This Excel spreadsheet prices an American option with a Binomial Tree. The spreadsheet also generates the pricing lattice, which can be viewed.
American options allow the holder to exercise an option contract at any time before the expiry. European options, on the hand, can only be exercised at the expiry date. This means that for any given situation, American options demand a higher price than European options because of their greater flexibility.
Unlike European puts, American puts cannot be valued analytically. Therefore numerical techniques (such as monte-carlo simulation, the method of lines, the Bjerksun-Stensland model, or binomial trees) must be used . This article, for example, describes a novel Monte-Carlo method to price American Options
Binomial trees divide time (from the current time to maturity) into a large number of slices. At each stage, stock price can either increase (with probability p) or decrease (with probability 1-p) in value. Call and puts are then priced by moving backwards in time (this is known as backwards induction).
This method gives the price of an option at multiple points in time (and not just at the expiry date, as with the standard Black-Scholes model). Binomial trees are hence particularly useful for American options, which can be exercised at any time before the expiry date.
Additionally, binomial trees can help analysts decide when best to exercise an American option because the change in option price is given over time.
Price an American Option with a Binomial Tree
The Excel spreadsheet is simple to use. Simply enter your parameters and then click the Draw Lattice button. The price of the option is given in the Results box.
Additionally, some clever VBA will draw the binomial lattice in the Lattice sheet.
The theory behind Binomial trees, and their implementation in Excel, are described in greater detail in this tutorial. The spreadsheet uses the Cox-Ross-Rubinstein method.
If you would like access to the VBA used to generate the binomial lattice, please use the Buy Unlocked Spreadsheet option.