Explanation

Volatility-weighted historical simulation is an enhancement to traditional historical simulation that accounts for changing volatility conditions over time. Here's how it works:

Correct Approach (Option A):

• First, conduct typical historical simulation on the return series to get the initial VaR estimate
• Then, adjust this VaR by multiplying by the ratio: volatility(0)/volatility(t)
• This scaling factor adjusts historical returns to reflect current market volatility conditions

Why Option A is correct:

• volatility(0) represents current volatility (higher in volatile markets)
• volatility(t) represents historical volatility at time t
• The ratio volatility(0)/volatility(t) scales up VaR when current volatility is higher than historical volatility
• This properly accounts for periods of high volatility by giving more weight to recent market conditions

Why Option B is incorrect:

• Using volatility(t)/volatility(0) would actually reduce VaR when current volatility is high, which is counter-intuitive and dangerous
• This would underestimate risk during volatile periods

Key Benefits of Volatility-Weighting:

• Better captures changing market conditions
• More responsive to recent volatility spikes
• Provides more accurate risk estimates during turbulent periods
• Maintains the non-parametric advantages of historical simulation while addressing volatility clustering issues