# Trinomial Option Pricing Model: Applications and Examples

Last updated 06/05/2024 by

Daniel Dikio

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Summary:
The Trinomial Option Pricing Model is an advanced financial tool used to value options by incorporating three possible price movements over discrete time intervals. Unlike simpler models such as the Binomial Model, the Trinomial Model allows for greater flexibility and accuracy in capturing complex price dynamics and option features. By expanding the number of possible price paths, this model offers a more nuanced approach to option valuation, catering to various market conditions and option structures.

## Understanding the trinomial option pricing model

At its core, the Trinomial Option Pricing Model shares similarities with the Binomial Model but introduces an extra level of complexity. Like its predecessor, the Trinomial Model employs a lattice framework to model the price movement of the underlying asset over time. However, instead of two possible price movements at each node, the Trinomial Model allows for three: an upward movement, a downward movement, and a no-change movement.
The components of the Trinomial Model include
1. Price movement tree: A graphical representation of the possible price paths of the underlying asset over time.
2. Probability calculations: Determining the probabilities of each price movement at each node of the tree.
3. Discounting future cash flows: Discounting the expected payoff of the option back to its present value using a risk-free interest rate.

## Applications and examples

The Trinomial Option Pricing Model finds wide-ranging applications in financial markets, including the valuation of European and American options. Unlike European options, which can only be exercised at expiration, American options can be exercised at any time before expiration. The Trinomial Model can accommodate early exercise features, making it particularly useful for valuing American options.
Consider a hypothetical example of valuing a call option using the Trinomial Model. Suppose a stock is currently trading at \$100, and a call option with a strike price of \$110 and expiration in three months is being priced. By constructing a trinomial price tree and calculating the option values at each node, we can determine the fair value of the option.

## Limitations and criticisms

While the Trinomial Option Pricing Model offers several advantages over simpler models like the Binomial Model, it is not without its limitations. One of the primary criticisms of the Trinomial Model is its sensitivity to parameter inputs. Small changes in input parameters, such as volatility and interest rates, can significantly impact option values, making accurate estimation challenging.
Furthermore, the Trinomial Model is more complex and computationally intensive compared to simpler models, which can pose challenges in implementation and interpretation. Real-world applications of the Trinomial Model may require sophisticated software and computational resources to handle the calculations efficiently.

## Evolution from binomial to trinomial model

Developed by Cox, Ross, and Rubinstein in the late 1970s, the Binomial Model provided a simple yet powerful framework for valuing options. It employed a discrete-time, multiperiod approach to model the price movement of the underlying asset, enabling the calculation of option values at each node of a price tree.
Despite its effectiveness, the Binomial Model had limitations, particularly in accurately capturing the dynamics of asset prices and volatility. As financial markets evolved, the need for more sophisticated pricing models became apparent. This led to the development of the Trinomial Option Pricing Model, which addressed many of the shortcomings of its predecessor.
The Trinomial Model expands upon the Binomial Model by introducing a third possible price movement at each node of the price tree, thus providing greater flexibility in modeling asset price dynamics. This additional level of granularity allows for more accurate valuation of options, especially in situations where asset prices exhibit complex behavior.

## FAQs

### What distinguishes the trinomial option pricing model from other models?

The Trinomial Model differs from other option pricing models in its ability to accommodate three possible price movements at each node of the price tree, providing greater flexibility and accuracy in valuing options.

### How does the trinomial model handle volatility?

Volatility is a critical input parameter in the Trinomial Model, influencing the probabilities of price movements at each node of the price tree. Higher volatility leads to wider price movements and vice versa.

### Can the trinomial model be applied to complex option structures?

Yes, the Trinomial Model can be adapted to handle complex option structures, including options with multiple exercise dates, dividend payments, and other features. However, the complexity of the model increases with the complexity of the option structure.

## Key takeaways

• The Trinomial Option Pricing Model offers greater accuracy and flexibility in valuing options compared to simpler models like the Binomial Model.
• Understanding the components and assumptions of the Trinomial Model is essential for effective implementation.
• Despite its advantages, the Trinomial Model has limitations and requires careful consideration of input parameters.