Volatility measures how much a price, value, or quantity fluctuates over time. In finance, it’s expressed as a standard deviation of returns, typically annualized so you can compare assets on equal footing. In chemistry, it describes how readily a substance vaporizes. The method you use depends on whether you’re measuring what already happened (historical volatility), what the market expects to happen (implied volatility), or the physical properties of a chemical mixture.
Historical Volatility From Price Data
Historical volatility is the most straightforward measure. You calculate it directly from past prices, and it tells you how much an asset’s returns have varied over a specific window, commonly 21 trading days (about one month). The process has three core steps.
First, calculate the logarithmic return for each day. Take the natural log of today’s closing price divided by the previous day’s closing price. Using log returns instead of simple percentage changes matters because log returns are additive across time and handle compounding correctly.
Second, find the standard deviation of those returns. Average all the daily log returns, then calculate how far each individual return deviates from that average. Square each deviation, sum them up, and divide by n minus 1 (where n is the number of returns). You divide by n minus 1 rather than n because you’re working with a sample, not the entire population of possible returns. Finally, take the square root. That gives you the daily volatility.
Third, annualize the result. Multiply the daily standard deviation by the square root of the number of trading days in a year, roughly 252. The square root of 252 is about 15.9, so a stock with 1% daily volatility has an annualized volatility of approximately 15.9%. This square root rule works because variance scales linearly with time when returns are independent, and standard deviation is the square root of variance.
Range-Based Estimators
Standard historical volatility only uses closing prices, which means it ignores everything that happened during the trading day. Range-based estimators fix this by incorporating high and low prices, capturing the full dispersion of intraday movement.
The Parkinson estimator is the simplest of these. It uses each day’s high and low price to estimate volatility, squaring the log of the high-to-low ratio and dividing by a constant (4 times the natural log of 2). Because it captures the full day’s price range rather than just the endpoint, it’s roughly 4.9 times more efficient than the standard close-to-close estimator. In practical terms, that means you need far fewer data points to get an equally reliable volatility estimate.
More sophisticated versions exist. The Garman-Klass estimator, which adds opening and closing prices to the high-low range, reaches an efficiency of about 7.4. The Rogers-Satchell estimator handles assets with a price trend (drift) better than either alternative. If you’re working with limited data or need a quick read on recent volatility, range-based estimators are worth considering over the standard approach.
Average True Range for Traders
Average True Range, or ATR, is a volatility indicator popular among active traders because it’s simple and visual. Rather than producing a percentage, it gives you a dollar (or point) value representing the typical price movement per period.
True range for a single period is the largest of three values: the current high minus the current low, the absolute difference between the current high and the previous close, or the absolute difference between the current low and the previous close. Including the previous close accounts for overnight gaps, which a simple high-minus-low calculation would miss.
The ATR itself is a smoothed average of true range values, typically over 14 periods. After the initial ATR is calculated as a simple average, each subsequent value uses a formula that weights the prior ATR and the new true range: multiply the previous ATR by (n minus 1), add the current true range, then divide by n. Traders use ATR to set stop-loss distances, size positions, and gauge whether a market is in a high- or low-volatility phase.
Implied Volatility From Options Prices
Historical volatility looks backward. Implied volatility looks forward by extracting the market’s expectation of future price swings from the cost of options contracts. When options are expensive, implied volatility is high, meaning traders expect large moves. When they’re cheap, the market expects calm.
The concept works by reversing an options pricing model. The standard Black-Scholes formula prices an option using five inputs: the stock price, the strike price, the time to expiration, the risk-free interest rate, and volatility. Four of those inputs are directly observable. Volatility is not. So you take the market price of the option and solve for the volatility value that makes the model output match that price. Because the Black-Scholes formula increases continuously with volatility, there’s always exactly one solution.
You can’t solve for implied volatility with simple algebra. It requires numerical methods, essentially an iterative guessing process that software handles instantly. What matters for interpretation is that implied volatility varies by strike price and expiration date. Options far from the current stock price often have higher implied volatility than at-the-money options, creating what’s called a volatility skew or smile. This tells you the market sees outsized risk in extreme price moves.
The VIX: A Market-Wide Volatility Benchmark
The Cboe Volatility Index (VIX) aggregates implied volatility across a wide range of S&P 500 options to produce a single number representing expected market volatility over the next 30 days. A VIX reading of 20 roughly implies the market expects annualized volatility of 20%.
The VIX calculation selects out-of-the-money put and call options across many strike prices. Starting from a central forward price, it moves outward to successively lower put strikes and higher call strikes, including each option as long as it has a nonzero bid and ask price. When two consecutive strikes in either direction have zero bids or asks, the selection stops. As of February 2025, the methodology was updated to also exclude any individual option with a bid or ask of zero, tightening the filter. If all out-of-the-money puts or all out-of-the-money calls are excluded, the VIX cannot be calculated for that expiration.
Beta: Volatility Relative to a Benchmark
Beta measures how volatile a stock is compared to the broader market rather than in absolute terms. A beta of 1.0 means the stock moves roughly in line with its benchmark index. A beta of 1.5 means it tends to move 50% more than the market in either direction. A beta of 0.7 means it’s 30% less reactive.
To calculate beta, collect historical returns for both the stock and a benchmark index over the same time period. Run a linear regression with the stock’s returns as the dependent variable and the index returns as the independent variable. The slope of the resulting line is the beta. In a spreadsheet, this takes just a few columns of return data and a SLOPE function. Most financial data providers publish pre-calculated betas, but understanding the calculation helps you evaluate whether the lookback period and benchmark choice match your needs.
GARCH Models for Volatility Forecasting
Standard historical volatility treats every day in your lookback window equally, which means it adjusts slowly to changing conditions. GARCH models solve this by recognizing that volatility clusters: periods of large price swings tend to follow other large swings, and calm periods follow calm ones.
The core GARCH(1,1) model predicts tomorrow’s variance as a weighted average of three things: a long-run average variance level, today’s predicted variance, and the most recent squared return (the “surprise” from the latest period). The model assigns a weight to each component, and these weights are estimated from historical data. As long as the weights on the predicted variance and the squared return sum to less than 1, the model remains stable and mean-reverting.
Robert Engle, who developed the original ARCH framework and won the Nobel Prize for it, described GARCH as providing “a volatility measure like a standard deviation that can be used in financial decisions concerning risk analysis, portfolio selection and derivative pricing.” For practical use, GARCH requires statistical software, but the intuition is accessible: recent shocks matter more than distant ones, and volatility today is a strong predictor of volatility tomorrow.
Relative Volatility in Chemistry
Outside of finance, volatility describes how easily a substance transitions from liquid to vapor. In chemistry and chemical engineering, relative volatility is the key metric for designing distillation processes, because it tells you how separable two components in a mixture are.
Relative volatility is the ratio of the vapor pressures of two pure components. If component A has a vapor pressure of 300 mmHg and component B has a vapor pressure of 100 mmHg, the relative volatility is 3.0. The higher this number is above 1.0, the easier it is to separate the two substances by distillation. A relative volatility very close to 1.0 means the components boil at nearly the same rate, making separation difficult or requiring many distillation stages.
For ideal mixtures (those that follow Raoult’s Law), relative volatility equals the ratio of pure-component vapor pressures directly. For real-world non-ideal mixtures, you need to account for how molecules interact in the liquid phase, which modifies the effective vapor pressures. The practical formula uses mole fractions in both the liquid and vapor phases: relative volatility equals the ratio of vapor-to-liquid composition for component A divided by the same ratio for component B.