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李庚熹 · 2020年12月03日

问一道题:NO.PZ201602270200001802 [ CFA II ]

* 问题详情,请 查看题干

问题如下:

Katrina Black, portfolio manager at Coral Bond Management, Ltd., is conducting a training session with Alex Sun, a junior analyst in the fixed income department. Black wants to explain to Sun the arbitrage-free valuation framework used by the firm. Black presents Sun with Exhibit 1, showing a fictitious bond being traded on three exchanges, and asks Sun to identify the arbitrage opportunity of the bond. Sun agrees to ignore transaction costs in his analysis.

Black shows Sun some exhibits that were part of a recent presentation. Exhibit 3 presents most of the data of a binomial lognormal interest rate tree fit to the yield curve shown in Exhibit 2. Exhibit 4 presents most of the data of the implied values for a four-year, option-free, annual pay bond with a 2.5% coupon based on the information in Exhibit 3.

Exhibit 4. Implied Values (in Euros) for a 2.5%, Four-year, Option-free, Annual pay bond based on Exhibit 3

Black asks about the missing data in Exhibits 3 and 4 and directs Sun to complete the following tasks related to those exhibits:

Task 1

Test that the binomial interest tree has been properly calibrated to be arbitrage-free.

Task 2

Develop a spreadsheet model to calculate pathwise valuations. To test the accuracy of the spreadsheet, use the data in Exhibit 3 and calculate the value of the bond if it takes a path of lowest rates in Year 1 and Year 2 and the second lowest rate in Year 3.

Task 3

Identify a type of bond where the Monte Carlo calibration method should be used in place of the binomial interest rate method.

Task 4

Update Exhibit 3 to reflect the current volatility, which is now 15%.


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.

这种题一遍计算出来的spot rate保留几位小数?我在保留2位小数的情况下,计算出来的答案是A😭,用1.25 1.5 1.7折现的
1 个答案
已采纳答案

吴昊_品职助教 · 2020年12月04日

同学你好: 这道题是原版书课后题,课后题的解答中也保留了四位小数。

保留小数的位数根据题目给出的条件来判断,比如这道题表格中给出的数据都是四位小数,那我们最后也保留四位小数。计算器可以设置成自动保留六到九位小数,这样确保答案是精确的,因为本身misprice就不会很大。

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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

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。 这题目问啥呢?‘Exhibit 4 presents most of the ta of the implievalues for a four-year, option-free, annupbonwith a 2.5% coupon baseon the information in Exhibit 3.。答案我也没看懂,怎么算的?

2023-02-19 18:38 1 · 回答

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2023-01-30 16:22 1 · 回答

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2022-09-05 17:16 1 · 回答