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Lydia · 2020年04月23日

问一道题:NO.PZ201602270200001802

* 问题详情,请 查看题干

问题如下:

2. Based on Exhibits 1 and 2, the exchange that reflects the arbitrage-free price of the bond is:

选项:

A.

Eurex.

B.

Frankfurt.

C.

NYSE Euronext.

解释:

C is correct.

The bond from Exhibit 1 is selling for its calculated value on the NYSE Euronext exchange. The arbitrage-free value of a bond is the present value of its cash flows discounted by the spot rate for zero coupon bonds maturing on the same date as each cash flow. The value of this bond, 103.7815, is calculated as follows:

Notes:

1. Spot rates calculated using bootstrapping; for example: Year 2 spot rate ( Z2 ): 100=1.5/1.0125+101.5/(1+Z2)2=0.015019 100=1.5/1.0125+101.5/{(1+Z_2)}^2=0.015019

2. Present value calculated using the formula PV=FV/(1+r)n PV=FV/{(1+r)}^n,where n= number of years until cash flow, FV= cash flow amount, and r= spot rate.

A is incorrect because the price on the Eurex exchange, €103.7956, was calculated using the yield to maturity rate to discount the cash flows when the spot rates should have been used. C is incorrect because the price on the Frankfurt exchange, €103.7565, uses the Year 3 spot rate to discount all the cash flows.

老师这道题我知道考点是bootstrapping, 如果我用YTM直接做IY=1.7, N=3, PMT=3, FV=100. 如果这样做的话问题在哪里?

1 个答案
已采纳答案

WallE_品职答疑助手 · 2020年04月24日

YTM是假设债券持有到期的收益率,可以看做是spot rate的平均数。现实生活中也是用spot rate折现来求债券价格。

我知道有些CFA的题目为了方便简化计算,只给了YTM的利率,只有在那个情况才可以用YTM求价格。一旦题目中给了spot rate 或者par rate。就必须要用spot rate 来求价格。

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NO.PZ201602270200001802 问题如下 2. Baseon Exhibits 1 an2, the exchange threflects the arbitrage-free priof the bonis: A.Eurex. B.Frankfurt. C.NYSE Euronext. C is correct.The bonfrom Exhibit 1 is selling for its calculatevalue on the NYSE Euronext exchange. The arbitrage-free value of a bonis the present value of its cash flows scountethe spot rate for zero coupon bon maturing on the same te eacash flow. The value of this bon 103.7815, is calculatefollows:Notes:1. Spot rates calculateusing bootstrapping; for example: Ye2 spot rate ( Z2 ): 100=1.5/1.0125+101.5/(1+Z2)2=0.015019 100=1.5/1.0125+101.5/{(1+Z_2)}^2=0.015019100=1.5/1.0125+101.5/(1+Z2​)2=0.0150192. Present value calculateusing the formula PV=FV/(1+r)n PV=FV/{(1+r)}^nPV=FV/(1+r)n,where n= number of years until cash flow, FV= cash flow amount, anr= spot rate.A is incorrebecause the prion the Eurex exchange, €103.7956, wcalculateusing the yielto maturity rate to scount the cash flows when the spot rates shoulhave been use C is incorrebecause the prion the Frankfurt exchange, €103.7565, uses the Ye3 spot rate to scount all the cash flows.考点Introction of Arbitrage Free Valuation债券的无套利价格是用spot rate对债券的现金流进行折现得到的。 Exhibit 2中给的是1,2,3年期的Prates,因此通过Bootstrapping的方式,由前向后推导出各个spot rate。已知1-yeprate等于1.25%,则1-yespot rate也等于1.25%第二年spot rate计算 100= 1.5/1.0125 + 101.5/(1+ Z2 )^2,所以Z2 =1.5019% 同理,我们可以计算出第三年的Spot rate:100= 1.7/1.0125 + 1.7/ (1.015019)^2 + 101.7/(1+ S3)^3,所以Z3 =1.7049%算得债券的价值为103.7815,所以NYSE Euronext这个交易所定价是合理的。 PMT=3FV=100I/Y=1.7%n=3

2024-07-22 22:18 1 · 回答

NO.PZ201602270200001802 问题如下 2. Baseon Exhibits 1 an2, the exchange threflects the arbitrage-free priof the bonis: A.Eurex. B.Frankfurt. C.NYSE Euronext. C is correct.The bonfrom Exhibit 1 is selling for its calculatevalue on the NYSE Euronext exchange. The arbitrage-free value of a bonis the present value of its cash flows scountethe spot rate for zero coupon bon maturing on the same te eacash flow. The value of this bon 103.7815, is calculatefollows:Notes:1. Spot rates calculateusing bootstrapping; for example: Ye2 spot rate ( Z2 ): 100=1.5/1.0125+101.5/(1+Z2)2=0.015019 100=1.5/1.0125+101.5/{(1+Z_2)}^2=0.015019100=1.5/1.0125+101.5/(1+Z2​)2=0.0150192. Present value calculateusing the formula PV=FV/(1+r)n PV=FV/{(1+r)}^nPV=FV/(1+r)n,where n= number of years until cash flow, FV= cash flow amount, anr= spot rate.A is incorrebecause the prion the Eurex exchange, €103.7956, wcalculateusing the yielto maturity rate to scount the cash flows when the spot rates shoulhave been use C is incorrebecause the prion the Frankfurt exchange, €103.7565, uses the Ye3 spot rate to scount all the cash flows.考点Introction of Arbitrage Free Valuation债券的无套利价格是用spot rate对债券的现金流进行折现得到的。 Exhibit 2中给的是1,2,3年期的Prates,因此通过Bootstrapping的方式,由前向后推导出各个spot rate。已知1-yeprate等于1.25%,则1-yespot rate也等于1.25%第二年spot rate计算 100= 1.5/1.0125 + 101.5/(1+ Z2 )^2,所以Z2 =1.5019% 同理,我们可以计算出第三年的Spot rate:100= 1.7/1.0125 + 1.7/ (1.015019)^2 + 101.7/(1+ S3)^3,所以Z3 =1.7049%算得债券的价值为103.7815,所以NYSE Euronext这个交易所定价是合理的。 请问 根据YTM计算spot rate 是在哪里讲到的?

2024-06-16 09:40 1 · 回答

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2022-09-05 17:16 1 · 回答