FRM Part I · FRM Exam Part I · Binomial Trees
In a three-step recombining binomial tree where an up move followed by a down move gives the same price as a down move followed by an up move, how many distinct terminal stock prices exist, and how many distinct paths lead to them?
There are 4 distinct terminal prices and 8 paths. A recombining tree gives n+1 terminal nodes after n steps, here 3+1 = 4, based on the number of up moves. The number of paths is 2^3 = 8.
- A3 distinct prices, 6 paths
- B4 distinct prices, 6 paths
- C4 distinct prices, 8 pathsCorrect
- D8 distinct prices, 8 paths
Explanation
After n steps a recombining tree has n+1 terminal prices, so three steps give 4 (uuu, uud, udd, ddd). Each step has two choices, so there are 2^3 = 8 paths. Prices depend only on the number of up moves, which is why the paths collapse into 4 prices. The 8-prices option describes a non-recombining tree.
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