Shouldering The Cost Of Employee Stock Options
Shouldering The Cost Of Employee Stock Options
by Viktor Mirkin and Jeffrey Green
This article sheds some light on the many questions about employee stock options.
Many North American, Japanese and European firms believe that executive stock option programs, as well as broader-based employee ownership schemes, are important for creating effective remuneration strategies.
Recent changes in American accounting standards, specifically the publication of Financial Accounting Standards Statement No. 123R (FAS 123R) and Staff Accounting Bulletin 107 (SAB 107), require firms to estimate and report the cost of the stock option grants. The new rules dictate that the cost should be estimated at fair value, as a contingent claim, consistently with the principles of financial economics.
Robust analysis of stock option schemes will not only meet regulator's requirements, but should also provide firms with insights regarding the true cost of employee pay packages. It should be anticipated that the disclosure of estimated stock option costs will be scrutinized by capital market commentators, with a potential for material impact on stock price. As a result, the cost accounting practices will have a significant influence on the design of remuneration schemes in the future, with the reported cost of the scheme inevitably becoming a key factor for consideration.
This article considers employee stock option (ESO) cost accounting. We review characteristics of ESO schemes, consider requirements and recommendations of FAS 123R and SAB 107 and explain why the lattice model is probably the best approach to measuring the cost of stock option grants.
Stock Options Grants in the United States and Abroad
According to the National Compensation Survey conducted in the United States in March 2003, 8 percent of all American workers had access to an ESO program. For white–collar workers and for workers whose wages exceed $15 per hour, this figure rises to 12 percent and 13 percent respectively. The National Centre for Employee Ownership estimates that approximately 10 million American workers are enrolled in stock option programs, and that the total of 4,000 such programs are operated across the United States in 2005.
Ledford, Lucy and LeBlanc (2004) report that almost without exception, American firms in high–tech industries run broad–based stock option schemes.
In Europe, according to Ferrarini and Moloney (2005), stock options grants are also common. Among Eurotop 300 stock index constituents, all of the 68 British, 40 out of 42 French, 25 out of 44 Italian, 17 out of 18 Dutch and 16 out of 19 Swedish companies operate well–established executive option schemes.
Ferrarini and Moloney (2005) go on to comment that in the United Kingdom, 78 percent of the total executive pay package is accounted for by variable pay incentives, including stock options. In France, variable pay benefits amount to 60 percent of total executive compensation with 13 percent attributable to stock options.
Japanese employee option granting practices are outlined by Utsonomiya (2002). Over 14 percent of all listed Japanese firms have issued ESOs. In the Japanese service sector, almost a third of all firms have issued ESOs.
Why Firms Grant Employee Stock Options
Economic reasoning underpinning the issue of ESOs relies on consideration of agency costs arising due to misalignment of interests between workers, managers and owners. By sharing ownership of the company with workers and managers, agency costs can be reduced, increasing the market valuation of the firm.
For more established firms, executive stock options can be a more effective way of compensating high–ranking managers than cash bonus schemes, the pervasiveness and generosity of which are in themselves often cited as an example of agency cost realization, while for start–ups with limited resources, issuing ESOs may be the only way to attract and retain leading talent.
Many researchers, for example Sesil, Kroumova, Kruse and Blasi (2004), conclude that the productivity of the workforce increases significantly where broad–based stock option programs are offered to employees, particularly in combination with other participative management incentives.
On the other hand, firms may be penalized by the markets for dilution of share capital. For example, "Motley Fool," a popular online investment community Web site, specifically advises to avoid investing in stock of the companies with generous option grants.
It has been also suggested that executive stock option grants can create incentives for excessive risk–taking. As the stock option value is a monotonously increasing function of share price volatility, executives would maximize the value of their options by pursuing risky corporate strategies.
Stock Options Treatment Debate
The treatment of stock–based employee compensation has been seen as an important corporate governance issue for a number of years. Whether to allow for the cost of options explicitly in the corporate accounts has been intensely debated.
