问一道题：NO.PZ201602270200001802 第2小题

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

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？

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？

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。 1.01253​ + 1.01523​ + 1.0173103​ =103.7956答案的计算方式我懂，我就是不懂为什么这里用的是spot rate，就是f(2,1)和f(3,1)？

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。 这个3，103是从哪来的呢？没找到。