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Developing volatility assumptions is a common practice in the financial community, where many sophisticated techniques have been developed that go beyond simply calculating volatilities based on historical stock prices. The Black-Scholes, Monte Carlo, and lattice models all use a volatility input, which may come from a variety of sources (e.g., historical data, implied market volatility, peer group volatility).
When using historical data to estimate volatility, a sufficient number of daily, weekly, or monthly prices should be used to make the subsequently annualized results statistically valid. Because the estimate of volatility reflects the variation in returns expressed as a percentage of the stock price, annualized volatilities can be compared across stocks on a normalized basis regardless of how frequently the prices are measured, length of the measurement period, or the stock prices of the companies being compared.
Many companies base their volatility assumptions on their historical stock prices, or use historical volatility as a starting point for setting this assumption under ASC 718. According to ASC 718-10-55-24, companies should also consider how future experience may differ from the past. This may entail using other factors to adjust historical volatility, such as implied volatility, peer group volatility, and the range and mean of volatility statistics over various historical periods.
Because ASC 718 does not endorse a particular method of estimating expected volatility, a company should consider all available data, including what marketplace participants would likely use in determining an exchange price for a traded option. When a company develops its volatility assumption to use in its option-pricing model, it should consider the following alternatives:
  • Historical volatility — a measurement of the amount by which the company's stock price changes have fluctuated in the past
  • Peer group volatility — historical volatility developed for comparable companies (typically used if historical volatility is unavailable)
  • Implied volatility — the assumption implied by the observed current market prices of the company's traded options or other convertible securities (if available)
  • Blended volatility — a volatility assumption developed by combining data from various sources (e.g., historical volatility calculated using different windows, peer group volatility or implied volatility)

As described in SAB Topic 14, companies should make good faith efforts to identify and utilize sufficient information in determining whether using historical volatility, implied volatility, or a combination of the two will result in the best estimate of expected future volatility. When using a combination of various estimates, significant judgment is required to determine the relative weighting of the different measures. ASC 718 does not contain prescriptive guidance related to the weighting of estimates. According to SAB Topic 14, a company should consider all available information but may, under certain circumstances, rely exclusively on historical or implied volatility. Furthermore, the SEC staff ". . . believes companies that have appropriate traded financial instruments from which they can derive an implied volatility should generally consider this measure." A company should also disclose in its footnotes why it used the volatility measure it selected.

9.4.1 Historical volatility

As discussed above, a company may conclude that historical results are the best indicator of the future. This section discusses the calculation of historical volatility and how to adjust for various circumstances, such as insufficient data and one-time events.

9.4.1.1 Calculation of historical volatility

Volatility is calculated by taking the standard deviation of continuously compounded historical returns on underlying stock prices (adjusted to remove shifts on ex-dividend dates) and then annualizing the result. Volatility is normally annualized by multiplying by the square root of the number of measurement dates used during a one-year period (e.g., volatility based on weekly prices is annualized using the square root of 52). An appropriate starting point is to measure historical stock prices with consistent frequency over the most recent historical period equal to (or greater than) the option's expected term (for the Black-Scholes model) or contractual term (for lattice models). Companies should have a consistent methodology about the length of the historical window used to estimate volatility, absent relevant changes, such as a significant change in the expected term of options currently granted. The consistency of volatility over other time windows should also be considered. See SC 9.4.1.2 for details on whether and how it may be necessary to consider different volatilities over different terms.
Because volatility usually changes slowly, it may not be necessary to make a separate calculation for each grant date. Grants might be grouped by interval (e.g., by one or three-month periods) and a volatility assumption developed for each period, provided that observed shifts in volatility are not significant. Awards may also need to be grouped and separate volatility assumptions used to reflect differences in contractual terms and vesting schedules. In addition, if a given historical volatility window includes short-term volatility that is not expected to occur in the future, companies should consider whether or not to exclude that data when developing an assumption.