Sircar and Xiong (2005) explain that in the United States, opinions were divided between the firms heavily reliant on stock options for executive compensation, mainly in the hi–tech industries, and the users of financial information, including investors and the Federal Reserve Board. The firms opposed stringent cost accounting, while investors and the Federal Reserve Board supported it.
Speaking at the Financial Markets Conference of the Federal Reserve Bank of Atlanta in 2002, Allan Greenspan, the chairman of the Federal Reserve Board, remarked that explicit option expensing was critically important for the accurate representation of corporate performance. According to Greenspan, imperfect disclosure of compensation cost inhibited the growth of the American economy.
Likewise Warren Buffet, speaking at the Berkshire Hathaway shareholder meeting in 2004, argued that appropriate treatment of option expensing was the issue of fundamental morality.
Concerns of Greenspan and Buffet are better understood in this context: according to Finnegan (2004), had AOL Time Warner expensed the executive stock option grants in 2001, the firm would have shown an operating loss of $1.7 billion instead of the reported profit.
The opponents of explicit expensing maintained that stricter accounting will damage hi–tech start–ups without improving comparability of financial statements as methodological ambiguity involved in estimating the cost of grants was likely to obscure true differences between firms.
In the United States, the attempts to introduce stricter reporting guidelines were blocked in the 1990s until the fallout from high profile corporate governance lapses intensified the focus on executive remuneration accounting and catalyzed the resolution of debate in favor of proponents of explicit expensing.
Imposition of Valuation Standards
In December 2004, the Financial Accounting Standards Board (FASB) issued a revised FAS 123 prescribing explicit expensing of share–based compensation at fair value.
ESOs are non–tradable, and hence there is no opportunity to observe fair values in the market. The fair value of the compensation cost is instead measured by applying a valuation technique consistent with requirements of FAS 123R. We will review specific requirements of FAS 123R here.
In Europe, a similar move towards re–assessment of executive remuneration accounting in the context of corporate governance resulted in the issuance of IAS 19 (IFRS 2-Share–Based Payment) in February 2004. In line with the International Accounting Standards Board's (IASB's) long–term goal of achieving convergence between IFRS and U.S. GAAP, and responding to the recommendation of the International Organisation of Securities Commissions report (2000), the standard prescribes valuation of employee stock options at fair value using a suitable valuation model.
Internationally, a report by the Organization for Economic Co–Operation and Development (OECD) expert group has concluded that employee remuneration by stock options represents a cost to the firm, and that the cost should be measured at fair value. To date, 38 countries have endorsed the concept of explicit stock option expensing in principle by filing official responses to report recommendations.
Neither FASB, nor IASB, nor the OECD expert group have recommended the use of one specific model over all other available models.
As the result, no single dominant valuation technique has emerged, although many parties have expressed preference for the binominal lattice model on the account of its flexibility and ease of implementation. Alternatives to the binomial lattice–pricing model are the Black–Scholes option pricing model and its modifications allowing for some of the ESO features, and pricing by Monte Carlo simulations.
Summary of FAS 123R Requirements
In general terms, FAS 123R requires accounting recognition of the costs of a company's own "equity" (broadly defined to include stock, stock options and other forms of equity such as stock appreciation rights and phantom stock) issued in exchange for goods or services provided by either employees or non–employees. Historically, the costs of such equity issuances have been valued using an intrinsic value approach not requiring a charge to earnings for most stock options per Accounting Principles Board Opinion No. 25 (APB 25). In 1993, FASB began to re–examine the basis for APB 25's non–recognition rules and progressively refined its position over the intervening decade, emphasizing its belief that compensatory equity issuances should be recognized at their fair value in company financial statements. Despite the significant amount of controversy generated by this position, FASB has now mandated its adoption in FAS 123R. These new requirements are generally effective as of the first reporting period (quarterly or annually) beginning on or after June 15, 2005 (i.e., July 1, 2005 for calendar year companies) for most public companies; the first reporting period (quarterly or annually) beginning after Dec. 15, 2005 (i.e., Jan. 1, 2006) for "small business issuers;" and the first annual reporting period beginning after Dec. 15, 2005 (i.e., Jan. 1, 2006) for non–public companies.
