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# Binomial Tree for Pricing American Options

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.

### 6 Responses to "Binomial Tree for Pricing American Options"

1. Gourier says:

Hi,
I would like to know if it would be possible to have the VBA code for the binomial tree for pricing the american options and the one forthe Excel spreadsheet for pricing American options with the Barone-Adesi & Whaley, and Ju & Zhong approximations.

Thank you for your help. All you are doing is very useful.

2. Eugene Ong says:

Hi, your lattice looks great. I would appreciate it if I can have access to the VBA codes. Thank you very much!

3. louis says:

Hi, is it possible if you could get me a code for trinomial tree for american option? thank you!

4. Samir says:

I’ll post VBA to price European Options with a trinomial tree soon. If you can wrap your head around trinomial trees, then you’ll understand binomial trees

5. Shaun says:

Do you perhaps have a spreadhseet that uses an additive binomial tree as opposed to a multiplicative one?