Historical Risk Analysis

Core Concepts

Close-to-Close Volatility

The simplest and most common volatility estimator. Compute the standard deviation of log returns and annualize.

sigma_annual = sigma_daily * sqrt(N)

where N = number of trading periods per year (typically 252 for daily, 52 for weekly, 12 for monthly).

Log returns are preferred: r_t = ln(P_t / P_{t-1}).

Parkinson (High-Low) Estimator

Uses intraday high and low prices to capture intraday volatility that close-to-close misses. More efficient than close-to-close when the true process is continuous.