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?
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.?
Answer：C
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.).