A binomial or trinomial model, often implemented through software, allows for the valuation of options and other derivatives. This computational approach constructs a branching diagram representing the possible evolution of an underlying asset’s price over time. At each node in the tree, the asset price can move up, down, or in some models, remain unchanged. Option values are then calculated at each node, starting from the final time period (expiration) and working backward to the present. For example, a European call option’s value at expiration is simply the maximum of zero and the difference between the underlying asset price at that node and the strike price.
These models provide a practical way to price derivatives, especially American-style options which can be exercised before expiration. The ability to incorporate factors like dividends and changing volatility makes these models versatile. Historically, before widespread computing power, these methods offered tractable solutions to complex valuation problems. Even today, they remain valuable tools for understanding option pricing principles and for benchmarking more complex models. Their relative simplicity aids in explaining the impact of various market parameters on derivative prices.
