomes the traded commodity. Arbitrageurs who focus their efforts on trading volatility (colloquially called
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vol traders
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) tend to think about bids and offers in terms of IV. In the mind of a vol trader, option prices are translated into volatility levels. A trader may look at a particular option and say it is 30 bid at 31 offer. These values do not represent the prices of the options but rather the corresponding implied volatilities. The meaning behind the trader’s remark is that the market is willing to buy implied volatility at 30 percent and sell it at 31 percent. The actual prices of the options themselves are much less relevant to this type of trader.
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Should HV and IV Be the Same?
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Most option positions have exposure to volatility in two ways. First, the profitability of the position is usually somewhat dependent on movement (or lack of movement) of the underlying security. This is exposure to HV. Second, profitability can be affected by changes in supply and demand for the options. This is exposure to IV. In general, a long option position benefits when volatility—both historical and implied—increases. A short option position benefits when volatility—historical and implied—decreases. That said, buying options is buying volatility and selling options is selling volatility.
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The Relationship of HV and IV
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It’s intuitive that there should exist a direct relationship between the HV and IV. Empirically, this is often the case. Supply and demand for options, based on the market’s expectations for a security’s volatility, determines IV.
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It is easy to see why IV and HV often act in tandem. But, although HV and IV are related, they are not identical. There are times when IV and HV move in opposite directions. This is not so illogical, if one considers the key difference between the two: HV is calculated from past stock price movements; it is what has happened. IV is ultimately derived from the market’s expectation for future volatility.
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If a stock typically has an HV of 30 percent and nothing is expected to change, it can be reasonable to expect that in the future the stock will continue to trade at a 30 percent HV. By that logic, assuming that nothing is expected to change, IV should be fairly close to HV. Market conditions do change, however. These changes are often regular and predictable. Earnings reports are released once a quarter in many stocks, Federal Open Market Committee meetings happen regularly, and dates of other special announcements are often disclosed to the public in advance. Although the outcome of these events cannot be predicted, when they will occur often can be. It is around these widely anticipated events that HV-IV divergences often occur.
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HV-IV Divergence
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An HV-IV divergence occurs when HV declines and IV rises or vice versa. The classic example is often observed before a company’s quarterly earnings announcement, especially when there is lack of consensus among analysts’ estimates. This scenario often causes HV to remain constant or decline while IV rises. The reason? When there is a great deal of uncertainty as to what the quarterly earnings will be, investors are reluctant to buy
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or
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sell the stock until the number is released. When this happens, the stock price movement (volatility) consolidates, causing the calculated HV to decline. IV, however, can rise as traders scramble to buy up options—bidding up their prices. When the news is out, the feared (or hoped for) move in the stock takes place (or doesn’t), and HV and IV tend to converge again.
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Expected Volatility
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Whether trading options or stocks, simple or complex strategies, traders must consider volatility. For basic buy-and-hold investors, taking a potential investment’s volatility into account is innate behavior. Do I buy conservative (nonvolatile) stocks or more aggressive (volatile) stocks? Taking into account volatility, based not just on a gut feeling but on hard numbers, can lead to better, more objective trading decisions.
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Expected Stock Volatility
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Option traders must have an even greater focus on volatility, as it plays a much bigger role in their profitability—or lack thereof. Because options can create highly leveraged positions, small moves can yield big profits or losses. Option traders must monitor the likelihood of movement in the underlying closely. Estimating what historical volatility (standard deviation) will be in the future can help traders quantify the probability of movement beyond a certain price point. This leads to better decisions about whether to enter a trade, when to adjust a position, and when to exit.
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There is no way of knowing for certain what the future holds. But option data provide traders with tools to develop expectations for future stock volatility. IV is sometimes interpreted as the market’s estimate of the future volatility of the underlying security. That makes it a ready-made estimation tool, but there are two caveats to bear in mind when using IV to estimate future stock volatility.
