Accounting Methods for Employee Stock Options

Stock options, a common form of employment compensation, raise the issue of valuation.

Employers generally expense the stock options that they issue to their employees according to: (a) the Black-Scholes-Merton formula, or (b) a lattice model or (c) a simulation-based model. The rules of the Financial Accounting Standards Board (FASB) allow for other choices, but these three models remain dominant.

Black-Scholes-Merton

Black swans, and extreme price moves, are not as rare as sometimes thought.

The Black-Scholes-Merton (BSM) formula values an option to buy a share of stock by making certain explicit simplifying assumptions. For example, BSM assumes that extreme price changes are very rare, because the movements in the value of the underlying stock follow lognormal distribution. The assumption, and certain other features of the formula, have been called into question by many scholars, but most agree that BSM offers a useful approximation of value.

Lattice Models

A lattice model divides the time between the issuance of an option and its expiration into a definite number of discrete time periods (e.g., months or quarters). Given input variables and assumptions that must be made explicit in the company's accounting, a probability is assigned to an "up" and to a "down" move in each period. This yields two (or more, depending on how the particular lattice is constructed) end points, which are then starting points (nodes) for the next jump. Jumps then continue to generate nodes in an ever-widening pattern until time runs out, that is, the date of expiration arrives. The whole lattice is employed to determine what would be the value of an option in the final time segment. At expiration, only two possibilities exist. Either the exercise price of the option is less than the current stock price or it is not, and that simplicity makes calculation straightforward. From there, you work backward step by step, coming eventually to a value for the option at time 0.

Simulation-based Models

You don't have to go there to do a Monte Carlo simulation--but it can't hurt.

Simulation-based models allow for the role of randomness in price movements, and they seek to model that randomness through computerized simulation runs. Thousands of simulation paths may be run, each generating a hypothetical option price. The valuers then take the average of all the option prices, and discount that to its present value.

Rich Tanenbaum, the president of Savvysoft, a financial software concern, has written, "Monte Carlo can be used for any type of distribution....[Y]ou're not limited to normal or lognormal returns, and you can change distributional parameters like volatility. Some of this is also possible with a [lattice], but it's more limited."

History

Until 2004, it was not part of generally accepted accounting principles (GAAP) in the United States for employers to recognize that in issuing stock options to their employees they had incurred an expense. That year, though, amid considerable controversy, the FASB made the expensing of stock options mandatory for all annual and interim reports, effective beginning June 15, 2005.

References

• Ohio State University: Valuing Stock Options: The Black-Scholes Model
• AllBusiness: Using Lattice Models to Value Employee Stock Options Under SFAS 123(R)
• Savvysoft: Battle of the Pricing Models

Resources

• "Lecturing Birds on Flying"; Nassim Nicholas Taleb and Pablo Triana; 2009
• Financial Accounting Standards Board: Statement of Financial Accounting Standards No. 123