I read with interest “ How to Excel at Options Valuation ” ( JofA , Dec. 05, page 57). It appears that the strength of the binomial model presented is inversely related to the number of assumptions made. In the example given in the article, for four years of stock options granted, there are 16 assumptions—perhaps not very persuasive. For n years, there would be an exponential number of assumptions, or 2^ n .
In general, one can create various simulations of stock option valuations, all based on statistically valid models. For example, a simulation based on a model whereby mean and standard deviation represent the basis for underlying assumptions can provide similar results to the binomial results but on a normal distribution scale. The latter has the added benefit of allowing the model to report a level of confidence for the simulated results.
The crux of the matter is in research that can show such a simulation is not only statistically valid but also realistic. For example, showing the value of stock options before and after an IPO vs. the simulated costing of such options may prove or disprove the validity of the valuation. A successful model that has bearing on reality can be put in the same class as the Black-Scholes method and be an acceptable alternative.
Yigal Rechtman, CPA, CFE
Person & Co. LLP
New York City