The first closed-form solution for valuing options on shares of stock was derived by Black Scholes (1973). Although widely known and applied, the model is derived under a fairly restrictive set of assumptions, including:

1. The stochastic behaviour of the underlying asset price is assumed to be well represented by a Geometric Brownian Motion process. In crude terms this means that prices follow a smooth random walk through time, without any 'extreme' price changes or price spikes.
2. The option can only be exercised at maturity.
3. The option does not pay a dividend of any kind during the life of the option. All of the option pricing models supported in Vanilla Options retain the first assumption. Some of the models are however designed to deal with options for which the second and third assumptions are relaxed. The following table indicates the option pricing models that are appropriate for each of the various option types supported by this component.