This model uses an iterative procedure, allowing for the specification of nodes during each time step in a given period. It works by constructing a tree-like diagram representing different potential price paths of the underlying asset over time. At each node in the tree, the asset can move up or down in price by a pre-defined factor. By working backward from the option’s expiration date, where the payoff is known, one can determine the option’s theoretical value at each preceding node until reaching the present. For example, a simple model might evaluate a stock’s potential price movements over a series of periods, factoring in its volatility to determine the probability of upward or downward price changes.
This approach provides a relatively straightforward and flexible method for valuing options, especially American-style options that can be exercised before expiration. It’s particularly useful when the underlying asset’s price is expected to follow a path with significant jumps or discontinuities, where other models might be less accurate. While computationally more intensive than some alternatives, advances in computing power have made this a practical method for a wide range of applications. Historically, it has been a significant tool for understanding and managing option risk.