9.4.1.2 Exclusive reliance on historical volatility

After considering all available information, a company may decide to exclusively rely on its historical volatility, because it believes that its historical volatility provides the most reliable indication of future volatility. According to SAB Topic 14 (section D.1, question 4), a company may rely exclusively on historical volatility when the following factors are present, so long as the methodology is consistently applied:
  • A company has no reason to believe that its future volatility over the expected or contractual term, as applicable, is likely to differ from its past;
  • The computation of historical volatility uses a simple average calculation method;
  • A sequential period of historical data at least equal to the expected or contractual term of the share option, as applicable, is used; and
  • A reasonably sufficient number of price observations are used, measured at a consistent point throughout the applicable historical period.

The following sections address adjustments that a company may need to consider when developing its historical volatility assumption, which may lead the company to conclude that exclusive reliance on historical volatility over the most recent period of time equal to the expected term is not appropriate.
Frequency of historical volatility measurement
The frequency of stock price measurement can significantly affect the expected volatility assumption. For example, volatility estimates vary depending on whether stock prices are measured on a daily, weekly, or monthly basis. While differences in annualized volatility estimates due to measurement frequency differences may be small, this is not always the case.
A high frequency of measurement (e.g., daily stock prices) provides the largest possible sample size, as discussed in ASC 718-10-55-37(d). According to that paragraph, a public company "would likely use daily price observations." On the other hand, it also may be appropriate to use lower frequency data (e.g., monthly), provided there is an adequate sample size.
ASC 718 does not provide detailed guidance on adequate sample sizes for computing historical volatility. SAB Topic 14, footnote 56, indicates that monthly data should not be used for periods shorter than three years due to insufficient data, indicating that more than 36 data points should be used to estimate historical volatility when using monthly data. Footnote 64 of SAB Topic 14 suggests that two years of daily (approximately 500 measurements) or weekly (approximately 100 measurements) data could provide a reasonable sample, though daily data may be more appropriate when there is an expected term shorter than two years.
When volatilities calculated based upon different measurement intervals (e.g., daily, weekly and/or monthly) differ significantly, a company may consider averaging the annualized volatility estimates from the different measurement intervals. When an option's expected term is much shorter than the available history or when there is less history available, generally it would be more appropriate to use an estimate based on daily or weekly data in order to assure an adequate sample, assuming daily or weekly prices are available and that sufficient trading occurs on each day to make these quotes reliable market indicators. Regardless of which measurement frequency is selected, it should be used consistently for all awards.
Insufficient historical stock price data
Some companies do not have historical stock prices that can be reliably determined for a period that is at least equal to the expected term of their options or do not believe that their recent historical volatility fairly reflects future expectations (e.g., a company that has been public for only three years and has estimated the expected term of its options to be five years). In such cases, it may be appropriate to blend the company's own volatility data with that of a peer group of public companies. Companies in the peer group should (1) be of similar size, (2) have similar histories and relatively comparable financial leverage, and (3) be in similar businesses (industry and geographical markets).
Peer-group volatility
To compute peer-group volatility, a company should use data from one or more relatively recent historical periods that are at least as long as its expected term. Though various weightings are possible, volatility data from the peer group companies are usually averaged, with each company given equal weight.
If a company that grants options with a five-year expected term is looking to use peer-group data to supplement its own last three years of historical data, it would be appropriate to obtain peer-group data for the two years preceding the past three years. In this way, the historical period would equal the five years of the expected term. The company could give the peer-group's average volatility for the two earliest years a two-fifths weighting and its own historical volatility three-fifths. In other fact patterns, other weightings of peer company and company-specific volatilities may be appropriate. A company generally should avoid using overlapping periods of data in this type of analysis (e.g., averaging the peer-group data over the full five-year window with the company's three-year historical data), because that approach would unevenly weight certain periods (see the section below on Mean-reversion and term structure of volatility).
Newly public companies
SAB Topic 14 also allows newly public companies (i.e., those that recently filed for an IPO, whether or not the IPO has yet occurred) to base their estimates of expected volatility on the historical, expected, or implied volatility of similar companies whose stock or option prices are publicly available, after considering the industry, stage of life-cycle, size, and financial leverage of the other companies.
A newly public company can develop peer-group volatility using some of the companies listed in an industry sector index (e.g., a computer vendor may look to a NASDAQ Computer Index, if there is one). However, the company may not use the volatility of the index itself as a substitute. The newly public companies should use the companies selected from the industry sector index consistently, unless circumstances change, or until it has either a sufficient amount of historical information regarding the volatility of its own stock price or other traded financial instruments become available to derive an implied volatility to support an estimate of its expected volatility.
Nonrecurring events
SAB Topic 14 and ASC 718 cite other instances when it may be appropriate to adjust historical volatility for past events that a marketplace participant would likely discount, such as a discrete event that is not expected to recur (e.g., failed takeover bid or major business restructuring). Historical data demonstrably affected by such events (e.g., the abnormally high volatility observed in the six-month period leading up to or following a significant transaction) might be reasonably excluded from the historical volatility calculation, provided the event is specific to the reporting company, under management's control, and not expected to recur during the expected term of the award. However, question 2(s) in Section D.1 of SAB Topic 14 indicates that such exclusions are expected to be rare.
