The first closedform 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.


Exercise Style 
Dividend Type 
Appropriate Model 


. 


European 
None 
BS, GBS, BIN, BIN2 



Continuous 
GBS, BIN, BIN2 



Discrete 
BSdd, RGW, BIN2 







American 
None 
BAW, BIN, BIN2 



Continuous 
BAW, BIN, BIN2 



Discrete 
BIN2 







Bermudan 
None 
BIN2 



Continuous 
BIN2 



Discrete 
BIN2 









Where, 
BS = Black Scholes. 


BSdd = Black Scholes with Discrete Dividends. 


GBS = Generalized Black Scholes. 


RGW = Roll Geske Whaley. 


BAW = BaroneAdesi Whaley. 


BIN = Binomial Option Pricing Model with constant timesteps. 


BIN2 = Binomial Option Pricing Model with variable timesteps. 



Note that while we list all of the pricing models that can be applied to each type of option, some models are more appropriate than others. For example, although both the Black Scholes model and the binomial option pricing model can be used to value a European option on a stock that pays no dividend, the Black Scholes model would be preferred in this case. As the binomial model involves a numerical approximation to the 'true' value (given by Black Scholes), it is slower to compute and less precise than the Black Scholes model. 



Copyright 2013 Hedgebook Ltd.