SHAO · 2023年09月18日
NO.PZ2018123101000061
问题如下：
Based on data in Exhibit 1, to calibrate a binomial interest rate tree starting with the calculation of implied forward rates shown in Exhibit 2.
Based on Exhibits 1 and 2, 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.
考点：考察利率二叉树模型
解析
需要计算的是Time 1时间点下面节点的利率，因为Volatility为25%，直接通过关系式可得：
0.058365 × e(-0.5) = 0.035400=3.5400%.
老师，请问一般情况下题目给的volatility指的不是sigma的平方吗？为什么这道题目指的是sigma呢
NO.PZ2018123101000061 问题如下 Baseon ta in Exhibit 1, to calibrate a binomiinterest rate tree starting with the calculation of implieforwarrates shown in Exhibit 2. Baseon Exhibits 1 an2, the value of the lower one-perioforwarrate is closest to: 3.5122%. 3.5400%. 4.8037%. B is correct.考点考察利率二叉树模型解析需要计算的是Time 1时间点下面节点的利率，因为Volatility为25%，直接通过关系式可得0.058365 × e(-0.5) = 0.035400=3.5400%. 另外为什么是e^(-2sigma)? 不是差值应该是e^(2sigma)吗？
NO.PZ2018123101000061问题如下 Baseon ta in Exhibit 1, to calibrate a binomiinterest rate tree starting with the calculation of implieforwarrates shown in Exhibit 2. Baseon Exhibits 1 an2, the value of the lower one-perioforwarrate is closest to: 3.5122%. 3.5400%. 4.8037%. B is correct.考点考察利率二叉树模型解析需要计算的是Time 1时间点下面节点的利率，因为Volatility为25%，直接通过关系式可得0.058365 × e(-0.5) = 0.035400=3.5400%.虽然题目没有要求，但还是想问用表2的数据计算，f(1,1)=5.8365%÷e^0.25=4.545471%但根据表1，f(1,1)=1.035^2÷1.025-1=4.5098%是因为题目没出好，还是我计算有问题？
NO.PZ2018123101000061 问题如下 Baseon ta in Exhibit 1, to calibrate a binomiinterest rate tree starting with the calculation of implieforwarrates shown in Exhibit 2. Baseon Exhibits 1 an2, the value of the lower one-perioforwarrate is closest to: 3.5122%. 3.5400%. 4.8037%. B is correct.考点考察利率二叉树模型解析需要计算的是Time 1时间点下面节点的利率，因为Volatility为25%，直接通过关系式可得0.058365 × e(-0.5) = 0.035400=3.5400%. 请问所以上下是决定了 sigma的正负吗？
NO.PZ2018123101000061 问题如下 Baseon ta in Exhibit 1, to calibrate a binomiinterest rate tree starting with the calculation of implieforwarrates shown in Exhibit 2. Baseon Exhibits 1 an2, the value of the lower one-perioforwarrate is closest to: 3.5122%. 3.5400%. 4.8037%. B is correct.考点考察利率二叉树模型解析需要计算的是Time 1时间点下面节点的利率，因为Volatility为25%，直接通过关系式可得0.058365 × e(-0.5) = 0.035400=3.5400%. T1 high 和 low与T0的值是什么关系？T0 * e (σ）得到？
