问题如下图：
选项：
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解释：
老师，这题的解答我看不懂，为什么YTM直接看成是coupon rate了？公式完全没见过。
发亮_品职助教 · 2018年06月20日
先求Exhibit 1这个三年期、coupon rate是3.0%，按年付息，par value=100债券的合理价值。
然后在对比哪个交易所的价格是合理的。
求债券现值就需要Spot rate。
但是注意Exhibit 2给的是Par rates。
所以我们需要用Par rates通过bootstrapping的方法求出来Spot rate。然后再用spot rate去折现。
这个Par rates其实就是一个付息债券的Coupon-rate，只不过这个Coupon rate很特殊会使得债券的现值等于其面值。
例如一年期的Par rate是1.25%，则代表这个1年期债券的Coupon rate=1.25%，所以用一年期spot rate折现这个债券，得到的价值等于去面值，所以就是：
这样可以反求出来一年期的Spot rate。当然这个肯定是1.25%，则第一年的spot rate等于第一年的par rate。
然后本题中2年期的par rate等于1.5%，它代表这个2年期的债券其Coupon rate等于1.5%的债券，用spot rate折现值后得到的现值是其面值；第一年的spot rate上面已经求出来了，所以未知数是第二年的spot rate：
这样就知道了第二年的Spot rate等于1.5019%。
同理，知道第三年的Par rate=1.70%，他代表这个三年期债券的coupon rate是1.7%，用spot rate折现，折现的现值是面值100：
同理S1，S2，我们在上面已经求出来了，只有一个未知数S3，求出来就是第三年的Spot rate。
这样，我们就有了三个Spot rate，再用spot rate去折现债券。
上面由par rate求Spot rate的过程就叫bootstrapping。这也是我们通常求Spot rate curve的方法。如果忘记了回看视频。
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。
