Historical Volatility Calculator

Historical volatility (HV), also called realized volatility, measures how much an asset's price has fluctuated over a specific past period. It is expressed as an annualized percentage and is one of the most widely used risk metrics in finance, portfolio management, and options pricing.

Unlike implied volatility — which reflects the market's forward-looking expectation of price movement — historical volatility is purely backward-looking. It tells you how volatile the asset actually was, not how volatile it is expected to be. This distinction matters enormously when evaluating whether options are over- or under-priced relative to recent realized price behavior.

Traders, risk managers, and analysts use historical volatility to:

• Compare current implied volatility against recent realized volatility to spot mis-priced options
• Size positions using volatility-adjusted metrics (e.g., value at risk)
• Identify regime changes — periods of unusually high or low price dispersion
• Calibrate quantitative models like Black-Scholes that require a volatility input

The standard approach uses the standard deviation of logarithmic (log) returns, which assumes that price changes follow a lognormal distribution — a common assumption in financial modeling. Log returns are preferred over simple percentage returns because they are time-additive and symmetric around zero, which makes statistical analysis cleaner and more robust.

The lookback window you choose matters significantly. A 10-day HV captures very recent price behavior and reacts quickly to new data. A 252-day HV smooths over a full trading year and provides a longer-term baseline. Neither is universally correct — your choice should match the trading horizon and decision you are making.

This calculator uses the close-to-close historical volatility method with population variance (dividing by n, not n − 1). The process follows five sequential steps:

1. Collect closing prices for the desired lookback period (minimum 2 prices to get at least 1 return).
2. Compute log returns: for each consecutive pair of prices, calculate the natural logarithm of the ratio.
3. Calculate the mean log return across all computed returns.
4. Calculate population variance: average of the squared deviations from the mean.
5. Annualize: multiply the daily standard deviation by the square root of the number of trading days per year (typically 252 for equities).

The result is an annualized volatility figure expressed as a percentage. For example, a 20% annualized HV on a stock means that, based on recent price history, you would expect the price to move roughly ±20% over the course of a full year (assuming normally distributed returns).

Because volatility scales with the square root of time under standard assumptions, the same daily standard deviation can be expressed across different horizons simply by multiplying by the appropriate square root factor. This calculator reports four horizons simultaneously:

The choice of 252 trading days reflects the approximate number of business days the U.S. stock market is open per year after accounting for holidays. Futures markets often use 260; cryptocurrency markets, which trade around the clock every day of the year, use 365. Make sure you select the correct convention for the asset class you are analyzing, because the annualized figure changes meaningfully across these choices.

The square-root-of-time rule assumes that daily returns are independently and identically distributed — an idealization that breaks down during market stress when serial correlations emerge. During crises, actual multi-day volatility can exceed what the square-root rule predicts.

This calculator also reports two additional estimators that attempt to capture information beyond simple close-to-close returns.

Parkinson Volatility Estimator

The Parkinson estimator was designed to use intraday high-low ranges and is theoretically more efficient than close-to-close volatility because it incorporates more price information per period. Since only closing prices are provided here, the calculator approximates it using the formula:

σ_Parkinson = σ_daily × √(N / (4 × ln 2))

The factor 1 / (4 × ln 2) ≈ 0.3607 means the Parkinson annualization divisor (√(N / 2.7726)) is smaller than the standard one (√N), so the Parkinson estimate is typically lower than the standard annualized volatility. In practice, the full Parkinson estimator uses daily high and low prices; the approximation here is illustrative.

Yang-Zhang Estimator (Simplified)

The Yang-Zhang estimator combines overnight and open-to-close return components. The calculator uses a simplified version that weights close-to-close variance at 34% and a proxy for intraday (open-to-close) variance at 66%:

σ_YZ = √(0.34 × σ² + 0.66 × σ²_open-to-close) × √N

where open-to-close returns are approximated as 70% of the log return and overnight as 30%. While not the full Yang-Zhang formula, this provides a directional sense of how the estimator differs from the standard approach. For production risk systems, use actual open, high, low, and close (OHLC) data with the full estimator.

Understanding what a given volatility number means in context is just as important as computing it correctly. The table below provides rough benchmarks for U.S. equities, though these thresholds shift across asset classes and market regimes:

The VIX index — the benchmark "fear gauge" — reflects the implied 30-day volatility of the S&P 500 and typically ranges between 12 and 20 during calm markets, spiking above 30 or even 80 during crises. Comparing HV to IV (implied volatility) reveals whether options are cheap or expensive relative to recent realized price behavior: when IV > HV, options sellers tend to find the market favorable; when IV < HV, options buyers may be getting a discount.

Historical volatility is not just an academic exercise — it feeds directly into several practical trading and risk workflows.

Options Pricing and Strategy Selection

The Black-Scholes model and virtually every derivative pricing framework require a volatility input. Plugging realized HV into Black-Scholes gives a baseline "fair value" for an option based on recent price behavior. Comparing that fair value to the market price helps identify whether the option is trading rich or cheap relative to history. Strategies such as volatility arbitrage, covered calls, and cash-secured puts depend heavily on this comparison.

Portfolio Risk Management

Value at Risk (VaR) models use historical volatility to estimate the probability of a portfolio loss exceeding a given threshold over a specified horizon. A 20% annualized HV on a single asset implies a daily 1-standard-deviation move of roughly 20% ÷ √252 ≈ 1.26%, meaning there is approximately a 16% probability of a daily loss exceeding 1.26% on that position. Risk managers aggregate these across correlated positions using covariance matrices.

Volatility Regime Analysis

Comparing short-window HV (e.g., 10-day) to long-window HV (e.g., 252-day) helps identify volatility regime shifts. When short-term HV spikes well above long-term HV, the market may be entering a stress period. Systematic strategies often reduce position size or tighten stop-losses when this signal fires.

Position Sizing with Volatility Targeting

Many institutional strategies target a constant annualized portfolio volatility (e.g., 10%). When realized HV rises, positions are scaled down proportionally; when HV falls, positions scale up. This volatility-targeting approach has been shown to improve risk-adjusted returns across multiple asset classes by systematically buying low volatility and selling high volatility.