Daily volatility (σ) is the typical day-to-day price swing for a stock, in dollars — the primary diffusion input that drives the width of a forecast's confidence band.
σ is computed over a trailing window and drives how widely the quantum model's simulated price paths spread — higher σ widens the CI90 band directly, because a stock that swings more day to day genuinely has a wider range of plausible future outcomes. Annualised volatility is roughly σ_daily × √252, the standard trading-day scaling.
Live example: over a recent trading day AAPL typically moved about $1.99 up or down. That is its volatility (sigma): the usual size of one day's move, not its direction. A bigger sigma means a wider, less certain forecast band, because the price has more room to wander. See the full AAPL forecast for the CI90 band this volatility estimate produces.
A large gap between realized and implied volatility is itself a signal worth watching, though the forecast band is driven by the realized figure. Volatility feeds directly into risk-first position sizing: higher σ means a wider stop-loss is needed to avoid normal noise, which shrinks recommended position size for a given dollar-risk budget.
Realized volatility is computed from actual historical price moves; implied volatility is backed out of current options prices and reflects forward-looking expectations. Quantustik's forecast band is driven by realized volatility.
The band width comes directly from the diffusion term in the quantum model's forecast equation — a larger daily standard deviation of price changes means a genuinely wider range of plausible outcomes.
Higher volatility requires a wider stop-loss, which reduces the recommended position size for a fixed dollar-risk budget.
AAPL analysis shows this metric in context, or browse all S&P 500 tickers.
Educational research only — not investment advice.