Key Aspects of SAB 107
On March 29, 2005, the Office of the Chief Accountant (OCA) of the Securities and Exchange Commission (SEC) issued Staff Accounting Bulletin 107 (SAB 107) to provide clarification of the OCA's interpretation of FAS 123R as it applies to share–based compensation arrangements for both employees and non–employees.1 In light of the anticipated significant administrative burdens associated with FAS 123R's requirements, SAB 107 emphasizes a degree of flexibility. Under this approach, companies will be given a substantial amount of latitude–at least initially–to estimate the fair value of share–based compensation, subject to the guidelines provided in SAB 107. Also noteworthy here is the staff's statement that it will not re–evaluate reasonable fair value estimates after the fact, even where the ultimate value of share–based compensation substantially exceeds a company's initial estimate.
In general, FAS 123R requires a company to estimate the fair value of the shares it will be obligated to issue when a stock option becomes exercisable at the initial grant date. Although the most desirable evidence of the value of stock options would be the value of the same or similar instruments in an observable market, FAS 123R recognizes that the value of many ESOs cannot be determined in this manner and therefore prescribes a number of criteria for selecting alternate valuation methodologies.
In selecting an appropriate valuation methodology, SAB 107 provides that the chosen method must: (1) be consistent with FAS 123R; (2) be based on established financial economic principles that are generally applicable in the field; and (3) reflect all substantive characteristics of the equity instrument at issue. SAB 107 does not require a company to use any particular valuation methodology as long as the chosen approach satisfies the fair value criterion. The staff comments that in order to comply with these requirements, a valuation methodology must take into account all of the relevant terms of the stock options under consideration. As an example, the staff cites the Black–Scholes–Merton model as a methodology that would not be appropriate for valuing stock options, the exercisability of which is conditioned on a specified increase in price in the underlying shares because that model does not take such a term into account. A slight extrapolation would suggest that Black–Scholes–Merton would not satisfy the fore– going test for any stock options that include performance–based or other terms that are not variables in the Black–Scholes–Merton calculation; for such options, an alternate valuation methodology would be required.
Although a company is permitted to change its valuation methodology from time to time, the OCA states that it does not expect to see frequent changes. In addition, the OCA confirms that such a change is not deemed to be a "change in accounting principle" and as a result may be set forth in a footnote disclosure and does not even require a "preferability" letter from outside auditors.
In addition, SAB 107 clarifies that companies need not hire outside valuation experts to make the determinations required by FAS 123R, although valuations should be performed by persons with the requisite expertise.
Assumptions for Valuation Methodologies
In order to satisfy FAS 123R, a company must make estimates regarding two key aspects of its stock options: their expected volatility and their term. FAS 123R does not specify a particular method for making these estimates, but it does supply a list of factors for consideration by the company. If, after initially selecting appropriate assumptions for these determinations, a company subsequently opts to make changes, it must disclose the new assumptions in its financial statement footnotes.
SAB 107 indicates that a company should make a good faith estimate of the volatility of its stock options, taking into account both historical and implied volatility (or a combination of the two), as appropriate. For companies with actively traded options or other financial instruments with embedded options, the staff notes that implied volatility could be the predominant or even exclusive measure of volatility for purposes of FAS 123R. The approach to data collection and analysis relating to share volatility should generally remain consistent over time, absent changed circumstances.
To determine historical volatility, the OCA suggests that a company estimate the expected future volatility of its stock options, consider applicable historical data, make regular price observations and consider the potential impact of future events. In addition, the OCA notes that in certain rare circumstances, a company could reasonably exclude anomalous periods of time from consideration, although if it chooses to do so, the company must be prepared to justify the exclusion.
