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Mar 31

Binomial Tree

Posted by bo at 09:29 | Others | Comments(1) | Reads(9201)
This post is by Bo, a guest author of the math finance blog, unlike biao's technical posts, I will be mainly writing introductory articles, which aims to help beginners have a rough idea, and I will try to link to other technical posts for a better understanding if possible.

Binomial options pricing model or BOPM, as it is popularly known is a generalized numerical method that is used for the valuation of options. This method was proposed by Rubinstein, Cox and Ross. This method is popular in the sense that it can be used for variety of conditions, while the other numerical methods have limited use. The main reason why it can be used in varied situations is that it is based on the underlying instrument spread over a period of time rather than a single point of time. It is slower, but much more accurate than any other method.

This method traces the evolution of options underlying variable spread over a period of time. This is done by using a binomial tree or binomial lattice. Each node in the binomial tree or lattice represents price of the underlying at a single point of time. The valuation is performed iteratively, i.e., it starts from the final node and goes backwards till it reaches the first node. The value that you will calculate in each node of the binomial tree is the value of the option at that point of time.

BOPM follows a three step process. In the first step, which is binomial tree generation, a tree comprised of prices is produced by working forward the date of valuation to expiration. It is assumed that at each step the value of underlying instrument is either moving down or up by a specific factor. The down and up factors are calculated using underlying volatility. The next step is to find the value of option at each final node. The option value which is obtained is called the exercise or intrinsic value. The third step is to find the value of options at earlier nodes, by moving backwards from the final nodes.

Check Nine Ways to Implement Binomial Tree Option Pricing for binomial tree implementation.


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