Forget Black-Scholes?

Why the traditional option-pricing model may not be the best way to value employee grants.

Another alternative, proposed by Stanford University professors Jeremy Bulow and John Shoven, would instead greatly shorten the time frame involved in modeling a grant’s value. Since most programs require employees who leave the company to exercise their options within 90 days, the Bulow-Shoven approach would assume that a new grant is made every quarter, requiring a company to subtract the value of extending its existing options another three months as an expense, along with the three-month cost of any newly granted options. The authors contend such an ongoing method would give a more-accurate picture of the cost of outstanding grants than any attempt to provide a once-and-for-all valuation.

FASB says it will take these issues into account in its deliberations over the final rule, due out by the end of the year. “We expect that over time, companies will move to the binomial method, because it provides a better measure of the option value,” says board member G. Michael Crooch. And he notes that the use of estimates is a necessary evil. “FASB must rely on management and auditors to properly apply our standards,” he says.

For Better and Worse

Meanwhile, however, some finance executives worry that the different results produced by the Black-Scholes and binomial models will make it harder for investors to compare companies’ performance. “Flexibility is nice,” says John Cox, chief accounting officer at Houston-based BMC Software Inc., “but it brings with it other issues.”

And, some experts predict that finance executives will find the binomial model difficult to apply, at least initially. “Black-Scholes is so widely used that there are lots of software packages to run the model,” says Rebecca McEnally, vice president of the Charlottesville, Virginia-based Association for Investment Management and Research — an analyst group that advocates expensing options — and an adviser to the International Accounting Standards Board (IASB), FASB’s counterpart outside the United States. In contrast, says McEnally, the binomial method “is not quite as easily adopted.”

None of these obstacles has stopped some companies that are already expensing options from using the binomial model, including such insurers as American International Group and Washington Mutual. Those raising capital abroad may have another reason to adopt the alternative: IASB has effectively endorsed the model in its own, already finalized rule requiring that employee option grants be expensed starting next year. In essence, the international standards-setter requires that companies decide which valuation model to use based on what “a knowledgeable, willing market participant,” such as a derivatives trader, would use. The rule also notes, “This may preclude the use of the Black-Scholes model.”

If it’s any solace, Kruse contends that reports of the binomial model’s relative difficulty of use are exaggerated. While he concedes that the method takes time to get used to, those who adopt it, he insists, will soon find it “quite simple.” What’s more, he says, “you can find an out-of-the-box [binomial] calculator for $100.”

Too bad the gap between the estimated and actual value of a company’s option grants is unlikely to always be that small.

Up the Lattice

In its proposed rule for expensing stock options, the Financial Accounting Standards Board has acknowledged that the most popular option-pricing model, known as Black-Scholes, may be less appropriate than a lattice-based method for valuing employee grants. That’s simply because a lattice-based method can take into account assumptions that reflect the conditions under which employee options are typically granted. The binomial model is the most commonly used lattice-based method, but other methods may be better suited to compensation programs that link vesting to specific performance objectives, as this summary provided by consulting firm Analysis Group illustrates:

Binomial. This model can calculate option values when the price of the underlying stock moves either up or down over a short interval. It is considered better than Black-Scholes at taking into account how factors such as forfeiture and exercise before expiration, as well as an employee’s risk aversion and lack of diversification, affect an option’s value at the time it is granted.

Trinomial. The trinomial model goes a step further by allowing for the underlying stock price to either remain unchanged or move up or down. That’s useful for valuing performance-based options that vest only if the stock price exceeds a certain level over time.

Multinomial. This model can take many more factors into account than either the binomial or trinomial framework. Such additional flexibility may be required to value options that cannot be exercised unless the underlying stock price exceeds the performance of one or more indices. But when there are more than two such sources of uncertainty, a Monte Carlo simulation may be preferable, since it is easier to apply than lattice models.


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