When considering its reliance on implied volatility based on traded options, a company should evaluate the volume of market activity; its ability to match the material characteristics of the traded options and employee stock options as closely as possible (i.e., through the selection of near–the–money or at–the–money options and the use of recent trading data); and the similarity between the exercise price and terms of its traded options and employee stock options.
Once a company has determined the assumptions upon which it will base its volatility determination, FAS 123R obligates it to disclose the expected volatility and the method used to estimate it. Under SAB 107, the OCA expects companies to include this information in footnote disclosure and to indicate whether the company has used historical volatility, implied volatility or some combination of the two. The OCA also expects an explanation of the method used to estimate volatility.
For companies with limited historical data, FAS 123R permits the use of comparable alternative data. SAB 107 expands upon this by permitting a company to use volatility data for similar companies in the same or a similar industry until it has at least two years of daily or weekly historical data to draw upon. A company opting to use this approach must apply it consistently.
In addition to estimating share volatility, a company must also estimate the expected term for its stock options. According to SAB 107, because ESOs are nontransferable and often subject to other limitations, their value is inherently less than traded options. To account for this, a fair value estimate of ESOs must be based on their expected term rather than their contractual term. Under SAB 107, the expected term of a stock option must be determined on the basis of the relevant facts and circumstances and, pursuant to FAS 123R, must be disclosed in the financial statement footnotes.
Because the expected term determination already reflects the limited transfer and hedging opportunities available to option holders, no additional discounting is permitted to account for an expected term that is less than a contractual term.
Forfeitures and terms relating to forfeitability should not be taken into account for purposes of determining an expected term. In no event can the expected term for an ESO be less than the applicable vesting period.
The determination of expected terms must be made using a reasonable and supportable approach consistent with likely marketplace behavior. In appropriate circumstances, historical experience regarding option exercises could be used as a reasonable basis for this determination. Under FAS 123R, in determining the expected term of stock options, a company must generally group individual awards by expected behavior; despite FAS 123R's implication that several such groups may be required, the staff believes that no more than one or two groups may be necessary to comply with this requirement.
SAB 107 provides a simplified formula2 that can be used to determine the expected term of "plain vanilla" stock options.3 Note that companies that have more detailed data regarding the terms of stock options are not required to use this simplified formula, and the simplified formula is not intended for use as a benchmark for more detailed analyses. Moreover, the OCA expressed its belief that the simplified formula will not generally be appropriate for use for option grants made after Dec. 31, 2007.
Management Discussion and Analysis Disclosures
As part of its focus on critical accounting policies and its desire to encourage companies to better advise investors and other users of financial statements, the OCA believes that companies should include certain disclosures relating to their adoption of FAS 123R in its MD&A. More specifically, the staff notes that a company should consider disclosing qualitative and quantitative information regarding the following:
- The selected transition method and resulting financial statement impact.
- The method used to account for stock options in prior periods.
- Any modifications made to outstanding stock options prior to the adoption of FAS 123R and the reason for such modifications.
- Any differences in valuation methodology or assumptions between the disclosed information and the fair value estimate made under FAS 123R.
- Any changes to the type or quantity of instruments used in the stock option program.
- Any changes to the terms of stock options.
- A description of the effects of adopting FAS 123R.
- The total compensation costs of non–vested stock options that have not been recognized and the weighted average period over which they are expected to be recognized.
Modification of Existing Options
As noted above, the OCA suggests that companies disclose and explain any modifications made to outstanding stock options prior to the adoption of FAS 123R. Beyond this suggestion, the OCA importantly notes that it will have no objection if a company that has previously accounted for stock option grants in accordance with APB 25 opts to accelerate vesting on outstanding stock options prior to adopting Statement 123R. In other words, a company's choice to accelerate vesting for underwater stock options prior to adopting FAS 123R will not result in subsequent accounting charges relating to those options. However, the OCA points out that any such modifications must be disclosed and accompanied by an explanation of the business justification for accelerating vesting for the affected stock options.
