The Black-Scholes model (BSM), a common formula used to value employee stock options (ESOs) and other options, may overvalue those with long holding periods, says Martin Greene (Greene Valuation Advisors LLC).
Trouble source: In an upcoming article in Business Valuation Update, Greene says a limitation of the BSM is that it does not test distribution properties of the underlying stock prices. “Without testing this underlying assumption that the underlying stock prices are normally distributed, can it be certain the BSM is providing a reasonable conclusion?” he writes. When applying the BSM to shorter time periods for the exercise date, even for higher volatilities, the distributions remain sufficiently normal, he points out. “For longer holding periods, this will impact the model’s shape and integrity. Therefore, it appears that the BSM may not be appropriate for longer holding periods without modification.”
In the article, Greene uses a Monte Carlo simulation to demonstrate his point. He recommends that valuators should conduct an analysis of the underlying distribution assumptions of the BSM and an analysis of the conclusions prior to applying the model to valuing options.
The article will appear in the November issue of Business Valuation Update (subscription required).
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