Binomial Model Stock Options

by Will Gish

The binomial model is an options pricing model. Options pricing models use mathematical formulae and a variety of variables to predict potential future prices of commodities such as stocks. These models also allow brokers to monitor actual prices in relation to predicted prices and revise predictions accordingly. Like all options pricing models, the binomial model offers advantages and disadvantages. In the digital age, computer programs exist to perform options pricing model calculations.

The Binomial Model

Developed in 1979, the binomial model provides a structure of potential future options prices known as a “tree” or “lattice.” Using this model, brokers calculate potential future stock prices for a number of situations. For instance, if a stock stands an equal chance of going up in value by 10 percent as it does going down in value by 12 percent over the period of a month, one “branch” of the binomial model tree shows the value of the stock at a 10 percent increase and another “branch” shows it at a 12 percent decrease. Each of these branches gives rise to its own branches as brokers continue to calculate potential future prices. Essentially, the binomial model of options pricing provides an extensive network of potential future prices presenting best and worst case scenarios, as well as the middle ground.

Advantages of the Binomial Model

The binomial model allows for the pricing of American and European stock options, a key advantage it offers over some other methods of options pricing. American stocks follow different models than European stocks and provide brokers with a different palette of buying and selling options. These differences prevent many pricing methods from working accurately with both types of options—not so with the binomial model. The binomial model also accommodates for adjustments to options values based on dividends paid.

Disadvantages of the Binomial Model

The primary disadvantage of the binomial options pricing model lies in its complexity. An enormous number of calculations and variables prove necessary when calculating potential options prices over a long period of time. Creating an accurate binomial model tree for a single stock option consumes vast amounts of time. According to investment software manufacturer Hoadley Trading and Investment Tools, computer programs based on the binomial model provide substantially fewer calculations than programs based on other pricing models in the same time period due to the complexity of the process.

Binomial Model Stock Options

Binomial model stock options constitute any option for which a broker calculates potential future prices using the binomial model. This essentially means that any stock option potentially qualifies as a binomial model stock option. However, “binomial model” is not something intrinsic to an option, but rather a label applied to a stock option from the outside, by a broker, accountant or other investor or analyst. For instance, if you calculate the value of Microsoft stock options using the binomial model, nothing about these options changes. The label “binomial stock options” comes from the analytical practices of individual investors and brokers, not the company providing the options.

Other Options Pricing Models

The Black-Scholes model uses variables such as stock price, strike price, volatility, time to expiration and short-term interest rate to predict potential future options prices. This model involves complex math but only calculates one price for each option, rather than the tree created through the binomial model. Because of this, it proves very quick, particularly when done by a computer program. However, this model cannot calculate prices on American options. Other methods include Roll, Geske and Whaley analytic solution, Black's approximation for American calls, the Barone-Adesi and Whaley quadratic approximation and the “Greek” methods -- delta, gamma, theta and rho.

References (5)

  • “Understanding Options”; Robert W. Kolb; 1995
  • “Introduction to the Economics and Mathematics of Financial Markets”; Jaksa Cvitanic et al; 2004
  • Hoadley Trading and Investment Tools: Options Pricing Models
  • “Economics for Financial Markets”; Brian Kettell; 2002
  • “Commodity and Financial Derivatives”; S. Kevin; 2010