Non–GAAP Financial Measures
SAB 107 indicates that it may be possible for a company to include a separate measure in its financial statement footnotes to show net income before taking into account the effects of share–based payments, even though such a measure is a non–GAAP measure for purposes of SEC Regulation G and Item 10(e) of Regulation S–K. The OCA references its prior statement that the elimination of a recurring expense for the purpose of smoothing earnings is impermissible and that a company proposing to remove such an expense for other reasons bears the burden of establishing the usefulness of the elimination. The OCA notes that the use of such a measure could be permissible if the company were to determine that the measure does not violate any of the prohibitions set forth in Item 10(e) of Regulation S–K and disclose the basis for the use of the measure and the extent to which the measure is used for purposes that are not otherwise disclosed. According to the OCA, the use of a non–GAAP measure relating to share–based compensation could be misleading unless certain specified disclosures are made. The staff believes that a company should disclose information in its MD&A regarding each component of its expenses, including any material information about expenses associated with share–based payments. Moreover, a company may not remove the net effects of share–based payment expenses from its pro forma income statements filed with the SEC.
Classification of Compensation Expenses
SAB 107 indicates that it may be appropriate for a company to distinguish between cash and share–based compensation in a parenthetical note to an income statement line item, on the cash flow statement, in the financial statement footnotes, or in MD&A. The staff notes that both cash and share–based compensation should be combined for disclosure as an expense in a company's income and financial statements.
Application of Valuation Principles
The problem with expensing stock options is that the value of an option is, at times, much more of an art than a science. Exchange–traded options exist in liquid and transparent markets; ascertaining value is a relatively simple matter of looking up the instrument in question. Investors and traders in these options markets have, over time, developed tools, formulas and methods for valuing these options.
In terms of its basic characteristics, a corporate stock option scheme is broadly similar to an exchange traded American–style call option issued on a firm's own stock. The receiver of a stock option acquires the right to purchase a specified number of a firm's stock at a fixed strike price at some future date. The option is exercised by the holder if the stock price is in excess of the strike price, so that stocks acquired at a fixed price according to the terms of the option scheme can then be resold in the open market at a profit. The holder of the option stands to gain from the increase of the firm's stock price, but avoids exposure to the downside as there is no obligation to exercise if the exercise is not profitable to the holder.
However, ESOs are not exchange–traded and have a number of features that make them differ radically from their exchange–traded cousins. Exchange–traded options are generally for a short term and are subject to exercise at any point during the option term (American exercise). ESOs typically have a term of 10 years, frequently, with a vesting provision–a restriction on the exercise period stating that the employee must complete, say, three years of service. They will also usually have a provision requiring exercise within a fixed period of days following termination of employment. There may also be further restrictions placed on exercise via blackout periods and insider trading restrictions.
To summarize, the characteristic features of ESOs are:
Long maturity. ESOs are normally issued for a 10–year term. It is unusual to see a traded option with maturity in excess of five years.
Vesting. A traded American option can be exercised at any point during its life. A European option can be exercised on a fixed maturity date only. Executive stock options tend to have a three–year vesting period, during which exercise is not permitted. However, thereafter the exercise is allowed at any time up until maturity. Alternatively, the option may become vested in tranches, for example, over a period of two years following the third anniversary of the grant.
Other exercise restrictions. Restrictions on exercise of the employee option can be lifted on attaining a specified level of performance.
Non–transferability. Unlike standard American options, executive stock options are non–tradable, and usually there are specific restrictions imposed to prevent the holder from re–selling.
Resetting. Resetting is an arrangement whereby an adjustment made to the strike price of the existing option following a drop of the share price relative to the strike price transforms a deeply out–of–the–money option into an at–the–money option.
Reloading. Reloading is an arrangement whereby extra options are granted to the option holder following the exercise of his existing options.
Blackout periods. Executives may not be allowed to exercise their options for a fixed period of time if it is deemed that they may have has access to the insider information.
Abrupt termination. An executive may get fired or die unexpectedly. In this case, the non–vested options are forfeited. The vested options must be exercised immediately; however, the right to the acquisition of extra options through reloading procedure is lost.
