NO.PZ2023040701000037
问题如下：
Tatton uses the benchmark yield curve provided in Exhibit 2 to consider arbitrage opportunities. The benchmark bonds in Exhibit 2 pay coupons annually, and the bonds are priced at par.
Exhibit 2. Benchmark Par Curve
Tatton then
identifies a mispriced three-year annual-pay bond.
The amount (in absolute terms) by which the Hutto-Barkley corporate bond is mispriced is closest to:
选项：
A.
0.3368 per 100 of par value.
B.
0.4682 per 100 of par value.
C.
0.5156 per 100 of par value.
解释：
Correct Answer: C
The first step in the solution is to find the correct spot rate (zero-coupon rates) for each year’s cash flow. The benchmark bonds in Exhibit 2 are conveniently priced at par so the yields to maturity and the coupon rates on the bonds are the same. Because the one-year issue has only one cash flow remaining, the YTM equals the spot rate of 3% (or z1 = 3%). The spot rates for Year 2 (z2) and Year 3 (z3) are calculated as follows:
Therefore, the bond is mispriced by 94.4828 – 94.9984 = –0.5156 per 100 of par value.
A is incorrect because the correct spot rates are not calculated and instead the Hutto-Barkley Inc. bond is discounted using the respective YTM for each maturity. Therefore, this leads to an incorrect mispricing of 94.6616 – 94.9984 = –0.3368 per 100 of par value.
B is incorrect because the spot rates are derived using the coupon rate for Year 3 (maturity) instead of using each year’s respective coupon rate to employ the bootstrap methodology. This leads to an incorrect mispricing of 94.5302 – 94.9984 = –0.4682 per 100 of par value.
spot rate计算的是无套利价格。
那么用forwar rate和YTM求的价格又分别是什么的？
- forward rate是隐含在spot rate里对未来实际spot rate的估计。
- YTM，假设收益率曲线是flat的，相当于spot rate的平均值或是打包价。
