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Chapter 4 — Measurement

4.9 Option Pricing Models

4.9 Option Pricing Models

ASC 718-10 — Glossary
Closed-Form Model
A valuation model that uses an equation to produce an estimated fair value. The Black-Scholes-Merton formula is a closed-form model. In the context of option valuation, both closed-form models and lattice models are based on risk-neutral valuation and a contingent claims framework. The payoff of a contingent claim, and thus its value, depends on the value(s) of one or more other assets. The contingent claims framework is a valuation methodology that explicitly recognizes that dependency and values the contingent claim as a function of the value of the underlying asset(s). One application of that methodology is risk-neutral valuation in which the contingent claim can be replicated by a combination of the underlying asset and a risk-free bond. If that replication is possible, the value of the contingent claim can be determined without estimating the expected returns on the underlying asset. The Black-Scholes-Merton formula is a special case of that replication.
Intrinsic Value
The amount by which the fair value of the underlying stock exceeds the exercise price of an option. For example, an option with an exercise price of $20 on a stock whose current market price is $25 has an intrinsic value of $5. (A nonvested share may be described as an option on that share with an exercise price of zero. Thus, the fair value of a share is the same as the intrinsic value of such an option on that share.)
Lattice Model
A model that produces an estimated fair value based on the assumed changes in prices of a financial instrument over successive periods of time. The binomial model is an example of a lattice model. In each time period, the model assumes that at least two price movements are possible. The lattice represents the evolution of the value of either a financial instrument or a market variable for the purpose of valuing a financial instrument. In this context, a lattice model is based on risk-neutral valuation and a contingent claims framework. See Closed-Form Model for an explanation of the terms risk-neutral valuation and contingent claims framework.
Time Value
The portion of the fair value of an option that exceeds its intrinsic value. For example, a call option with an exercise price of $20 on a stock whose current market price is $25 has intrinsic value of $5. If the fair value of that option is $7, the time value of the option is $2 ($7 – $5).
ASC 718-10
30-7 The fair value of an equity share option or similar instrument shall be measured based on the observable market price of an option with the same or similar terms and conditions, if one is available (see paragraph 718-10-55-10).
30-8 Such market prices for equity share options and similar instruments granted in share-based payment transactions are frequently not available; however, they may become so in the future.
30-9 As such, the fair value of an equity share option or similar instrument shall be estimated using a valuation technique such as an option-pricing model. For this purpose, a similar instrument is one whose fair value differs from its intrinsic value, that is, an instrument that has time value. For example, a share appreciation right that requires net settlement in equity shares has time value; an equity share does not. Paragraphs 718-10-55-4 through 55-47 provide additional guidance on estimating the fair value of equity instruments, including the factors to be taken into account in estimating the fair value of equity share options or similar instruments as described in paragraphs 718-10-55-21 through 55-22.
Valuation Techniques
55-15 Valuation techniques used for share options and similar instruments granted in share-based payment transactions estimate the fair value of those instruments at a single point in time (for example, at the grant date). The assumptions used in a fair value measurement are based on expectations at the time the measurement is made, and those expectations reflect the information that is available at the time of measurement. The fair value of those instruments will change over time as factors used in estimating their fair value subsequently change, for instance, as share prices fluctuate, risk-free interest rates change, or dividend streams are modified. Changes in the fair value of those instruments are a normal economic process to which any valuable resource is subject and do not indicate that the expectations on which previous fair value measurements were based were incorrect. The fair value of those instruments at a single point in time is not a forecast of what the estimated fair value of those instruments may be in the future.
55-16 A lattice model (for example, a binomial model) and a closed-form model (for example, the Black-Scholes-Merton formula) are among the valuation techniques that meet the criteria required by this Topic for estimating the fair values of share options and similar instruments granted in share-based payment transactions. A Monte Carlo simulation technique is another type of valuation technique that satisfies the requirements in paragraph 718-10-55-11. Other valuation techniques not mentioned in this Topic also may satisfy the requirements in that paragraph. Those valuation techniques or models, sometimes referred to as option-pricing models, are based on established principles of financial economic theory. Those techniques are used by valuation professionals, dealers of derivative instruments, and others to estimate the fair values of options and similar instruments related to equity securities, currencies, interest rates, and commodities. Those techniques are used to establish trade prices for derivative instruments and to establish values in adjudications. As discussed in paragraphs 718-10-55-21 through 55-50, both lattice models and closed-form models can be adjusted to account for the substantive characteristics of share options and similar instruments granted in share-based payment transactions.
55-17 This Topic does not specify a preference for a particular valuation technique or model in estimating the fair values of share options and similar instruments granted in share-based payment transactions. Rather, this Topic requires the use of a valuation technique or model that meets the measurement objective in paragraph 718-10-30-6 and the requirements in paragraph 718-10-55-11. The selection of an appropriate valuation technique or model will depend on the substantive characteristics of the instrument being valued. Because an entity may grant different types of instruments, each with its own unique set of substantive characteristics, an entity may use a different valuation technique for each different type of instrument. The appropriate valuation technique or model selected to estimate the fair value of an instrument with a market condition must take into account the effect of that market condition. The designs of some techniques and models better reflect the substantive characteristics of a particular share option or similar instrument granted in share-based payment transactions. Paragraphs 718-10-55-18 through 55-20 discuss certain factors that an entity should consider in selecting a valuation technique or model for its share options or similar instruments.
55-18 The Black-Scholes-Merton formula assumes that option exercises occur at the end of an option’s contractual term, and that expected volatility, expected dividends, and risk-free interest rates are constant over the option’s term. If used to estimate the fair value of instruments in the scope of this Topic, the Black-Scholes-Merton formula must be adjusted to take account of certain characteristics of share options and similar instruments that are not consistent with the model’s assumptions (for example, exercising before the end of the option’s contractual term when estimating expected term). Because of the nature of the formula, those adjustments take the form of weighted-average assumptions about those characteristics. In contrast, a lattice model can be designed to accommodate dynamic assumptions of expected volatility and dividends over the option’s contractual term, and estimates of expected option exercise patterns during the option’s contractual term, including the effect of blackout periods. Therefore, the design of a lattice model more fully reflects the substantive characteristics of particular share options or similar instruments. Nevertheless, both a lattice model and the Black-Scholes-Merton formula, as well as other valuation techniques that meet the requirements in paragraph 718-10-55-11, can provide a fair value estimate that is consistent with the measurement objective and fair-value-based method of this Topic.
55-19 Regardless of the valuation technique or model selected, an entity shall develop reasonable and supportable estimates for each assumption used in the model, including the share option or similar instrument’s expected term, taking into account both the contractual term of the option and the effects of grantees’ expected exercise and postvesting termination behavior. The term supportable is used in its general sense: capable of being maintained, confirmed, or made good; defensible. An application is supportable if it is based on reasonable arguments that consider the substantive characteristics of the instruments being valued and other relevant facts and circumstances.

Footnotes

1
If the award contains market conditions, the use of this practical expedient is not permitted.
[2]
The OCA memorandum states, “Under the proposals that we have seen, the amount of market instruments that would be issued is a fraction of the total option grant (generally 5–15 percent of the grant). Alternatively, a company could transfer part or all of its grant obligations to a third party that would meet the grant’s stock delivery obligation. We have not evaluated the adequacy of any grant size or volume to the achievement of the valuation objective.”
[3]
The OCA memorandum states that the “net payment may be in the form of securities or cash.”