The model reduces possibilities of price changes, removes the possibility for arbitrage, assumes a perfectly efficient market, and shortens the duration of the option. Under these simplifications, it is able to provide a mathematical valuation of the option at each point in time specified.
The binomial model takes a risk-neutral approach to valuation. It assumes that underlying security prices can only either increase or decrease with time until the option expires worthless. A simplified example of a binomial tree might look something like this:
Due to its simple and iterative structure, the model presents certain unique advantages. For example, since it provides a stream of valuations for a derivative for each node in a span of time, it is useful for valuing derivatives such as American options which allow the owner to exercise the option at any point in time until expiration . The model is also somewhat simple mathematically when compared to counterparts such as the Black-Scholes model, and is therefore relatively easy to build and implement with a computer spreadsheet.
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