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The first is that the market can be wrong. The market can wrongly price stocks. This mispricing can lead to a correction (up or down) in the prices of those stocks, which can lead to additional volatility, which may not be priced in to the options. Although there are traders and academics believe that the option market is fairly efficient in pricing volatility, there is a room for error. There is the possibility that the option market can be wrong.
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Another caveat is that volatility is an annualized figure—the annualized standard deviation. Unless the IV of a LEAPS option that has exactly one year until expiration is substituted for the expected volatility of the underlying stock over exactly one year, IV is an incongruent estimation for the future stock volatility. In practice, the IV of an option must be adjusted to represent the period of time desired.
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There is a common technique for deannualizing IV used by professional traders and retail traders alike.
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1
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The first step in this process to deannualize IV is to turn it into a one-day figure as opposed to one-year figure. This is accomplished by dividing IV by the square root of the number of trading days in a year. The number many traders use to approximate the number of trading days per year is 256, because its square root is a round number: 16. The formula is
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For example, a $100 stock that has an at-the-money (ATM) call trading at a 32 percent volatility implies that there is about a 68 percent chance that the underlying stock will be between $68 and $132 in one year’s time—that’s $100 ± ($100 × 0.32). The estimation for the market’s expectation for the volatility of the stock for one day in terms of standard deviation as a percentage of the price of the underlying is computed as follows:
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In one day’s time, based on an IV of 32 percent, there is a 68 percent chance of the stock’s being within 2 percent of the stock price—that’s between $98 and $102.
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There may be times when it is helpful for traders to have a volatility estimation for a period of time longer than one day—a week or a month, for example. This can be accomplished by multiplying the one-day volatility by the square root of the number of trading days in the relevant period. The equation is as follows:
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If the period in question is one month and there are 22 business days remaining in that month, the same $100 stock with the ATM call trading at a 32 percent implied volatility would have a one-month volatility of 9.38 percent.
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Based on this calculation for one month, it can be estimated that there is a 68 percent chance of the stock’s closing between $90.62 and $109.38 based on an IV of 32 percent.
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Expected Implied Volatility
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Although there is a great deal of science that can be applied to calculating expected actual volatility, developing expectations for implied volatility is more of an art. This element of an option’s price provides more risk and more opportunity. There are many traders who make their living distilling direction out of their positions and trading implied volatility. To be successful, a trader must forecast IV.
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Conceptually, trading IV is much like trading anything else. A trader who thinks a stock is going to rise will buy the stock. A trader who thinks IV is going to rise will buy options. Directional stock traders, however, have many more analysis tools available to them than do vol traders. Stock traders have both technical analysis (TA) and fundamental analysis at their disposal.
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Technical Analysis
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There are scores, perhaps hundreds, of technical tools for analyzing stocks, but there are not many that are available for analyzing IV. Technical analysis is the study of market data, such as past prices or volume, which is manipulated in such a way that it better illustrates market activity. TA studies are usually represented graphically on a chart.
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Developing TA tools for IV is more of a challenge than it is for stocks. One reason is that there is simply a lot more data to manage—for each stock, there may be hundreds of options listed on it. The only practical way of analyzing options from a TA standpoint is to use implied volatility. IV is more useful than raw historical option prices themselves. Information for both IV and HV is available in the form of volatility charts, or vol charts. (Vol charts are discussed in detail in Chapter 14.) Volatility charts are essential for analyzing options because they give more complete information.
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To get a clear picture of what is going on with the price of an option (the goal of technical analysis for any asset), just observing the option price does not supply enough information for a trader to work with. It’s incomplete. For example, if a call rises in value, why did it rise? What greek contributed to its value increase? Was it delta because the underlying stock rose? Or was it vega because volatility rose? How did time decay factor in? Using a volatility chart in conjunction with a conventional stock chart (and being aware of time decay) tells the whole, complete, story.
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Another reason historical option prices are not used in TA is the option bid-ask spread. For most stocks, the difference between the bid and the ask is equal to a very small percentage of the stock’s price. Because options are highly leveraged instruments, their bid-ask width can equal a much higher percentage of the price.
