Tree and Lattice Terminology in Derivative Valuation

Summary

The document clarifies terminology used for discrete-time derivative valuation. It says that “tree” and “lattice” are commonly used interchangeably, rather than naming fundamentally different valuation approaches. Either structure can be recombining, where different paths lead to the same state, or non-recombining, where those paths remain distinct. The latter structure may also be called a bush.

This distinction helps when reading descriptions of numerical pricing methods, since the label alone does not establish whether states merge across paths. The answer does not discuss how to build a tree or lattice, assign transition probabilities, calibrate a model, or price a particular contract. It offers a concise terminology clarification, so further implementation or valuation detail must come from other sources.

Key ideas

• Tree and lattice are commonly used as interchangeable terms in derivative valuation.
• A recombining structure maps some different move sequences to the same state.
• A non-recombining structure keeps those path outcomes separate and may be called a bush.
• The names alone do not specify a model’s probabilities, calibration, or pricing procedure.

Tags

# Difference between tree and lattice approach


# Difference between tree and lattice approach












Is there any difference between the tree and lattice approach for valuing derivatives? I was under the impression that both are the same.

## Answer by RandyF (score 1)

https://quant.stackexchange.com/a/44897

A tree and a lattice are the same thing and are most often used interchangeably. Both a tree and a lattice can either be recombining (an up move followed by a down move is equal in value to a down move followed by an up move) or not recombining. A non-recombining lattice is sometimes considered a bush.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.