Valuation Method Alternatives: the Black–Scholes method
The oldest and most famous valuation method is the Black–Scholes method. This method uses a stochastic differential equation with implicit embedded assumptions. By plugging key variables into the Black–Scholes formula–the price and price–volatility of the underlying stock and the rate of return on a risk–free investment (the risk–free interest rate)–the Black–Scholes formula produces a value for an option. Black–Scholes and Black–Scholes–derived formulas have been effectively used for years in valuing exchange–traded options. And in that context they are generally regarded as theoretically and empirically sound.
Adapting Black–Scholes to employee options has, however, proved cumbersome. Let's review the problems employee options present.
Black–Scholes assumes trading in the underlying stock, and the ability to exercise the option, is continuous and unrestricted. But as already mentioned, employee options are subject to a number of restrictions–vesting periods, blackouts and securities law insider trading restrictions.
Black–Scholes assumes a constant risk–free interest rate. For a three–month option such an assumption may be reasonable, but not for the 10–year term typical for employee options.
Similarly, Black–Scholes assumes volatility is constant over the option period. Again, a reasonable assumption for three months, but probably not for 10 years. Dividend–paying stocks pose additional complications in setting assumptions for both the risk–free rate and volatility under the model.
Black–Scholes assumes existence of a frictionless, complete, arbitrage free market. But in many respects, an employee option holder represents a market of one. The completeness of market, and therefore ability to hedge contingent claims, is in doubt.
If the individual employee has a conservative risk preference, he or she may not be able to realize the full value of the option predicted and exercise too soon.
A number of extensions of the Black–Scholes method have been developed to accommodate individual features of ESO programs (See, for example, Sricar and Xiong (2005) and Ball, Cockerton, Neate and Wise (2005)). However, a more complex model will not necessarily produce a more robust answer, as the addition of non–observable parameters inevitably undermines reliability of calibration.
Instead, practitioners tended to apply Black–Scholes to employee options in a "rough answer," rule–of–thumb manner to discount for, for instance, the effect on value of restrictions on trading. These discounts may not always have a theoretical justification.
How the Different Features of Employee Options Affect Valuation?
To get a feel for the significance of the foregoing factors for option valuation, let's go into a little more detail.
Sub–optimal exercise. When dividends are not involved, American call options achieve their highest value only if held for their full term, and exchange traded options are priced with an assumption that they will be held to the end of their term. For a variety of reasons, employee options are often not held for their full term. Some employees just exercise early–as soon as their options vest, they pull the trigger. Other employees exercise when the value of the underlying stock increases by a target amount-50 percent or 100 percent. There is also a forced early exercise on termination of employment. Terminating employee–option holders typically have 90 days after termination in which to exercise.
For any given company, the extent of this "suboptimal exercise" behavior can be predicted with some accuracy (based on past behavior), and its effect on option value can–with the right valuation model–be measured.
Vesting. Early exercise is regarded as "always bad," and the earlier the exercise, the worse its effect, i.e., the greater the decrease in the value of the option. By forcing "late" exercise via a vesting provision, the value of an option is increased.
Changes in interest rate and volatility. If the valuation "horizon" is 10 years, and not three months, it is probably unreasonable to assume that the current level of interest rates and volatility are good for the entire term. Interest rate and volatility assumptions used in valuing employee options should be flexible. While a stock's price may be volatile now–with higher volatility driving up option value–it is unreasonable to assume high volatility will continue for 10 years.
The Lattice Model
Black–Scholes was developed before the advent of the desktop computer age, when the calculating power available to most market participants was very limited. One rule–of–thumb equation worked nicely for valuations of short–term exchange traded options made on the fly. But the subtlety of the calculations needed to accommodate all the factors at work in an employee option does not fit easily with the standard Black–Scholes methodology. A more flexible valuation methodology known as the lattice (or binomial model) is better suited to dealing with more complex options.
