An American Option is an option which can be exercised at any time up to and including the expiry date of the option. This added flexibility over European options results in American options having a value of at least equal to that of an identical European option, although in many cases the values are very similar as the optimal exercise date is often the expiry date.
The early exercise feature of these options complicates the valuation process as the standard Black-Scholes continuous time model cannot be used. The most common model for valuating American Options in the binomial model. The binomial model begins by evolving an seet price over a lattice with the asset price moving either up or down at each node of the the lattice. Once a lattice of asset prices has been determined the model iterates back through the lattice of prices to determine at each node if early exercise is optimal or not. The binomial model is simple to implement but is slower and less accurate than 'closed-form' models such as Black Scholes.
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