NO.PZ201602270200001802
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 ):
2. Present value calculated using the formula ,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.
考点:Introduction 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Par rates,因此通过Bootstrapping的方式,由前向后推导出各个spot rate。已知1-year par rate等于1.25%,则1-year spot 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=3
FV=100
I/Y=1.7%
n=3