an option holder will exhibit. Considerations include:
• vesting period – the expected term of the option must be at least as long as its
vesting period. The length of time employees hold options after they vest may vary
inversely with the length of the vesting period;
• past history of employee exercise and termination patterns for similar grants
(adjusted for current expectations) – see 8.5.2 below;
• expected volatility of the underlying share – on average, employees tend to
exercise options on shares with higher volatility earlier;
• periods during which exercise may be precluded and related arrangements (e.g.
agreements that allow for exercise to occur automatically during such periods if
certain conditions are satisfied);
• employee demographics (age, tenure, sex, position etc.); and
• time from vesting date – the likelihood of exercise typically increases as time passes.
As discussed at 8.4 above, IFRS 2 notes that the effect of early exercise can be reflected:
• by treating the expected, rather than the contractual, life of the option as an input
to a pricing model, such as the Black-Scholes-Merton formula (see 8.5.1.A below);
or
• by using contractual life as an input to a binomial or similar model. [IFRS 2.B16-17].
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8.5.1.A
Expected term under the Black-Scholes-Merton formula
An estimate of expected term based on the types of inputs described above can be used
in the Black-Scholes-Merton formula as well as a lattice model. However, the formula
requires only a single expected term to be used. This is one of the reasons why the
Black-Scholes-Merton formula may provide a higher valuation for the same options
than a lattice model.
The difference in value that arises from using only a single expected term results, in
part, from the convex shape of a typical option valuation curve, as illustrated below.
Option value
€4.00
€3.50
€3.00
€2.50
€2.00
€1.50
€1.00
€0.50
€0.00
1
2
3
4
5
6
7
8
9
10
Year
It is assumed, for the purposes of this illustration, that an at-the-money option on a
€10 share with a 10-year contractual term is equally likely to be exercised at the end of each
year beginning with year two. An average expected term of six years [(2+3+4+...10)/9] would
be used in a Black-Scholes-Merton calculation giving a fair value of €3.10 for the option. If,
instead, nine separate valuations were performed, each with a different expected term
corresponding to each of the possible terms (from two to ten years), the average of those
valuations (also calculated using the Black-Scholes-Merton formula) would be €2.9854. The
latter amount is lower than €3.10 because of the convex shape of the valuation curve,
reflecting the fact that the value increases at a decreasing rate as the term lengthens.
Therefore, the value of the share option with an average expected term of six years will
exceed the value derived from averaging the separate valuations for each potential term.
In a lattice model, exercise can occur at any time based on the rules specified in the
model regarding exercise behaviour. The lattice model can therefore be thought of as
analogous to the calculation in the above example in which the fair value was calculated
as the average of the valuations from periods two to ten. In contrast, the Black-Scholes-
Merton valuation allows only a single expected term to be specified. Therefore, it is
analogous to the valuation described in the above example based on a single average
expected term of six years.
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Therefore, even if the expected term derived from a lattice model were used as an input
in the Black-Scholes-Merton formula (and all other inputs were identical), the two
models would give different values.
To mitigate the impact of the convex shape of the valuation curve, an entity with a broad-
based share option plan might consider stratifying annual awards into different employee
groups for the purposes of estimating the expected option lives (see 8.5.2 below).
Determining a single expected term can be quite challenging, particularly for an entity
seeking to base its estimate on the periods for which previously granted options were
outstanding, which would have been highly dependent on the circumstances during
those periods. For example, if the entity’s share price had increased significantly during
the option period (as would be the case for share options granted by certain entities at
the beginning of a bull market), it is likely that employees would have exercised options
very soon after vesting. Alternatively, if options were granted at the end of a bull market
and the share price declined significantly after the grant date, it is likely that the options
would be exercised much later (if at all). These relationships would exist because, as
discussed previously, the extent to which an option is in-the-money has a significant
impact on exercise behaviour. Accordingly, deriving a single expected term in these
situations involves considerable judgement.
8.5.2
Exercise and termination behaviour
IFRS 2 notes that employees often exercise options early for a number of reasons, most
typically:
• restrictions on transferability mean that this is the only way of realising the value
of the option in cash;
• aversion to the risk of not exercising ‘in the money’ options in the hope that they
increase in value; or
• in the case of leavers, a requirement to exercise, or forfeit, all vested options on or
shortly after leaving (see 8.5.2.B below).
