A lattice-based computational model used for valuing options represents the underlying asset’s price evolution as a series of up and down movements over discrete time intervals. This model allows for the calculation of an option’s theoretical price at each node in the tree, working backward from the option’s expiration date to its present value. For example, a simple representation might depict a stock’s price either increasing by 10% or decreasing by 10% over each period. By assigning probabilities to these movements, the model can estimate the expected payoff of the option at expiration and discount these payoffs back to determine the option’s current price.
This approach offers a flexible and relatively simple method for option valuation, particularly for American-style options that can be exercised before their expiration date. It provides insights into how an option’s value changes with variations in the underlying asset’s price, volatility, and time to expiration. Historically, this method served as a crucial tool before the widespread availability of more complex numerical techniques. Its ease of implementation and pedagogical value continue to make it a relevant concept in financial education and for understanding fundamental option pricing principles.