The Black-Scholes Option Pricing Model (“BSOPM”), while theoretically correct and elegant, is applicable only to the calculation of “European-style options” without dividends, where the holder of the option can exercise the option only on its maturity date, and the underlying stock does not pay dividends. The BSOPM can be utilized when it comes to quantifying the “fair market value” of employee stock options under the above circumstances.
The Monte Carlo Path Dependent Simulation Method is appropriate for complex stock options where the complexity of the option itself makes closed form approached such as Black-Scholes intractable. Rather than solve the differential equations that define the option value in relation to the underlying stock price, a Monte Carlo Simulation model determines the fair market value of the option for a set of randomly generated economic scenarios (e.g. future stock prices, stock price volatility, option exercise behavior, stock price vs. stock index behavior). The resulting simulation yields an expected value for the stock option.
Myron Scholes (left) and Fisher Black (right), developed the Black-Scholes Option Pricing Model.
Sample Model Results: