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What is a Binomial Tree?

By Deanira Bong
Updated May 16, 2024
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A graphical representation of a scenario with two possible outcomes at each stage, a binomial tree is basically a tree diagram that starts with a node that leads to two more nodes that could each lead to two more nodes, and so on. In finance, a binomial tree can trace the movements of asset prices. A binomial tree is also ideal for valuing call and put options, because investors either lose or win, so there are always two possible outcomes.

A binomial tree for asset prices begins with a node that states the initial asset price, and then divides into two nodes, each with a probable price of the underlying asset at a future point in time. The asset price can go up or down from the price at the originating node. The investor can create a binomial tree that traces probable movements of the asset price at several points in time. The binomial tree can also value call and put options using the probable price movements of the underlying asset.

Call and put options are related to an underlying asset, which could be stocks, futures or commodities. At every point in time, the value of an option depends on the price of the underlying asset. Call and put options have an exercise price, and the investor earns profits or suffers losses depending on whether the price of the underlying asset at the expiration date is above or below the exercise price.

Also known as the binomial options pricing model, the binomial tree that values call and put options uses a formula based on the Black-Scholes model to determine the value of an option at any point before its expiration date. The Black-Scholes model helps investors determine if the current option price is at its fair value, overvalued or undervalued. To calculate the option value, the investor needs to know the initial asset and option prices, the option's exercise price, the length of time left until expiration, volatility, risk-free rate of return and interest rate.

The fundamental problem with a binomial tree is that it assumes the price of the underlying asset can only be either one value or another value; in fact, it can be any value. The Black-Scholes model also has assumptions, including that the asset pays no dividends, the options are European options that can only be exercised on the expiration date, the investor pays no commissions, interest rates remain constant and volatility remains constant. These assumptions make the binomial tree less relevant to real-life situations.

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