One-time events may also lead to increased expected volatility as compared to unadjusted historical volatility. For example, if a company recently announced a merger that would increase its business risk in the future, then it would consider the impact of the merger in estimating its expected future volatility if it is reasonable that a marketplace participant would also consider this event.
In the rare situations when nonrecurring events such as those described above imply that historical data may not be representative of the future, a company may simply exclude stock-price data from the affected period(s) and use the remaining history so long as there remains sufficient historical data to make an estimate. Companies should carefully analyze volatility estimates from periods that include breaks to ensure that those gaps are not treated as market-price movements. In some cases, such as when the excluded period is an extended period of time, a company may consider using a blended estimate that incorporates peer-group data for the excluded period.
Some companies may be tempted to exclude historical volatility data caused by extraordinary market conditions, such as the effects of the credit crunch in 2008 and the COVID-19 pandemic. We generally believe that data should only be excluded when the volatility relates to one-time events specific to the reporting company that are reasonably within the control of the company’s management or shareholders. Data related to events affecting the broader market should not be excluded from a company’s analysis, even when those events are considered extremely unlikely to recur. In addition, data from periods of significant stock price changes over a short period of time, such as may occur due to lawsuits, failed product trials, or recalls, generally should not be excluded.
Mergers, acquisitions, divestitures and changes in financial leverage
The volatility of a merged company may differ from either predecessor, while a spin-off may affect volatility of the new entity and its former parent. With merged companies, each of which represents a major component of the merged entity, typically a weighted average of the two entities' historical volatility is appropriate, with the volatility of each company weighted by relative market capitalization prior to the transaction. Spin-off companies will probably have to use peer-group data to estimate volatility, and their former parent may have to do the same if the spin-off fundamentally changes the parent.
Lastly, financial leverage needs to be considered as a factor in examining historical volatility. If a company's debt-to-equity ratio has shifted dramatically over recent history whether due to a merger, spinoff, or just re-leveraging, consideration of other data points such as peer group information may be appropriate.
Mean reversion and term structure
A statistical phenomenon referred to as mean reversion occurs when a series of values is more likely to move towards its longer-term mean than away from it. Volatility is often observed to be cyclical, moving between temporary or short-term highs and lows but then reverting back to the long-term average. Therefore, if a stock’s price has been extraordinarily volatile for the past year when compared to a longer period, it may be reasonable to assume that, within another year, the stock price volatility will begin to migrate toward its longer term average volatility level. Under these circumstances, the long-term volatility assumption for options granted in the next year might fall between that of the more volatile recent period and the less volatile long-term average. The mean-reversion theory would also apply when recent volatility has been extremely low compared to long-term average volatility. Companies should consider mean reversion when significant cyclical swings in volatility are observed in the historical data.
Term structure refers to how historical volatilities may vary over specific intervals. This may be relevant in determining the volatility assumptions over the option's expected term (or contractual term when a lattice model is used). The justification for incorporating term structure into an estimate of expected volatility would ordinarily be based on mean-reversion. Thus, if last year's volatility was 20%, but average annual volatility over the previous five years was 40%, the annual volatility assumption for each of the next five years might be closer to 20% at the beginning of the expected term and eventually move toward 40%. An explicit term structure approach to the expected volatility assumption might be used in a more refined lattice model instead of a single fixed volatility assumption, where exercises and vested cancelations are assumed to occur not just after a single weighted average expected term, but throughout the option's entire contractual life. However, the mean-reversion concept may also be applied to a single-value volatility forecast input into the Black-Scholes model.
Mean reversion will generally be most applicable in developing the volatility assumption when expected term is relatively long and recent short-term volatility is very different from long-term average historical volatility. In practical terms, applying the concepts of mean reversion and term structure to expected volatility assumptions involves looking for evidence of possible mean reversion by examining volatility over at least two historical periods of varying lengths, assuming a company has the data. According to ASC 718-10-55-37(a)(2), a company using the Black-Scholes model should start with a period equal in length to the option's expected term, then use progressively shorter periods to determine whether there is a pattern of changing volatility (though longer periods may be examined as well).
If consistent volatility experience is exhibited by using periods of varying lengths, or if actual experience exhibits no clear pattern over various sub-periods of the historical period that corresponds with the option's expected term, then it may be more appropriate to use an unadjusted volatility estimate based on data from a consistent historical period equal to or greater than the length of the expected term. While mean reversion may not be apparent in the historical data based on periods shorter than the expected term, companies should also consider whether it applies on a longer time scale. A company that has typically used five-year volatility for an award with a five-year expected term might also consider data over seven- and ten-year windows, as well as over periods shorter than five years. If the five-year volatility appears unusual, using a blend with longer-term data may be more appropriate. However, using data that is too old (much longer than the typical contractual terms of ten years) is likely to be less relevant and not the best predictor of expected volatility.
It may be difficult to assess whether changes in volatility relate to mean reversion or are due to specific circumstances, such as a company's growth, diversification, reorganization, merger, or spin-off. Careful examination of year-by-year volatility in this context compared to volatility measured over the entire expected term may be helpful in assessing whether a mean-reversion adjustment is appropriate.

