Module volatility 

Volatility estimation from return series: realized (close-to-close) and EWMA (RiskMetrics).

Functions

ewma_volatility

EWMA (RiskMetrics) volatility: sigma_t^2 = lambda sigma_{t-1}^2 + (1 - lambda) r_t^2, seeded with the first squared return. Returns the annualized latest estimate; lambda = 0.94 is the classic daily-decay choice.

realized_volatility

Annualized realized volatility of a per-period return series (sample standard deviation, mean removed).