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If a trader uses the last trade to graph an option’s price, it could look as if a very large percentage move has occurred when in fact it has not. For example, if the option trades a small contract size on the bid (0.80), then on the offer (0.90) it would appear that the option rose 12.5 percent in value. This large percentage move is nothing more than market noise. Using volatility data based off the midpoint-of-the-market theoretical value eliminates such noise.
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Fundamental Analysis
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Fundamental analysis can have an important role in developing expectations for IV. Fundamental analysis is the study of economic factors that affect the value of an asset in order to determine what it is worth. With stocks, fundamental analysis may include studying income statements, balance sheets, and earnings reports. When the asset being studied is IV, there are fewer hard facts available. This is where the art of analyzing volatility comes into play.
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Essentially, the goal is to understand the psychology of the market in relation to supply and demand for options. Where is the fear? Where is the complacency? When are news events anticipated? How important are they? Ultimately, the question becomes: what is the potential for movement in the underlying? The greater the chance of stock movement, the more likely it is that IV will rise. When unexpected news is announced, IV can rise quickly. The determination of the fundamental relevance of surprise announcements must be made quickly.
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Unfortunately, these questions are subjective in nature. They require the trader to apply intuition and experience on a case-by-case basis. But there are a few observations to be made that can help a trader make better-educated decisions about IV.
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Reversion to the Mean
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The IVs of the options on many stocks and indexes tend to trade in a range unique to those option classes. This is referred to as the mean—or average—volatility level. Some securities will have smaller mean IV ranges than others. The range being observed should be established for a period long enough to confirm that it is a typical IV for the security, not just a temporary anomaly. Traders should study IV over the most recent 6-month period. When IV has changed significantly during that period, a 12-month study may be necessary. Deviations from this range, either above or below the established mean range, will occur from time to time. When following a breakout from the established range, it is common for IV to revert back to its normal range. This is commonly called
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reversion to the mean
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among volatility watchers.
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The challenge is recognizing when things change and when they stay the same. If the fundamentals of the stock change in such a way as to give the options market reason to believe the stock will now be more or less volatile on an ongoing basis than it typically has been in the recent past, the IV may not revert to the mean. Instead, a new mean volatility level may be established.
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When considering the likelihood of whether IV will revert to recent levels after it has deviated or find a new range, the time horizon and changes in the marketplace must be taken into account. For example, between 1998 and 2003 the mean volatility level of the SPX was around 20 percent to 30 percent. By the latter half of 2006, the mean IV was in the range of 10 percent to 13 percent. The difference was that between 1998 and 2003 was the buildup of “the tech bubble,” as it was called by the financial media. Market volatility ultimately leveled off in 2003.
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In a later era, between the fall of 2010 and late summer of 2011 SPX implied volatility settled in to trade mostly between 12 and 20 percent. But in August 2011, as the European debt crisis heated up, a new, more volatile range between 24 and 40 percent reigned for some time.
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No trader can accurately predict future IV any more than one can predict the future price of a stock. However, with IV there are often recurring patterns that traders can observe, like the ebb and flow of IV often associated with earnings or other regularly scheduled events. But be aware that the IV’s rising before the last 15 earnings reports doesn’t mean it will this time.
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CBOE Volatility Index
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®
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Often traders look to the implied volatility of the market as a whole for guidance on the IV of individual stocks. Traders use the Chicago Board Options Exchange (CBOE) Volatility Index
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®
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, or VIX
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®
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, as an indicator of overall market volatility.
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When people talk about the market, they are talking about a broad-based index covering many stocks on many diverse industries. Usually, they are referring to the S&P 500. Just as the IV of a stock may offer insight about investors’ feelings about that stock’s future volatility, the volatility of options on the S&P 500—SPX options—may tell something about the expected volatility of the market as a whole.
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VIX is an index published by the Chicago Board Options Exchange that measures the IV of a hypothetical 30-day option on the SPX. A 30-day option on the SPX only truly exists once a month—30 days before expiration. CBOE computes a hypothetical 30-day option by means of a weighted average of the two nearest-term months.
