吴昊_品职助教 · 2025年05月16日
嗨，努力学习的PZer你好：
Bianchi determines that the AI bond is currently trading at an option-adjusted spread (OAS) of 13.95 bps relative to the benchmark yield curve.下图中的二叉树是benchmark yield curve，而我们计算AI bond，需要在每个节点上都加上OAS（13.95bps=0.1395%）
比如针对shift down by 30 bps的情况来说：
year0，3.7%+0.1385%=3.8395%，
year1的上节点：5.1968%+0.1395%=5.3363%，year1的下节点：4.2548%+0.1395%=4.3943%
year2的上节点：7.0037%+0.1395%=7.1432%，year2的中节点：5.7342%+0.1395%=5.8737%，year2的下节点：4.6947%+0.1395%=4.8342%
shift up by 30 bps的情况也是如此，每一个节点都需要加上OAS。
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努力的时光都是限量版，加油！
NO.PZ2018123101000091 问题如下 Note: Eabonha remaining maturity of three years, annucoupon payments, ana cret rating of BBB.Bianchi constructs binomiinterest rate tree baseon a 10% interest rate volatility assumption ana current one-yerate of 1%. Panel A of Exhibit 2 provis interest rate tree assuming the benchmark yielcurve shifts wn 30 bps. Panel B provis interest rate tree assuming the benchmark yielcurve shifts up 30 bps.Bianchi termines ththe bonis currently trang option-austespre(OAS) of 13.95 bps relative to the benchmark yielcurve.Baseon Exhibits 1 an2, the effective ration for the bonis closest to: A.1.98. B.2.15 C.2.73 B is correct.考点考察Effective ration的计算解析本题的计算比较多，需要利用利率向上平移的二叉树计算出PV(+)，并且利用利率向下平移的二叉树计算出PV(-)。PV0为100.200为表一中已知信息。利率向下平移30 bps，债券价格 (PV – ) 为100.78.利率向上平移30 bps，债券价格(PV+) 为99.487.利用Effective ration公式有E(PV−)−(PV+)2×(ΔCurve)×(PV0)=100.780−99.4872×0.003×100.200=2.15E\frac{(PV_-)-(PV_+)}{2\times(\lta Curve)\times(PV_0)}=\frac{100.780-99.487}{2\times0.003\times100.200}=2.15E2×(ΔCurve)×(PV0)(PV−)−(PV+)=2×0.003×100.200100.780−99.487=2.15 向上30个bp,不是用向下的直接+60个就行吗，为什么是向下的还要加OAS，本来向下的已经加过OAS了，为什么向上话要再加一次？如果我理解错了，麻烦一下向上移和向下的利率分别是怎么详细计算来的。另外1bp=0.01%对吗？
NO.PZ2018123101000091 问题如下 Note: Eabonha remaining maturity of three years, annucoupon payments, ana cret rating of BBB.Bianchi constructs binomiinterest rate tree baseon a 10% interest rate volatility assumption ana current one-yerate of 1%. Panel A of Exhibit 2 provis interest rate tree assuming the benchmark yielcurve shifts wn 30 bps. Panel B provis interest rate tree assuming the benchmark yielcurve shifts up 30 bps.Bianchi termines ththe bonis currently trang option-austespre(OAS) of 13.95 bps relative to the benchmark yielcurve.Baseon Exhibits 1 an2, the effective ration for the bonis closest to: A.1.98. B.2.15 C.2.73 B is correct.考点考察Effective ration的计算解析本题的计算比较多，需要利用利率向上平移的二叉树计算出PV(+)，并且利用利率向下平移的二叉树计算出PV(-)。PV0为100.200为表一中已知信息。利率向下平移30 bps，债券价格 (PV – ) 为100.78.利率向上平移30 bps，债券价格(PV+) 为99.487.利用Effective ration公式有E(PV−)−(PV+)2×(ΔCurve)×(PV0)=100.780−99.4872×0.003×100.200=2.15E\frac{(PV_-)-(PV_+)}{2\times(\lta Curve)\times(PV_0)}=\frac{100.780-99.487}{2\times0.003\times100.200}=2.15E2×(ΔCurve)×(PV0)(PV−)−(PV+)=2×0.003×100.200100.780−99.487=2.15 如题
NO.PZ2018123101000091问题如下 Note: Eabonha remaining maturity of three years, annucoupon payments, ana cret rating of BBB.Bianchi constructs binomiinterest rate tree baseon a 10% interest rate volatility assumption ana current one-yerate of 1%. Panel A of Exhibit 2 provis interest rate tree assuming the benchmark yielcurve shifts wn 30 bps. Panel B provis interest rate tree assuming the benchmark yielcurve shifts up 30 bps.Bianchi termines ththe bonis currently trang option-austespre(OAS) of 13.95 bps relative to the benchmark yielcurve.Baseon Exhibits 1 an2, the effective ration for the bonis closest to:A.1.98.B.2.15C.2.73B is correct.考点考察Effective ration的计算解析本题的计算比较多，需要利用利率向上平移的二叉树计算出PV(+)，并且利用利率向下平移的二叉树计算出PV(-)。PV0为100.200为表一中已知信息。利率向下平移30 bps，债券价格 (PV – ) 为100.78.利率向上平移30 bps，债券价格(PV+) 为99.487.利用Effective ration公式有E(PV−)−(PV+)2×(ΔCurve)×(PV0)=100.780−99.4872×0.003×100.200=2.15E\frac{(PV_-)-(PV_+)}{2\times(\lta Curve)\times(PV_0)}=\frac{100.780-99.487}{2\times0.003\times100.200}=2.15E2×(ΔCurve)×(PV0)(PV−)−(PV+)=2×0.003×100.200100.780−99.487=2.15答案中折现率7.1432%等是怎么算的，能举一个例子不
NO.PZ2018123101000091 问题如下 Note: Eabonha remaining maturity of three years, annucoupon payments, ana cret rating of BBB.Bianchi constructs binomiinterest rate tree baseon a 10% interest rate volatility assumption ana current one-yerate of 1%. Panel A of Exhibit 2 provis interest rate tree assuming the benchmark yielcurve shifts wn 30 bps. Panel B provis interest rate tree assuming the benchmark yielcurve shifts up 30 bps.Bianchi termines ththe bonis currently trang option-austespre(OAS) of 13.95 bps relative to the benchmark yielcurve.Baseon Exhibits 1 an2, the effective ration for the bonis closest to: A.1.98. B.2.15 C.2.73 B is correct.考点考察Effective ration的计算解析本题的计算比较多，需要利用利率向上平移的二叉树计算出PV(+)，并且利用利率向下平移的二叉树计算出PV(-)。PV0为100.200为表一中已知信息。利率向下平移30 bps，债券价格 (PV – ) 为100.78.利率向上平移30 bps，债券价格(PV+) 为99.487.利用Effective ration公式有E(PV−)−(PV+)2×(ΔCurve)×(PV0)=100.780−99.4872×0.003×100.200=2.15E\frac{(PV_-)-(PV_+)}{2\times(\lta Curve)\times(PV_0)}=\frac{100.780-99.487}{2\times0.003\times100.200}=2.15E2×(ΔCurve)×(PV0)(PV−)−(PV+)=2×0.003×100.200100.780−99.487=2.15 如果是putable bon那低于100 的取不到对吧？
