Even at a glance you can appreciate that a detailed evaluation of this model is beyond the scope of this class. Our Resource area can refer you to books and links on this and other pricing models.
In practice, most professional traders and investors with large option positions rely on frequent theoretical value updates as a way to monitor the changing risk and value of their overall option positions, to adjust price interrelationships, and to facilitate quick trading decisions. In contrast, most individual investors find that understanding the ultimate risk and reward of their positions tends to be more useful than constant updates of input values and any specific differences between the outputs of various pricing formulas. Almost all of the elements that go into option pricing models are in flux during the lifetime of an option contract - that is before it expires. It follows that an option position's theoretical value is also subject to perpetual changes based on new input values.
An option pricing calculator accessible on this web site offers you the choice of three theoretical models. The Black-Scholes (1973) was originally formulated to price European-style options, and does not account for dividend payment and early exercise. The Cox-Ross-Rubenstein Binomial model (1979) is a variation on the original Black-Scholes. The Barone-Adessi & Whaley, or "Whaley" model (1987), accounts for early exercise of call options due to dividend payment and is widely used among individual investors for pricing American-style equity options.