volatility weighted

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.).