Black-Scholes Valuations

Expensing stock options

The requirement of expensing stock options resulted in a reduction of the number of options granted. This has hurt the recruitment efforts of small- and medium-size companies that are strapped for cash but have good prospects down the road. Many of these companies are in high-tech industries that represent a large business sector.

What's more, many options offered to lower-level employees, not executives, have been discontinued.

Opponents also attack the Black-Scholes method of valuing stock options.

Criticisms of Black-Scholes

While the Black-Scholes option pricing model is the most popular method for determining the expected present value for executive and employee stock options, many executives are suspicious that the model yields meaningless values. Opponents of expensing stock options make two separate types of arguments when criticizing the Black-Scholes model:

  • The model is inapplicable to employee stock options.
  • The model itself can be manipulated.

Black-Scholes is inapplicable.

The Black-Scholes model was developed to value a European-style option — either a put or a call.

The conditions aren’t the same for European-style options and employee stock options.

European-style option Employee stock option

Market. There’s a market for the option (it can be traded).

Time frame. The time frame is months at most.

Exercise date. There is a set date on which the options must be exercised, or they are forfeited.

Market. Employee stock options can’t be traded.

Time frame. The time frame is typically up to 10 years.

Vesting. These options are subject to vesting. While there’s a date similar to an expiration date of a put or call, this is only the first date on which the option may be exercised.

The lack of trading ability refers to the fact that some options will never be exercised since the options will be lost if the employee leaves their employment before exercising the options.

The above factors probably mean the value of employee stock options are overstated by Black-Scholes estimates.

Black-Scholes can be manipulated.

Most of the factors in the Black-Scholes model are known figures. But volatility is an estimate.

Volatility. Many critics show that by manipulating the volatility variable, the valuation of the stock options changes significantly. The less the volatility, the less likely the value is to rise sufficiently to make the option profitable enough to exercise. As a result, the option’s value is reduced, and its expense is lower.

Dividend yield. Another factor that can influence the valuation is the estimate of dividend yield. The estimate of the dividend yield isn’t a basic factor in the Black-Scholes model, but most modified models use this factor. When they do, the option value typically decreases as the dividend yield increases. This is because option holders don’t receive dividends on their unexercised options. They only benefit from the appreciation of the stock price. Mismeasuring the dividend yield can skew option values greatly over time.

Memory Jogger

What’s the most easily manipulated factor in the Black-Scholes model?

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