9.4.2 Implied volatility

As discussed above, a company may need to consider adjusting its historical volatility when developing its expected volatility assumption. After analyzing its data, a company with available implied volatility information may conclude that its historical results are not the best indicator of the future and instead consider blending implied volatility with historical volatility or, in some cases, relying solely upon implied volatility.
Implied volatility is based on the market price of a company's exchange-traded financial instruments and is sometimes thought to be a market forecast of a company's future stock price volatility. Because current market trades may suggest more about a company's future stock prices than its historical volatility, many believe implied volatility is superior to historical volatility as a tool for predicting future stock price volatility. In our experience, implied volatility tends to correlate with shorter-term historical volatility levels and therefore may be more applicable to shorter-term than to longer-term forecasts. Generally, we do not expect companies to solely use current short-term implied volatility as their best estimate of long-term volatility for measuring the fair value of employee stock options.

9.4.2.1 Calculating implied volatility

It can be difficult to use implied volatility for valuing employee options because most implied volatilities are based on traded financial instruments (e.g., exchange-traded options) with substantially shorter terms than those of employee stock options. Typically, exchange-traded options have terms less than one year. A select group of large companies have long-term traded options called LEAPs that have terms of two to four years, but other companies have only exchange-traded options with terms less than eighteen months, and many companies have no exchange-traded options at all. Thus, the expected term for most of a company's employee options is much longer than the contractual terms of exchange-traded options on the company's stock. Exchange-traded options are also often thinly traded, so reliable price quotes may be lacking even when option terms are comparable.
To calculate implied volatility, a company should use the Black-Scholes model to find a volatility input that makes the fair value of an employee stock option equal to the market price of the exchange-traded option on a specific date. Because exchange-traded options—unlike employee stock options—are generally held for their full contractual term, there is no judgment involved in estimating their expected term. It simply equals the remaining contractual term of the exchange-traded option on the specific date. Options embedded in certain forms of traded convertible debt may also be used to determine implied volatility.
One pragmatic approach to deciding whether implied volatility is stable enough to rely upon is to perform at least several measurements using the longest duration, market-traded, at- or near-the-money options to ensure that the calculated implied volatilities remain reasonably stable. If the volatilities do not appear stable, they should either not be used as the sole determinant of the volatility assumption (even if the length of the remaining contractual life of the exchange-traded options and the expected term of the employee options are comparable) or they should be weighted less than historical volatility when using a blended rate.

