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oBIN2( ) Model Definition

The Binomial Option Pricing Model is a well known numerical approximation method that is used to value options for which there are no closed-form solutions. The most common applications relate to pricing American style options on stocks, stock indices, currencies, and commodities. In many cases, this model is also referred to as a binomial tree or a simple lattice pricing method. The oBIN2( ) function is based on a tree for which the timestep between the branches in the tree are variable.

A tree with variable timesteps is required for more accurate valuations of options which have either:

  • Bermudan style exercise
  • A schedule of discrete dividend payments over the life of the option

 

In both cases, values derived from a constant step binomial tree are very sensitive to the placement of the branches in relation to either the exercise date (for Bermudan options) or the dividend payment date. That effectively means that the value calculated with a 150 step tree might be significantly different from values derived from a 160 step tree. The best way to avoid this instability is to construct a binomial tree such that a branch in the tree falls exactly on the exercise and/or dividend dates. This can be achieved by allowing for the timespan between adjacent branches in the tree to differ.

Apart from variable timesteps, the binomial tree that underlies the oBIN2( ) function is build in exactly the same way as for the oBIN( ) function. More detail is therefore available in the following topics:

Binomial Option Pricing Model (Constant Timestep) Definition

Binomial Option Pricing Model (Constant Timestep) Derivation

Binomial Option Pricing Model (Constant Timestep) Greeks

 

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