Formula and conventions
The calculator implements the Black-Scholes-Merton closed-form value of a European option with a continuous dividend yield. It shows d1, d2, N(d1) and N(d2) and the call and put values satisfy put-call parity. The normal distribution function is computed to double precision. Rates are entered as annual percentages and used as continuously compounded; the term is in years.
Where it applies
ASC 718 requires share-based awards to employees to be measured at grant-date fair value, estimated with an option pricing model when market prices are not available. This tool recomputes the value per option for a plain vanilla award. Expense is then recognized over the requisite service period, with forfeitures either estimated or accounted for as they occur, and the tool's forfeiture field only reduces the total shown on the page. For the asset side of other long-lived items, see the depreciation calculator.
Limits
Constant volatility and rate, no early exercise and no performance or market conditions. The formula is not an accounting policy: the selection of inputs, the expected term estimate and the choice of model must be supported and documented. Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What is the Black-Scholes-Merton formula?
Call = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2) and put = K·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1), where d1 = [ln(S ÷ K) + (r − q + σ²÷2)·T] ÷ (σ√T) and d2 = d1 − σ√T. S is the stock price, K the exercise price, T the term in years, r the continuously compounded risk-free rate, q the continuous dividend yield, σ the volatility and N the standard normal distribution function.
Which inputs does ASC 718 require for an option pricing model?
The model must reflect the exercise price, the current price of the underlying stock, the expected term of the option, expected volatility of the stock price, expected dividends and the risk-free interest rate for the expected term. Expected term and expected volatility usually take the most judgment. The inputs must be reasonable and supportable and reflect the award’s substantive terms.
Is Black-Scholes an acceptable model under ASC 718?
Yes. A closed-form model such as Black-Scholes-Merton and a lattice model can both produce a fair value that meets the Topic, provided the entity selects the model that suits the award and applies it to reflect the award’s substantive characteristics. Awards with market or performance conditions, or with early-exercise features that matter, may need a lattice or Monte Carlo model.
What should I use for the risk-free rate and volatility?
The risk-free rate is commonly the U.S. Treasury zero-coupon yield for the expected term; convert it to a continuously compounded rate, ln(1 + y), before entering it here. Volatility can come from the entity’s own trading history, implied volatility on traded options, or peer companies. A nonpublic entity that cannot reasonably estimate its volatility may be able to use a calculated value based on an appropriate industry sector index.
How does an auditor use this?
To recompute the grant-date fair value the client reports, by agreeing each input to support and re-performing the valuation, and to test sensitivity: small changes in volatility and expected term move value a lot. The tool gives the arithmetic. Whether the inputs are supportable is the auditor’s judgment, and for a specialist’s valuation the auditor evaluates the specialist’s work under the firm’s methodology.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.