9.4.2.2 Exclusive reliance on implied volatility

SAB Topic 14 provides additional guidance on determining when and how to use implied volatility. According to SAB Topic 14 (Section D.1, question 4), a company may, in limited circumstances, rely exclusively on implied volatility. Based on that guidance, the SEC staff will not object to exclusive reliance on implied volatility if all of the following criteria are met and the methodology is consistently applied:
  • The company's valuation model is based on a constant volatility assumption (e.g., Black-Scholes model).
  • Implied volatility is derived from options that are actively traded.
  • Market prices (i.e., trades or quotes) of both traded options and underlying shares are measured concurrently, synchronized with the grant of the employee stock options. If this is not practicable, a company should at least derive implied volatility as of a point in time that is as reasonably close as practicable to the grant of the options.
  • Traded options have exercise prices that are (1) near-the-money and (2) similar to the exercise prices of employee stock options.
  • The remaining maturities of the traded options are at least one year

The term "actively traded" is not defined in SAB Topic 14; however, Rule 101(c) of SEC Regulation M provides criteria (average daily trading volume of $1 million and a public float value of at least $150 million) that may be used by analogy to determine if sufficient trading volume meets this condition.
Based on the guidance in SAB Topic 14, a company could potentially use the implied volatility of an exchange-traded option with a remaining term of one year to estimate the expected volatility of an employee stock option with an expected term longer than one year. In determining whether and to what extent the use of implied volatility is appropriate under these circumstances, companies should consider (1) the other factors from SAB Topic 14, (2) how much longer the expected term of the employee option is than the remaining contractual life of the exchange-traded options, and (3) the historical comparability of implied volatility levels with longer-term observed historical volatility experience. Companies should also note that implied volatilities themselves often vary widely over time relative to observed volatilities calculated using long-term historical prices. Therefore, only implied volatilities measured within a few weeks prior to the measurement date should be considered.

9.4.3 Blended volatility

Using a blend of historical and implied volatility may be appropriate in the following circumstances:
  • A company meets some, but not all, of the SAB Topic 14 required conditions to exclusively rely on historical or implied volatility,
  • the term structure of implied volatility is unstable, or
  • the expected term of the option is significantly greater than the contractual term of traded options.

