Accordingto Espen (2007), pricing options are contracts that provide theholder with the right to sell or buy any product at a specified pricebefore or on the specified date. The option buyer is not supposed toexercise the option.On the other hand, theseller is obligated to sell or buy the underlying product if inany casethe option isexercised.Severalvariables can impact options.This paper seeks to compare the Black-Scholes model and the Binomialmodels as variables affectingpricing options.
The black-Scholes model was introduced back in 1993. The formula wasdeveloped by three economists Robert Merton, Myron Scholes andFischer Black. The model is used to calculate the theoreticalprice of the European call and put options. It ignores dividend paidduring the option. The Black-Scholes modeldid not consider effects of the dividends that werepaid. The model should be used to account for the dividendsby determining the date value of ex-dividend of the underlying stock(Aswath, 2012).The following formula can be used in theBlack-Scholes model.
Thebinomial model always breaks down time to expiration into varioustime intervals. The Stockprices tree isproducedand works forward to expiration. In every step, there is anassumption that the price of the stock will always go up and down bythe amount that is calculated using the expiration time andvolatility.  The tree always represents possible paths the stockprices can take during the option`slife (Hoadley,2015).
Comparisonbetween Black-Scholesand Binomial Models
Oneof the attributes of the binomial modelsis that it can accurately be used to priceoptions in America as compared to the Black-Scholes model. This ispossible since while using Binomial models, one cancheck every point in the life of the optionfor early exercise possibility. For example,a put deeply in money of the price option at any point is less thanthe intrinsic value. When early exerciseis found, an assumption is made that theholder of the option may elect to exercise.The price option can, in this case, beadjusted to be equal to the intrinsic value at that point. TheBlack-Scholes model cannot be used accurately to calculate priceoptions using the American style since it calculates only priceoption at one point at a time. It does not consider any step on theway whereby the possibility of an earlyexercise of the option of America can arise (Hoadley, 2015).
Anotherattribute of the binomial model is that itsolves same equations by use of computational procedure while theBlack-Scholes model solves the same equations by use of the analyticapproach. By doing this, it providesopportunity along the way to verify early exercise options inAmerica. (Hoadley, 2015).
Again,Black-Scholes model is faster as compared to the binomial model.Black-Scholes allows individuals to calculate within a short time alarge number of price opinions. The binomialmodel is slow in speed. The binomial isbest in calculations for half dozen at a given time but even with thefastest PCs today, the binomial modelcannot be used to calculate thousands of different prices within afew seconds (Hoadley, 2015).
TheBlack- Scholes and Binomial models are examples of variables thatsignificantlyaffect the pricing options. Traders and investors should have properknowledge of the two models in order to use them appropriately intheir businesses. The formula may be intimidating to the traders,but there are online calculators thatcan help them calculate price options. The two models arewidely usedin determining costoptions as compared to other variables.
AswathD. (2012).InvestmentValuation: Techniques and Tools for Determining the Value of any.Hoboken:JohnWiley & Sons
EspenG. (2007).TheComplete Guide to Option Pricing Formulas.New York: McGraw-HillEducation, Hoadley p. (2015). OptionPricing Models and the "Greeks” Retrievedfrom ttp://www.hoadley.net/options/bs.htm