Black-Scholes and Binomial Models
The variables that impact the pricing of options consist of the following basic factors: the underlying stock price, the strike price of the option, the time until expiration of the option, volatility, interest rates, and dividends (Folger, 2015). However, how these factors are perceived differs according to the model used to gauge the value of the option. The Black-Scholes model and the binomial model differ in their approach to valuing options.
The Black-Scholes model was developed for European put and call options and makes certain assumptions -- namely, that the option cannot be exercised early, that dividends are not a factor (though an ex-dividend addendum to the model has been produced in more recent years), that there are no commission fees involved, that volatility is constant and that the underlying's returns are normally distributed.
The Binomial Model also makes some assumptions -- namely that the market is efficient (which in today's world of centrally planned markets that rise and fall on a few words from Yellen or Draghi seems to be not the case at all) -- and it also simplifies the option by shortening its time and removes the possibility...
It essentially gauges how much the option should be worth at any specific time in its life. The model is especially helpful for American puts and calls, as these can be exercised prior to expiration.
Volatility is not really removed in the binomial model but it is factored into the framework. The name "binomial" comes from the fact that two numbers or price points are given as a part of finding the price of the option. Say that the underlying is valued at $90: the binomial model may pose that it could go up to $100 over one year's time or down to $80. These two price points set the stage for valuing the price of the option, depending on the perception of likelihood that the underlying moves one way or the other.
Of course, the Binomial Model can utilize more than two price points and this is done by way of simple mathematical calculations that essentially play out in a honeycomb-style of charting, providing a price for a range of points as they spread out over a binomial pattern beginning with the first set. This is the binomial tree.
In the end, the results of the calculations of this model are similar to the Black-Scholes. While the Black-Scholes…
