Volatility Modeling

Core Concepts

EWMA (Exponentially Weighted Moving Average)

A simple volatility model that gives more weight to recent observations. RiskMetrics popularized this approach with a standard decay factor.

sigma^2_t = lambda * sigma^2_{t-1} + (1 - lambda) * r^2_{t-1}

where:

• lambda = decay factor (RiskMetrics standard: 0.94 for daily, 0.97 for monthly)
• r_{t-1} = return in period t-1 (typically demeaned, but for daily returns the mean is often assumed to be zero)
• sigma^2_{t-1} = previous period's variance estimate