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# Trinomial Option Pricing Model

## What is Trinomial Option Pricing Model?

The trinomial option pricing model is an option pricing model incorporating three possible values that an underlying asset can have in one time period. The three possible values the underlying asset can have in a time period may be greater than, the same as, or less than the current value.

The trinomial model uses an iterative procedure, allowing for the specification of nodes, or points in time, during the time span between the valuation date and the option's expiration date.

### Key Takeaways

• The trinomial option pricing model values options using an iterative approach that utilizes multiple periods to value American options.
• With the model, there are three possible outcomes with each iteration—a move up, a move down, or no change—that follow a trinomial tree.
• The model is intuitive, but is used more frequently in practice than the well-known Black-Scholes model or the binomial model that uses only two possible outcomes per step.

## Understanding Trinomial Option Pricing Model

Of the many models for pricing options, the Black-Scholes option pricing model and the binomial option pricing model are the most popular.

The Black Scholes model, also known as the Black-Scholes-Merton model, is a model of price variation over time of financial instruments such as stocks that can, among other things, be used to determine the price of a European call option. The binomial option pricing model, which was developed in 1979, uses an iterative procedure, allowing for the specification of nodes, or points in time, during the time span between the valuation date and the option's expiration date.

A trinomial model is a useful tool when pricing American options and embedded options. Its simplicity is its advantage and disadvantage at the same time. The tree is easy to model out mechanically, but the problem lies in the possible values the underlying asset can take in one period of time. In a trinomial tree model, the underlying asset can only be worth exactly one of three possible values, which is not realistic, as assets can be worth any number of values within any given range.

The trinomial option pricing model, proposed by Phelim Boyle in 1986, is considered to be more accurate than the binomial model, and will compute the same results, but in fewer steps. However, the trinomial model has not gained as much popularity as the other models.

## Trinomial vs. Binomial Models

The trinomial option pricing model differs from the binomial option pricing model in one key aspect by incorporating another possible value in one time period. Under the binomial option pricing model, it is assumed that the value of the underlying asset will either be greater than or less than, its current value.

The trinomial model, on the other hand, incorporates a third possible value, which incorporates a zero change in value over a time period. This assumption makes the trinomial model more relevant to real life situations, as it is possible that the value of an underlying asset may not change over a time period, such as a month or a year.

For exotic options, or an option that has features that makes it more complex than commonly traded vanilla options such as calls and puts that trade on an exchange, the trinomial model is sometimes more stable and accurate.

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