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NO.PZ2018122701000044

问题如下：

Under these assumptions - in particular: a flat yield curve and constant yield volatility of 1.0% - why can we expect cash flow mapping to produce a lower diversified VaR than either duration and principal mapping?

选项：

The risk measures are non-linear.

Due to imperfect correlations between pairwise risk factors.

Fewer total cash flows will be mapped.

We cannot expect a lower diversified VaR.

解释：

B is correct.

考点 $：$ Mapping to Fixed Income Portfolios

解析 $：$ The diversified VaR is lower due to two factors. First, risk measures are not perfectly linear with maturity. Second, correlations are below unity, which reduces risk even further.

选项A为什么错了呢

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1 个答案

李坏_品职助教 · 2025年04月17日

嗨，从没放弃的小努力你好：

本题是假设利率期限结构稳定，波动率也稳定，而且没有任何非线性的资产（比如期权）。

现金流映射（cash flow mapping）本身基于线性风险因子的假设（例如债券不同期限的现金流与利率变动呈线性关系）。在题目条件中，收益率曲线平坦且波动率恒定，cash flow mapping计算VaR主要依赖方差-协方差矩阵，当不同的风险因子之间的相关性较低的时候，会体现出分散化效果，但这个效果依然是线性关系。

只有当我们对非线性资产进行mapping的时候才会用到非线性（non linear）的方法。

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