Factors to consider in estimating early exercise include:
(a) the length of the vesting period, because the share option cannot be exercised until
the end of the vesting period. Hence, determining the valuation implications of
expected early exercise is based on the assumption that the options will vest;
(b) the average length of time similar options have remained outstanding in the past;
(c) the price of the underlying shares. Experience may indicate that employees tend
to exercise options when the share price reaches a specified level above the
exercise price;
(d) the employee’s level within the organisation. For example, experience might
indicate that higher-level employees tend to exercise options later than lower-
level employees (see also 8.5.2.A below); and
(e) the expected volatility of the underlying shares. On average, employees might tend
to exercise options on highly volatile shares earlier than on shares with low volatility.
[IFRS 2.B18].
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In addition, the pattern of terminations of employment after vesting may be relevant
(see 8.5.2.B below).
In our view, past exercise behaviour should generally serve as the starting point for
determini
ng expected exercise behaviour. That behaviour should be analysed,
correlated to the factors above, and extrapolated into the future. However,
significant changes in the underlying share price or in other salient characteristics of
the entity, changes in option plans, tax laws, share price volatility and termination
patterns may indicate that past exercise behaviour is not indicative of expected
exercise behaviour. The expected life may also be estimated indirectly, by using a
modified option pricing model to compute an option value, an input to which is an
assumption that the options will be expected to be exercised when a particular share
price is reached.
Some entities, including recently listed entities, or entities for which all outstanding
grants have been out-of-the-money for a long period, may simply not be able to observe
any exercise behaviour or may not possess enough history to perform a reasonable
analysis of past exercise behaviour. In these cases, in our view, entities may have to look
to the exercise history of employees of similar entities to develop expectations of
employee exercise behaviour. At present there is only limited publicly-available
information about employee exercise patterns, but valuation professionals and human
resource consultants may have access to relevant data, based on which they may have
articulated specific exercise patterns. In such circumstances, considerable judgement is
required in assessing the comparability and appropriateness of the historic data used.
In the absence of extensive information regarding exercise behaviour, another solution
could be to use a midpoint assumption – i.e. selecting as the expected date of exercise
the midpoint between the first available exercise date (the end of the vesting period)
and the last available exercise date (the contracted expiry date). However, this should
be undertaken only when the entity is satisfied that this does not lead to a material
misstatement. It is also plausible to assume exercise at the earliest possible time or to
undertake a reasonable analysis of past behaviour and set up the amount of intrinsic
value which, when exceeded, will trigger exercise of the option.
8.5.2.A
Grouping employees with homogeneous exercise behaviour
IFRS 2 emphasises that the estimated life of an option is critical to its valuation.
Therefore, where options are granted to a group of employees, it will generally be
necessary to ensure that either:
(a) all the employees are expected to exercise their options within a relatively narrow
time-frame; or
(b) if not, that the group is divided into sub-groups of employees who are expected to
exercise their options within a similar relatively narrow time-frame.
IFRS 2 suggests that it may become apparent that middle and senior management tend
to exercise options later than lower-level employees, either because they choose to do
so, or because they are encouraged or compelled to do so as a result of required
minimum levels of ownership of equity instruments (including options) among more
senior employees. [IFRS 2.B19-21].
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8.5.2.B Post-vesting
termination
behaviour
Most employee share options provide that, if employment is terminated, the former
employee typically has only a short period (e.g. 90 days from the date of termination of
employment) in which to exercise any vested options, the contractual expiry of which
would otherwise be some years away. Accordingly, an entity should look at its prior
termination patterns, adjust those patterns for future expectations and incorporate
those expected terminations into a lattice model as expected early exercises.
Patterns of employee turnover are not necessarily linear and may be a non-linear
function of a variety of factors, such as:
• employee demographics (age, sex, tenure, position, etc.);
• path of share price – for example, if options are deeply out-of-the-money, they
may have little retention value and more employees may leave than if the options
were at- or in-the-money; and
• economic conditions and other share prices.