A combination of both volatility measures may provide the best estimate of expected volatility because it captures the mean reversion concept by weighing both historical (longer term) and implied (near term future) volatilities, and offers the most flexibility to adapt to a company's specific facts and circumstances. We believe this approach is consistent with how most marketplace participants would likely consider using available information to estimate expected volatility, as illustrated in Example SC 9-1.
While SAB Topic 14 stresses that a company's process to gather and review available information to estimate expected volatility should be consistently applied, if facts and circumstances change to indicate new or different information may be useful in estimating expected volatility, then a company should incorporate that information. Situations occasionally arise in which shifts in methodology will be necessary (for example, when previously-used historical or implied information is no longer available or has changed greatly in its apparent reliability). Any such change is not a change in accounting policy, but must nevertheless be supported by sound rationale that the new or different information produces a better estimate of expected volatility. This would include a change in the relative weightings of contributory sources of information—for example, switching from a 50%/50% average of historical and implied volatility, to either a 100% historically-based estimate or a 100% implied-based estimate.
Example SC 9-1 illustrates an approach of using available information from multiple data sources to estimate expected volatility.
EXAMPLE SC 9-1
An approach for estimating volatility using multiple data sources
In early 20X4, Company A acquired Company B in a stock transaction. Company A's stock has historically been much more volatile than Company B's. However, from the transaction's announcement to its closing date, Company B's shares have become much more volatile, moving in tandem with Company A's shares since late 2004. Once the deal closed, the combined company's shares became less volatile, closer to Company B's pre-announcement historical volatility levels.
On January 1, 20X7, the combined company issues employee stock options. Because this was a significant acquisition and it has only three years of data as a combined company, Company A also looked at peer-group volatility data for the post-acquisition period. During this time, historical one-year volatilities for the peer-group of companies were consistently below the historical one-year volatility of the combined company.
Pre-acquisition volatilities of the separate companies based on weekly prices were as follows:
Year
Company A
Company B
Average of Company A and Company B
20X1
65.4%
33.8%
49.6%
20X2
77.3%
43.3%
60.3%
20X3
69.7%
71.1%
70.4%
The post-acquisition volatilities for Company A and its peer group were as follows:
Year
Combined company
Average peer group
20X4
56.5%
48.1%
20X5
53.8%
45.8%
20X6
39.3%
33.5%
Three-year historical volatility
50.8%
43.3%
Most recent two-year historical volatility
48.0%
39.0%
View table
Management believes that each company's volatility was elevated during the year prior to the acquisition (20X3) and the combined companies' volatility was elevated during the year after the acquisition (20X4) due to the market's uncertainty about the integration of the two companies.
The volatility of exchange-traded options on the combined company's shares was also assessed for dates near the end of December 20X6. These traded options have contractual terms of four to eight months. Management excluded information on thinly traded options from its analysis and used three specific options that have larger trading volumes, believing that their implied volatility is reliable. The specific options included in management's analysis were near-the-money at the end of 20X6.
The implied volatilities calculated from the traded options are lower than the historical volatilities of either the predecessor companies or of the peer group:
Trade date
Remaining term
(as of trade date)
Implied volatility
December 28, 20X6
8 months
32.4%
December 29, 20X6
4 months
31.3%
December 30, 20X6
8 months
29.8%
Average
31.2%
Average (excluding four-month option)
31.1%
View table
How should management use this data to develop an expected volatility assumption for the options granted in early 20X7 with a three-year expected term, a ten-year contractual term, and a one-year cliff-vesting service condition?
Analysis
Because the company uses the Black-Scholes model, it would develop a single volatility estimate for the options' expected term, beginning with the combined company's three-year historical volatility of 50.8%.
Assuming the combined company does not envision an acquisition of this magnitude in the foreseeable future, it may expect near-term future volatility to be much lower, perhaps as low as the 20X6 level of 39.3%. The consistently lower peer-group volatilities from 20X4 to 20X6 appear to support this assumption.
However, if management believes that the combined company has unique features that might affect future performance, the average volatility that its own stock experienced in the last two years (48.0% over 20X5 through 20X6) may be a more reliable basis for a historical volatility forecast than the peer-group data, and is not inconsistent with the average of Company A and Company B volatilities of 55.0% in 20X1 and 20X2.
Management should also consider the much lower implied volatilities of its traded options. These appear to show that market expectations regarding near-term future volatility are considerably below historical levels. However, the traded options have terms of less than a year, while the employee stock options have expected terms of three years. Consistent with ASC 718 and SAB Topic 14, management should consider all of the above factors when estimating its expected volatility estimate, weighting the historical and implied volatility. Given that the only available exchange-traded options with remaining contractual terms to expiration greater than 6 months have a total term of only eight months (compared to the employee options' term of 3 years), a relatively lower weighting for the implied volatility would be reasonable. Assume this results in a 37.5% weighting for the implied volatility and a 62.5% weighting for the two-year historical volatility.
Using these percentages to weight the average implied volatility for traded options with eight-month terms and the company's own two-year historical average yields the following blended volatility estimate:
(Implied average × weighting) + (Historical average × weighting) = Expected
(31.1% × 37.5%) + (48.0% × 62.5%) = 41.7%
Company A would use this weighted average as the expected volatility assumption in determining the fair value of its new employee stock options.
This example is intended to illustrate the potentially relevant data points in developing a volatility estimate and one potentially appropriate approach. The determination of volatility is a matter of judgment and will vary depending on each specific set of facts and circumstances. For example, the historical three-year-average peer-group volatility of 43.3% was not used directly but helps corroborate the reasonableness of the applied approach. Also, the company could have considered peer group implied volatility.

9.4.4 Comparing volatility assumptions under different models

The Black-Scholes model uses a single volatility estimate over an option's expected term. In contrast, lattice models can incorporate dynamic volatility assumptions that vary over the option's contractual term, along with more sophisticated assumptions where volatility changes with stock-price fluctuations.
In Example SC 9-1, the combined company's averaged volatility estimates considered both its own and peer-group historical periods of varying lengths and near term implied volatility to arrive at a single expected volatility estimate for the Black-Scholes model. A lattice model could incorporate a period-by-period future expected volatility in different parts of the lattice rather than a single combined volatility forecast. This also means that a longer historical period might become relevant, since the lattice model should simulate the entire contractual term of the option, not just its expected term.
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