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410140980 · 2023年06月29日

volatility weighted

NO.PZ2018122701000013

问题如下:

If volatility (0) is the current (today’s) volatility estimate and volatility (t) is the volatility estimate on a previous day (t), which best describes volatility-weighted historical simulation?

选项:

A.

First conduct typical historical simulation (HS) on return series. Then multiply VaR by volatility(0)/volatility(t)

B.

First conduct typical historical simulation (HS) on return series. Then multiply VaR by volatility(t)/volatility(0)

C.

Each historical return (t) is replaced by: return (t)*volatility (0)/volatility (t). Then conduct typical historical simulation (HS) on adjusted return series.

D.

Each historical return (t) is replaced by: return (t)*volatility (t)/volatility (0). Then conduct typical historical simulation (HS) on adjusted return series.

解释:

C is correct.

考点 Weighted Historic Simulation Approaches

解析 Each historical return (t) is replaced by: return(t) × volatility(0)/volatility(t). Then conduct typical historical simulation (HS) on adjusted return series

For example, if on the historical day (t), the return(t) was -2.0% and volatility(t) was 10%, while today’s volatility estimate is 20%, then the adjusted return is -2.0% × 20%/10% = - 4.0% . In this way, "Actual returns in any period t are therefore increased (or decreased), depending on whether the current forecast of volatility is greater (or less than) the estimated volatility for period t. We now calculate the HS P/L using [the adjusted returns] instead of the original data set, and then proceed to estimate HS VaRs or ESs in the traditional way (i.e., with equal weights, etc.).

老师First conduct typical historical simulation (HS) on return series怎么理解?

1 个答案
已采纳答案

李坏_品职助教 · 2023年06月29日

嗨,努力学习的PZer你好:


A选项的意思是要先对收益率序列进行历史模拟法估计,这个说法是错误的。


Volatility-weighted HS正确的做法是:每一个历史收益率都要替换为return (t)*volatility (0)/volatility (t),然后再对调整后的收益率序列进行历史模拟法估计。


所谓的历史模拟法就是对收益率的时间序列进行排序,然后找到亏损最严重的前95%或者99%的分位点作为VAR:

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虽然现在很辛苦,但努力过的感觉真的很好,加油!