Binomial Model

Analyze, calibrate, and price financial derivatives using the binomial model

The Cox-Ross-Rubinstein binomial model is a discrete-time numerical method you use to price contingent claim financial derivatives such as European options, American options, and exotic options with nonstandard structures.

Visualization of a binomial tree.

Binomial model option pricing generates a pricing tree in which every node represents the price of the underlying financial instrument at a given point in time. You can use this pricing tree to price options with nonstandard features such as path dependence, lookback, and barrier events. For more complex structures, it is better to use Monte Carlo simulation-based option pricing, because it is less computationally intensive.

Leading financial institutions use MATLAB to build and calibrate option pricing models such as the binomial model. MATLAB toolboxes such as those for finance and financial instruments support derivatives modeling tasks, enabling you to:

• Build custom pricing models based on a choice of Cox-Ross-Rubinstein trees, Equal Probabilities trees, Leisen-Reimer trees, or Implied Trinomial trees
• Set up and manipulate pricing models mathematically
• Price vanilla and exotic options, compute sensitivities, and calibrate with market prices
• Analyze market prices of options to identify trading opportunities
• Design hedging strategies based on option greeks to measure and control market risk exposure

Examples and How To

• Teaching and Research of Computational Finance Using Binomial Models in MATLAB (Webinar)
• Pricing European Call Options Using Different Equity Models – Including CRR, Leisen-Reimer, and Black-Scholes (Example)
• Teaching Numerical Methods in Finance with MATLAB (Conference Video)
• SinoPac Securities Builds Structured Products Using MATLAB (User Story)
• Exotic Option Pricing on a GPU Using a Monte Carlo Method (Example)
• Numerical Methods in Finance and Economics: A MATLAB Based Introduction, 2e (Book)

Software Reference

• Pricing Stock Options Using the Binomial Model (Documentation)
• Construct Equal Probability Trees to Price Equity Derivatives (Function)
• Fixed-Income Analysis and Option Pricing (Product Description)
• Pricing and Analyzing Equity Derivatives (Documentation)
• Equity Tree Models (Function Reference)
• Monte Carlo Simulation for Equity Derivatives (Function Reference)
• Black-Scholes Option Pricing Model (Function Reference)

See also: Fixed Income, Financial Derivatives, Econometrics Toolbox, Global Optimization Toolbox, Symbolic Math Toolbox, Pricing and valuation