Forget Black-Scholes?

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

That difference hasn’t been lost on FASB. As proposed, the new rule recommends use of a lattice-based model unless a company lacks sufficient historical data.

Troublesome Variables

Thanks to its additional flexibility, the binomial model tends to produce a lower estimate of option value than Black-Scholes. A study by Analysis Group found that the Black-Scholes model overstated the value of some grants by anywhere from 28 percent to 56 percent.

But some critics worry that the flexibility of the binomial model could help unscrupulous executives manipulate their financial results. The fear is that they will take advantage of the model’s flexibility to underestimate their compensation costs and overstate their earnings. “My concern is that people will use the more-powerful models in the wrong ways,” says Mark Rubinstein, a finance professor at the University of California at Berkeley who helped create the binomial model. Rubinstein says the first question he gets from managers is, “Can you tell me how I can get lower numbers?”

For better or worse, small changes in the assumptions concerning an option grant’s features can produce wildly different estimates of its value, and that’s obviously a bigger problem under the binomial method than under Black-Scholes, notes Chris Kruse, a consultant with New York­based CFX Inc. who studied under Rubinstein. “You can incorporate a lot of things in the binomial model that will significantly reduce the value of the option,” warns Kruse.

Forfeiture assumptions represent a particularly troublesome variable, he says, since they are something of “a random element.” That’s because at least some option recipients quit before their options vest, and thereby relinquish the right to exercise them. In those cases, of course, a company would not incur any expense at all. So simply by projecting a higher-than-likely rate of employee attrition, explains Kruse, a company could artificially deflate the expense it reports for its grants. It may be easy enough to convince auditors to go along, he contends, since the probability of forfeiture is related to such difficult-to-quantify factors as an employee’s opportunities elsewhere. “This is probably highly variable, especially when moving up the food chain to the executive suite,” says Kruse. “It is also highly idiosyncratic, since a firm’s outlook may affect employee attrition.” This variable alone, he cautions, gives companies tremendous leeway in estimating option values.

To address this problem, FASB’s proposed rule would require companies to disclose all the assumptions they have used to calculate the expense of their options. Those disclosures would not be limited to a grant’s standard assumptions — regarding such elements as stock price, option strike price, interest rate, dividend yield, stock volatility, and term — but would also include those concerning vesting restrictions and forfeiture requirements.

Even so, some experts say FASB should either move away from option-price models entirely or try to minimize their room for error. Rubinstein himself recommends that the board simply require companies to calculate the present value of options based on the stock’s price at the time of the grant, and then adjust that as the price changes. That way, a company would have to “true up” any difference between the value of the option estimated at the time it was granted and the actual value when exercised.


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