The Trinomial model is an extension of the Binomial options pricing model and is commonly used to value options.
The Trinomial model provides more accuracy than the Binomial model by allowing for three possible price movements at each time step: an upward movement, a downward movement, and a stable (no change) movement.
Key Components of the Trinomial Model
- Underlying Asset Movements
Up Move (U): The price of the underlying asset increases by a factor of ‘u’.
Down Move (D): The price of the underlying asset decreases by a factor of ‘d’.
No Move (M): The price of the underlying asset remains the same. - Time Steps
The life of the option is divided into N discrete time steps. Each step represents a short time interval, and during each interval, the price of the underlying asset can move up, down, or remain unchanged. - Probabilities
Upward movement, the probability of a downward movement, and the probability of no movement. - Price Tree
The Trinomial model constructs a tree where each node represents a possible price of the underlying asset at a specific time step.
At each node, the price can move to one of three nodes in the next time step, corresponding to the up, down, or no-move scenario.
Advantages of the Trinomial Model
- Accuracy: It provides more precise pricing, by accounting for more potential price paths compared to the Binomial model.
- Flexibility: The model allows for different probabilities and outcomes, offering flexibility in capturing the dynamics of the underlying asset’s price movements.
Trinomial Model Visualization
