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梦梦 · 2025年05月09日

哪里计算错误了呢?

NO.PZ2023100703000129

问题如下:

An analyst on the fixed-income desk at Bank PNMS has been asked to complete the construction of a zero-coupon bond price tree that was started by another team member. The analyst is given an interest rate tree of semi-annual spot interest rates quoted on an annualized basis, and the partially completed price tree, both with semi-annual time steps, as shown below (time t in years and price P in USD):


When completing the price tree, which of the following is a correct estimate of price P(1,1)?

选项:

A.

USD 954.15

B.

USD 954.81

C.

USD 956.25

D.

USD 956.92

解释:

B is correct. For a full example see page 160. The analyst first needs to solve for q using the following system of equations:

Equation 1: (0.72*P1,1 + 0.28*P1,0) / (1 + 0.042/2) = 937.489

Equation 2: (975.13q + 979.43(1-q)) / (1 + 0.0465/2) = P1,1

Equation 3: (979.43q + 983.77(1-q)) / (1 + 0.0375/2) = P1,0

Substituting equations 2 and 3 into equation 1 allows for q to be solved for, yielding a result of q=0.563.

Then to find P1,1, the value of q can be substituted back into equation 2.

(975.13*0.563 + 979.43*(1-0.563)) / (1 + .0465/2) = (548.998 + 428.011) / (1.02325) = 954.81

A is incorrect. The probabilities of up and down moves given in the rate tree are incorrectly used as values for q and 1-q.

(975.13*0.72 + 979.43*(1-0.72)) / (1 + .0465/2) = (702.094 + 274.24) / (1.02325) = 954.15

C is incorrect. The probabilities of up and down moves given in the rate tree are incorrectly used as values for q and 1-q AND the interest rate at the initial node is incorrectly used as the discount rate.

(975.13*0.72 + 979.43*(1-0.72)) / (1 + .042/2) = (702.094 + 274.24) / (1.021) = 956.25

D is incorrect. The interest rate at the initial node is incorrectly used as the discount rate.

(975.13*0.563 + 979.43*(1-0.563)) / (1 + .042/2) =

(548.998+428.011) / (1.021) = 956.91

老师好,这个计算过程哪里错误了呢?

1 个答案

李坏_品职助教 · 2025年05月12日

嗨,爱思考的PZer你好:


-2.969q + 674.995- 1.168q+ 264.824 = 937.49,

所以q = 0.563


我建议同学计算的时候,按计算器仔细一些,不要慌。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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NO.PZ2023100703000129问题如下 analyst on the fixeincome sk Bank PNMS hbeen asketo complete the construction of a zero-coupon bonpritree thwstarteanother temember. The analyst is given interest rate tree of semi-annuspot interest rates quoteon annualizebasis, anthe partially completepritree, both with semi-annutime steps, shown below (time t in years anpriP in US:When completing the pritree, whiof the following is a correestimate of priP(1,1)? A.US954.15B.US954.81C.US956.25US956.92 B is correct. For a full example see page 160. The analyst first nee to solve for q using the following system of equations: Equation 1: (0.72*P1,1 + 0.28*P1,0) / (1 + 0.042/2) = 937.489 Equation 2: (975.13q + 979.43(1-q)) / (1 + 0.0465/2) = P1,1 Equation 3: (979.43q + 983.77(1-q)) / (1 + 0.0375/2) = P1,0 Substituting equations 2 an3 into equation 1 allows for q to solvefor, yielng a result of q=0.563. Then to finP1,1, the value of q csubstitutebainto equation 2. (975.13*0.563 + 979.43*(1-0.563)) / (1 + .0465/2) = (548.998 + 428.011) / (1.02325) = 954.81 A is incorrect. The probabilities of up anwn moves given in the rate tree are incorrectly usevalues for q an1-q. (975.13*0.72 + 979.43*(1-0.72)) / (1 + .0465/2) = (702.094 + 274.24) / (1.02325) = 954.15 C is incorrect. The probabilities of up anwn moves given in the rate tree are incorrectly usevalues for q an1-q ANthe interest rate the initino is incorrectly usethe scount rate. (975.13*0.72 + 979.43*(1-0.72)) / (1 + .042/2) = (702.094 + 274.24) / (1.021) = 956.25 is incorrect. The interest rate the initino is incorrectly usethe scount rate. (975.13*0.563 + 979.43*(1-0.563)) / (1 + .042/2) = (548.998+428.011) / (1.021) = 956.91 老师好,这道题由前往后推为什么不可以呢?见黄框。

2025-05-07 20:34 2 · 回答