李同學(xué)
2021-08-02 20:34以及pathwise valuation，若N是二叉樹期數(shù)，路徑是2的N次方，即4條路徑，這個我明白，不明白是為什么N是債券期數(shù)時，路徑是2的(n-1)次方，比如，n是2期債券，2（2-1），不就對應(yīng)的是2期路徑？不是2年期債券 3條路徑這個概念了？
所屬：CFA Level II > Fixed Income 視頻位置 相關(guān)試題
來源： 視頻位置 相關(guān)試題
1個回答
Nicholas助教
2021-08-03 21:02
該回答已被題主采納
同學(xué)，晚上好。
這里應(yīng)該是2的n-1次方，假設(shè)是2期，那么就是2的1次方，為2條路徑；假設(shè)是3期，就是2的2次方，為4條路徑。原文如下：
An “N-period” recombining tree has N + 1 terminal nodes at time N. There are 2N paths through the tree to those (N + 1) nodes. So a 3-period tree has 4 terminal nodes and 8 paths to those nodes. However, for instruments whose terminal payment/value is the same for all paths, e.g., fixed coupon bonds, we really only need interest rates at times 0, 1, …, (N – 1). That is, an (N – 1)-period tree and hence 2N–1 paths. So to value an annual-pay, 3-year bond there are really only 4 paths, not 8. Note, however, that for instruments with terminal payments that depend on the interest rate at maturity (time N) we need all 2N paths. As an example, this would be the case for an “arrears” swap.
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