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 ):
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.
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