Explanation:
The correct answer is C.
Both (I) and (II) are recombining trees. A recombining tree, in the context of arbitrage pricing, is a tree in which the up-down and down-up states have the same value. This means that an upward movement followed by a downward movement leads to the same rate as a downward movement followed by an upward movement. In the given diagrams, both trees (I) and (II) follow this pattern. In tree (I), the rates at the end of the tree, regardless of the path taken (up-down or down-up), are the same (6.00%, 5.00%, and 4.00%). Similarly, in tree (II), the rates at the end of the tree, regardless of the path taken, are the same (6.00%, 4.95%, and 4.05%). Therefore, both trees are recombining trees, making choice C the correct answer.
Choice A is incorrect. This choice suggests that Tree I is a recombining tree and Tree II is not, which contradicts the correct answer. Both trees are recombining as they merge back into a single node after branching out.
Choice B is incorrect. This choice suggests that Tree I is not a recombining tree while Tree II is, which again contradicts the correct answer. Both trees are indeed recombining as they converge back into one node after diverging.
Choice D is incorrect. As explained above, both trees are recombining and not non-recombining as this option suggests.
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Q.1630 While performing arbitrage pricing in a multi-period setting, recombining trees are considered to be economically reasonable. Consider the following tree diagrams and choose the correct option:
I.
II.
A
(I) is a recombining tree while (II) is a no recombining tree
B
(I) is a non-recombining tree while (II) is a recombining tree
C
Both (I) and (II) are recombining trees
D
Both (I) and (II) are non-recombining trees
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