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When the S&P 500 rises or falls, it is common to see individual stocks rise and fall in sympathy with the index. Most stocks have some degree of market risk. When there is a perception of higher risk in the market as a whole, there can consequently be a perception of higher risk in individual stocks. The rise or fall of the IV of SPX can translate into the IV of individual stocks rising or falling.
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Implied Volatility and Direction
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Who’s afraid of falling stock prices? Logically, declining stocks cause concern for investors in general. There is confirmation of that statement in the options market. Just look at IV. With most stocks and indexes, there is an inverse relationship between IV and the underlying price.
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Exhibit 3.2
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shows the SPX plotted against its 30-day IV, or the VIX.
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EXHIBIT 3.2
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SPX vs. 30-day IV (VIX).
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The heavier line is the SPX, and the lighter line is the VIX. Note that as the price of SPX rises, the VIX tends to decline and vice versa. When the market declines, the demand for options tends to increase. Investors hedge by buying puts. Traders speculate on momentum by buying puts and speculate on a turnaround by buying calls. When the market moves higher, investors tend to sell their protection back and write covered calls or cash-secured puts. Option speculators initiate option-selling strategies. There is less fear when the market is rallying.
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This inverse relationship of IV to the price of the underlying is not unique to the SPX; it applies to most individual stocks as well. When a stock moves lower, the market usually bids up IV, and when the stock rises, the market tends to offer IV creating downward pressure.
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Calculating Volatility Data
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Accurate data are essential for calculating volatility. Many of the volatility data that are readily available are useful, but unfortunately, some are not. HV is a value that is easily calculated from publicly accessible past closing prices of a stock. It’s rather straightforward. Traders can access HV from many sources. Retail traders often have access to HV from their brokerage firm. Trading firms or clearinghouses often provide professional traders with HV data. There are some excellent online resources for HV as well.
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HV is a calculation with little subjectivity—the numbers add up how they add up. IV, however, can be a bit more ambiguous. It can be calculated different ways to achieve different desired outcomes; it is user-centric. Most of the time, traders consider the theoretical value to be between the bid and the ask prices. On occasion, however, a trader will calculate IV for the bid, the ask, the last trade price, or, sometimes, another value altogether. There may be a valid reason for any of these different methods for calculating IV. For example, if a trader is long volatility and aspires to reduce his position, calculating the IV for the bid shows him what IV level can be sold to liquidate his position.
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Firms, online data providers, and most options-friendly brokers offer IV data. Past IV data is usually displayed graphically in what is known as a volatility chart or vol chart. Current IV is often displayed along with other data right in the option chain. One note of caution: when the current IV is displayed, however, it should always be scrutinized carefully. Was the bid used in calculating this figure? What about the ask? How long ago was this calculation made? There are many questions that determine the accuracy of a current IV, and rarely are there any answers to support the number. Traders should trust only IV data they knowingly generated themselves using a pricing model.
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Volatility Skew
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There are many platforms (software or Web-based) that enable traders to solve for volatility values of multiple options within the same option class. Values of options of the same class are interrelated. Many of the model parameters are shared among the different series within the same class. But IV can be different for different options within the same class. This is referred to as the
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volatility skew
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. There are two types of volatility skew: term structure of volatility and vertical skew.
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Term Structure of Volatility
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Term structure of volatility—also called
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monthly skew
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or
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horizontal skew
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—is the relationship among the IVs of options in the same class with the same strike but with different expiration months. IV, again, is often interpreted as the market’s estimate of future volatility. It is reasonable to assume that the market will expect some months to be more volatile than others. Because of this, different expiration cycles can trade at different IVs. For example, if a company involved in a major product-liability lawsuit is expecting a verdict on the case to be announced in two months, the one-month IV may be low, as the stock is not expected to move much until the suit is resolved. The two-month volatility may be much higher, however, reflecting the expectations of a big move in the stock up or down, depending on the outcome.