The lattice model is in concept simpler than Black–Scholes. Starting with similar data about price and similar assumptions about interest and volatility (similar, that is, to the assumptions we would use in applying Black–Scholes), the lattice model maps a range of results one time step by time step.
If we use the same data about price and make the same assumptions about interest rates and volatility as we do under Black–Scholes, then, using the lattice model, we get the same result as we do under Black–Scholes. But unlike the Black–Scholes, the lattice model allows adjust assumption at each time step. So it is possible to assume that volatility is high (say 50 percent) for the first 18 months (and for the first 18 time steps) and then drops down to a more reasonable level (say 20 percent) thereafter.
To sum up, the lattice model allows using the same assumptions about the relationships between prices, interest rates and volatility that underlie Black–Scholes, while allowing us to add to and elaborate on these variables, using the brute calculating power of modern computers to do the "billions and billions" of calculations required.
Consider an example of using the lattice model as shown in Table 1.
If we use the same data about price and make the same assumptions about interest rates and volatility as we do under Black–Scholes, then, using the lattice model, we get the same result as we do under Black–Scholes. The basic lattice model becomes a progressively better approximation of Black–Scholes as the number of nodes on the tree is increased. (Table 2)
Beginning with the kind of assumptions that are used in Black–Scholes valuation:
- Initial Stock Price = $20
- Stock Price Volatility = 25 percent
- Time Interval = one year
- Risk–free rate = 5.0 percent
Add on some provisions typical of an employee option:
- Vesting Period = 100 percent after three years
- Early Exercise Allowed after Vesting
- Potential forfeiture due to termination
- Mandatory exercise following termination
- Lack of transferability
The extra assumptions map seamlessly and intuitively onto the lattice. In this case, the inclusion of these limitations has the net effect of decreasing the value of the stock option by approximately 47 percent.
Valuation Method Alternatives: Monte Carlo Simulations
A Monte Carlo model, simulating future paths of financial indices, necessarily on the market consistent, arbitrage free basis, is a highly versatile tool. The model can be straight–forward to use for valuation of contingent claims, but only if the claims are allowed to occur at one fixed time point in future. Using the same assumptions as the other two methods, a Monte Carlo model will replicate Black–Scholes and the lattice model results, bar the sampling error.
However, for the reasons outlined above, an employee stock option cannot be simply treated as a basic contingent claim. The need to allow for the possibility of the early exercise is the main problem. Extension of basic Monte Carlo simulation methods, for instance, by Andersen (2000) involves determination of an early exercise boundary to estimate the behavior of the option holder.
Monte Carlo models are easy to interpret and communicate to non–specialists; however, they require significant computational power, and will necessarily involve approximations when estimating the cost of employee stock options.
As the modeling capability is upgraded, Monte Carlo models and Black–Scholes type closed form solution formulae that rival in usefulness the lattice model may emerge, however for the time being it remains the most robust approach to estimating the cost of employee stock options.
Viktor Mirkin works in the Actuarial and Insurance team for Deloitte in the United Kingdom. He can be contacted at firstname.lastname@example.org.
Jeffrey Green is principal, Capital Markets, Deloitte & Touche LLP, New York. He can be contacted at email@example.com.
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- Remarks by Chairman Alan Greenspan, at the 2002 Financial Markets Conference of the Federal Reserve Board of Atlanta, Stock options and related matters.
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- Zweig, Warren Buffet wants to know, Money Magazine, 3.05.2004.
- Note that the guidance provided in SAB 107 is not regarded as an official interpretation or regulation of the SEC, nor does it modify or supersede the requirements set forth in FAS 123R. Instead, SAB 107 describes the interpretations and practices that will be followed by the OCA in administering disclosure requirements under Federal securities laws.
- Under this simplified formula, a stock option's expected term is equal to the sum of its vesting term and original contractual term divided by two.
- The example cited in SAB 107 involves at–the–money option grants that are subject to a standard employment based vesting schedule, exercisable for a limited period of time after termination of employment, and non–transferable and non–hedgeable.