volatility
Historical Volatility
Measures the actual, realized price fluctuations of a stock over a past period. Also called "realized volatility" or "statistical volatility."
Formula
HV = σ_daily × √252 σ_daily = StdDev(ln(Sᵢ / Sᵢ₋₁))
Variables
- HV
- Annualized historical volatility
- σ_daily
- Standard deviation of daily log returns
- 252
- Trading days per year
- Sᵢ
- Closing price on day i
- ln
- Natural logarithm
Worked Example
Inputs
- Period
- 20 trading days
- Daily returns
- σ_daily = 1.2%
Calculation Steps
- 1
σ_daily = 0.012 - 2
HV = 0.012 × √252 - 3
HV = 0.012 × 15.875 = 0.1905
Result: HV ≈ 19.05% annualized
Intuition
HV tells you what the stock actually did. Compare it to IV to find edge: if IV > HV, options might be overpriced (good for sellers). If IV < HV, options might be cheap (good for buyers). This HV vs IV comparison is the core of volatility trading.