皓皓心 · 2024年09月27日
NO.PZ2020011303000053
问题如下：
A one-year project has a 3% chance of losing USD 10million, a 7% chance of losing USD 3 million, and a 90% chance of gaining USD 1 million. What are (a) the VaR and (b) the expected shortfall when the confidence level is 95% and the time horizon is one year?
选项：
解释：
VaR is USD 3 million. Expected shortfall (USD) is 10 × 0.6 + 3 × 0.4 = 7.2.
有一个项目，3%的概率会损失10m，7%损失3m，90%概率会获得1m，求95%置信区间下的VaR与ES？
VaR=3m
ES=10 × 0.6 + 3 × 0.4 = 7.2m
什么这里的VaR不是用插值法？ES又是按比例算？
pzqa39 · 2024年09月27日
嗨，从没放弃的小努力你好：
题目说“有3%的概率损失10m美元，7%的概率损失3m美元，90%概率是损失1m美元。” 损失是具体的数字而不是一个范围，这句话可以看出是离散的，离散分布不用插值法。
ES的定义是尾部数据取加权平均，在这道题中ES是指的损失超过尾部95% var那部分损失的数学期望（均值），由于损失超过95%的概率就是1-95% = 5%，而-10 million的概率只有3%，这个3%在5%里面占了60%，另外的40%只好用-3million损失来填补，所以ES就是10 × 0.6 + 3 × 0.4 = 7.2
----------------------------------------------虽然现在很辛苦，但努力过的感觉真的很好，加油！
皓皓心 · 2024年09月27日
离散型尾部ES不足的地方要用更高的来填补，这个在讲义哪里讲到了吗？
NO.PZ2020011303000053 问题如下 A one-yeprojeha 3% chanof losing US10million, a 7% chanof losing US3 million, ana 90% chanof gaining US1 million. Whare (the Van(the expecteshortfall when the confinlevel is 95% anthe time horizon is one year? Vis US3 million. Expecteshortfall (US is 10 × 0.6 + 3 × 0.4 = 7.2. 有一个项目，3%的概率会损失10m，7%损失3m，90%概率会获得1m，求95%置信区间下的VaR与ES？VaR=3mES=10 × 0.6 + 3 × 0.4 = 7.2m 离散型的尾部ES都不能用算数平均，要用这种按比例的算法吗？讲义上有提到吗？
NO.PZ2020011303000053 问题如下 A one-yeprojeha 3% chanof losing US10million, a 7% chanof losing US3 million, ana 90% chanof gaining US1 million. Whare (the Van(the expecteshortfall when the confinlevel is 95% anthe time horizon is one year? Vis US3 million. Expecteshortfall (US is 10 × 0.6 + 3 × 0.4 = 7.2. 有一个项目，3%的概率会损失10m，7%损失3m，90%概率会获得1m，求95%置信区间下的VaR与ES？VaR=3mES=10 × 0.6 + 3 × 0.4 = 7.2m
NO.PZ2020011303000053问题如下A one-yeprojeha 3% chanof losing US10million, a 7% chanof losing US3 million, ana 90% chanof gaining US1 million. Whare (the Van(the expecteshortfall when the confinlevel is 95% anthe time horizon is one year? Vis US3 million. Expecteshortfall (US is 10 × 0.6 + 3 × 0.4 = 7.2. 有一个项目，3%的概率会损失10m，7%损失3m，90%概率会获得1m，求95%置信区间下的VaR与ES？VaR=3mES=10 × 0.6 + 3 × 0.4 = 7.2m 完全不明白，以前的解答不明白，请详细说说，在讲义哪里。谢谢
NO.PZ2020011303000053问题如下A one-yeprojeha 3% chanof losing US10million, a 7% chanof losing US3 million, ana 90% chanof gaining US1 million. Whare (the Van(the expecteshortfall when the confinlevel is 95% anthe time horizon is one year? Vis US3 million. Expecteshortfall (US is 10 × 0.6 + 3 × 0.4 = 7.2. 讲义308页说the ES gives tail losses equweight... 与此处答案的ES计算方法是否冲突？该如何理解？
