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

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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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