Model turned that guessing game into a mathematical science which helped develop the options market into the lucrative industry it is today. There are several assumptions underlying the Black-Scholes model of calculating options pricing. Sixth, the Black-Scholes Model tends to misprice options that involve high-dividend stocks. However, despite these known limitations, the classic Black-Scholes model is still the most popular with options traders today due to its simplicity. The prevailing price of a stock option is usually much higher than its theoretical value due to implied volatility.
The three young Black-Scholes Model researchers -- who were then in their twenties -- set about trying to find an answer to derivatives pricing using mathematics, exactly the way a physicist or an engineer approaches a problem.
As it is much more complex than the Blac-Scholes Model, it is slow and not useful for calculating thousands of option prices quickly.

American options allow the holder to exercise an option contract at any time before the expiry.
Binomial trees divide time (from the current time to maturity) into a large number of slices. This method gives the price of an option at multiple points in time (and not just at the expiry date, as with the standard Black-Scholes model). Additionally, binomial trees can help analysts decide when best to exercise an American option because the change in option price is given over time. The theory behind Binomial trees, and their implementation in Excel, are described in greater detail in this tutorial. If you would like access to the VBA used to generate the binomial lattice, please use the Buy Unlocked Spreadsheet option. Let's remember that the Black-Scholes model was initially invented for the purpose of pricing European style options.

It is commonly known as the Binomial Option Pricing Model or simply, the Binomial Model was invented in 1979. However, it soon became apparent that the binomial model is a more accurate pricing model for American Style Options. This means that for any given situation, American options demand a higher price than European options because of their greater flexibility.

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