Binomial Trees for Discrete-Time Option Valuation

Summary

The document introduces binomial trees as discrete-time, lattice-based models for option valuation. At each step, the underlying instrument is assumed to have two possible price moves, producing a branching set of possible paths through time. This structure supports numerical valuation when a closed-form option-pricing solution is unavailable.

The discussion identifies the Cox–Ross–Rubinstein model as a foundational example and points readers toward further material for methodology and implementation. It does not provide the tree construction, risk-neutral probabilities, option payoff recursion, or a worked valuation. As a result, it establishes the model's basic idea and purpose but leaves the practical pricing procedure and its assumptions to the cited references.

Key ideas

• A binomial tree models an underlying price through discrete time steps with two possible moves at each step.
• The resulting lattice provides a numerical framework for valuing options.
• The Cox–Ross–Rubinstein model is cited as a standard example.
• The document gives a conceptual overview but no implementation details or worked pricing example.

Tags

# What are binomial trees and how are they used?


# What are binomial trees and how are they used?












What are the applications of binomial trees?

## Answer by phil (score 1, accepted)

https://quant.stackexchange.com/a/812

From wiki's entry

> In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein (1979). Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument. In general, binomial options pricing models do not have closed-form solutions.

See the full post, http://en.wikipedia.org/wiki/Binomial_options_pricing_model, for methodology/implementation guidelines.

## Answer by SBF (score 1)

https://quant.stackexchange.com/a/813

You can also read about Cox-Ross-Rubinstein model (see e.g. Shreve, Stochastic Calculus for Finance I). Binomial trees are discrete-time models assuming that at each step there are only two possibilities for the change of the price.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.