8.5.3
Expected volatility of share price
Expected volatility is a measure of the amount by which a price is expected to fluctuate
during a period. Share price volatility has a powerful influence on the estimation of the
fair value of an option, much of the value of which is derived from its potential for
appreciation. The more volatile the share price, the more valuable the option. It is
therefore essential that the choice of volatility assumption can be properly supported.
IFRS 2 notes that the measure of volatility used in option pricing models is the
annualised standard deviation of the continuously compounded rates of return on the
share over a period of time. Volatility is typically expressed in annualised terms that are
comparable regardless of the time period used in the calculation (for example, daily,
weekly or monthly price observations).
The expected annualised volatility of a share is the range within which the continuously
compounded annual rate of return is expected to fall approximately two-thirds of the
time. For example, to say that a share with an expected continuously compounded rate
of return of 12% has a volatility of 30% means that the probability that the rate of return
on the share for one year will be between minus 18% (12% – 30%) and 42% (12% + 30%)
is approximately two-thirds. If the share price is €100 at the beginning of the year, and
no dividends are paid, the year-end share price would be expected to be between
€83.53 (€100 × e–0.18) and €152.20 (€100 × e0.42) approximately two-thirds of the time.
The rate of return (which may be positive or negative) on a share for a period measures
how much a shareholder has benefited from dividends and appreciation (or
depreciation) of the share price. [IFRS 2.B22-24].
IFRS 2 gives examples of factors to consider in estimating expected volatility including
the following: [IFRS 2.B25]
• Implied volatility from traded share options
Implied volatility is the volatility derived by using an option pricing model with the
traded option price (if available) as an input and solving for the volatility as the
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unknown on the entity’s shares. It may also be derived from other traded
instruments of the entity that include option features (such as convertible debt).
Implied volatilities are often calculated by analysts and reflect market expectations
for future volatility as well as imperfections in the assumptions in the valuation
model. For this reason, the implied volatility of a share may be a better measure of
prospective volatility than historical volatility (see below). However, traded
options are usually short-term, ranging in general from one month to two years. If
the expected lives are much longer than this, both the implied and historical
volatilities will need to be considered.
• Historical volatility
It may be relevant to consider the historical volatility of the share price over the
most recent period that is generally commensurate with the expect
ed term of the
option (taking into account the remaining contractual life of the option and the
effects of expected early exercise). However, this assumes that past share price
behaviour is likely to be representative of future share price behaviour. Upon any
restructuring of an entity, the question of whether or not past volatility will be
likely to predict future volatility would need to be reassessed.
The historical volatilities of similar entities may be relevant for newly listed
entities, unlisted entities or entities that have undergone substantial restructuring
(see 8.5.3.A to 8.5.3.C below).
• The length of time the entity’s shares have been publicly traded
A newly listed entity might have a high historical volatility, compared with similar
entities that have been listed longer. Further guidance for newly listed entities is
given in 8.5.3.A below.
• ‘Mean-reverting tendency’
This refers to the tendency of volatility to revert to its long-term average level, and
other factors indicating that expected future volatility might differ from past
volatility. For example, if an entity’s share price was extraordinarily volatile for
some identifiable period of time because of a failed takeover bid or a major
restructuring, that period could be disregarded in computing historical average
annual volatility. However, an entity should not exclude general economic factors
such as the effect of an economic downturn on share price volatility.
• Appropriate and regular intervals for price observations
The price observations should be consistent from period to period. For example,
an entity might use the closing price for each week or the opening price for the
week, but it should not use the closing price for some weeks and the opening price
for other weeks. Also, the price observations should be expressed in the same
currency as the exercise price. In our view, at least thirty observations are
generally required to calculate a statistically valid standard deviation. Our
experience has been that, in general, it is more appropriate to make such
observations daily or weekly rather than monthly.
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8.5.3.A Newly
listed
entities
As noted under ‘Historical volatility’ at 8.5.3 above, an entity should consider the historical
volatility of the share price over the most recent period that is generally commensurate
International GAAP® 2019: Generally Accepted Accounting Practice under International Financial Reporting Standards Page 525