NO.PZ201712110200000206
问题如下：
Meredith Alvarez is a junior fixed-income analyst with Canzim Asset Management.Her supervisor, Stephanie Hartson, asks Alvarez to review the asset price and payoff data shown in Exhibit 1 to determine whether an arbitrage opportunity exists.
Exhibit 1.₤Price and Payoffs for Two Risk-Free Assets
Hartson also shows Alvarez data for a bond that trades in three different markets in the same currency. These data appear in Exhibit 2.
Exhibit 2.₤2% Coupon, Five-Year Maturity, Annual Pay Bond
Hartson asks Alvarez to value two bonds (Bond C and Bond D) using the binomial tree in Exhibit 3. Exhibit 4 presents selected data for both bonds.
Exhibit 3.₤Binomial Interest Rate Tree with Volatility = 25%
Exhibit 4.₤Selected Data on Annual Pay Bonds
Hartson tells Alvarez that she and her peers have been debating various viewpoints regarding the conditions underlying binomial interest rate trees. The following statements were made in the course of the debate.
Statement 1 The only requirements needed to create a binomial interest rate tree are current benchmark interest rates and an assumption about interest rate volatility.
Statement 2 Potential interest rate volatility in a binomial interest rate tree can be estimated using historical interest rate volatility or observed market prices from interest rate derivatives.
Statement 3 A bond value derived from a binomial interest rate tree with a relatively high volatility assumption will be different from the value calculated by discounting the bond’s cash flows using current spot rates.
Based on data in Exhibit 5, Hartson asks Alvarez to calibrate a binomial interest rate tree starting with the calculation of implied forward rates shown in Exhibit 6.
Exhibit 5.₤Selected Data for a Binomial Interest Rate Tree
Exhibit 6.₤Calibration of Binomial Interest Rate Tree with Volatility= 25%
Hartson mentions pathwise valuations as another method to value bonds using a binomial interest rate tree. Using the binomial interest rate tree in Exhibit 3, Alvarez calculates the possible interest rate paths for Bond D shown in Exhibit 7.
Exhibit 7.₤Interest Rate Paths for Bond D
Before leaving for the day, Hartson asks Alvarez about the value of using the Monte Carlo method to simulate a large number of potential interest rate paths to value a bond. Alvarez makes the following statements.
Statement 4 Increasing the number of paths increases the estimate’s statistical accuracy.
Statement 5 The bond value derived from a Monte Carlo simulation will be closer to the bond’s true fundamental value.
Based on Exhibits 5 and 6, the value of the lower one-period forward rate is closest to:
选项：
A.3.5122%.
B.3.5400%.
C.4.8037%.
解释：
B is correct.
The value of the lower one-period forward rate is closest to 3.5400%, calculated as 0.058365 × e–0.50 = 0.035400.
请问本题不用表五(1+s2)^2=(1+s1)(1+f1)吗？