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The term
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structure of volatility
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also varies with the normal ebb and flow of volatility within the business cycle. In periods of declining volatility, it is common for the month with the least amount of time until expiration, also known as the front month, to trade at a lower volatility than the back months, or months with more time until expiration. Conversely, when volatility is rising, the front month tends to have a higher IV than the back months.
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Exhibit 3.3
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shows historical option prices and their corresponding IVs for 32.5-strike calls on General Motors (GM) during a period of low volatility.
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EXHIBIT 3.3
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GM term structure of volatility.
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In this example, no major news is expected to be released on GM, and overall market volatility is relatively low. The February 32.5 call has the lowest IV, at 32 percent. Each consecutive month has a higher IV than the previous month. A graduated increasing or decreasing IV for each consecutive expiration cycle is typical of the term structure of volatility.
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Under normal circumstances, the front month is the most sensitive to changes in IV. There are two reasons for this. First, front-month options are typically the most actively traded. There is more buying and selling pressure. Their IV is subject to more activity. Second, vegas are smaller for options with fewer days until expiration. This means that for the same monetary change in an option’s value, the IV needs to move more for short-term options.
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Exhibit 3.4
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shows the same GM options and their corresponding vegas.
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EXHIBIT 3.4
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GM vegas.
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If the value of the September 32.5 calls increases by $0.10, IV must rise by 1 percentage point. If the February 32.5 calls increase by $0.10, IV must rise 3 percentage points. As expiration approaches, the vega gets even smaller. With seven days until expiration, the vega would be about 0.014. This means IV would have to change about 7 points to change the call value $0.10.
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Vertical Skew
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The second type of skew found in option IV is vertical skew, or strike skew. Vertical skew is the disparity in IV among the strike prices within the same month for an option class. The options on most stocks and indexes experience vertical skew. As a general rule, the IV of downside options—calls and puts with strike prices lower than the at-the-money (ATM) strike—trade at higher IVs than the ATM IV. The IV of upside options—calls and puts with strike prices higher than the ATM strike—typically trade at lower IVs than the ATM IV.
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The downside is often simply referred to as puts and the upside as calls. The rationale for this lingo is that OTM options (puts on the downside and calls on the upside) are usually more actively traded than the ITM options. By put-call parity, a put can be synthetically created from a call, and a call can be synthetically created from a put simply by adding the appropriate long or short stock position.
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Exhibit 3.5
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shows the vertical skew for 86-day options on Citigroup Inc. (C) on a typical day, with IVs rounded to the nearest tenth.
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EXHIBIT 3.5
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Citigroup vertical skew.
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Notice the IV of the puts (downside options) is higher than that of the calls (upside options), with the 31 strike’s volatility more than 10 points higher than that of the 38 strike. Also, the difference in IV per unit change in the strike price is higher for the downside options than it is for the upside ones. The difference between the IV of the 31 strike is 2 full points higher than the 32 strike, which is 1.8 points higher than the 33 strike. But the 36 strike’s IV is only 1.1 points higher than the 37 strike, which is also just 1.1 points higher than the 38 strike.
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This incremental difference in the IV per strike is often referred to as the slope. The puts of most underlyings tend to have a greater slope to their skew than the calls. Many models allow values to be entered for the upside slope and the downside slope that mathematically increase or decrease IVs of each strike incrementally. Some traders believe the slope should be a straight line, while others believe it should be an exponentially sloped line.
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If the IVs were graphed, the shape of the skew would vary among asset classes. This is sometimes referred to as the volatility smile or sneer, depending on the shape of the IV skew. Although
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Exhibit 3.5
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is a typical paradigm for the slope for stock options, bond options and other commodity options would have differently shaped skews. For example, grain options commonly have calls with higher IVs than the put IVs.
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Volatility skew is dependent on supply and demand. Greater demand for downside protection may cause the overall IV to rise, but it can cause the IV of puts to rise more relative to the calls or vice versa. There are many traders who make their living trading volatility skew.
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Note
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1
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. This technique provides only an estimation of future volatility. |