Volatility Calculator
Calculate sample volatility from pasted closing prices, or solve a European option's implied volatility under explicit model assumptions. Manual inputs; no account or live data feed required.
Match the observation frequency: daily equities often use 252.
Paste one numeric closing price per line or separate prices with commas. No headers, thousands separators, blank entries or ticker lookup. Defaults are illustrative manual prices. Use equally spaced observations with a consistent split/dividend adjustment convention.
Annualized Historical Volatility
20 closes / 19 returns used; requested 30 return periods.
Price History Visualization
Calculated using the standard deviation of logarithmic returns.
Understanding Volatility
Historical volatility describes dispersion in an observed return sample. It does not capture every risk: jumps, illiquidity, leverage and permanent capital loss need separate analysis. Implied volatility is the parameter that matches an entered option premium to a chosen pricing model; it is not a guaranteed future realized volatility.
Historical calculation and a checkable example
For n returns, compute rᵢ = ln(Pᵢ) − ln(Pᵢ₋₁), their mean, then √[Σ(rᵢ − mean)² / (n − 1)] × √A, where A is periods per year. At least two returns are required. The calculator takes the latest lookback + 1 prices, or the shorter supplied sample, and reports the count.
For closes 100, 110, 100, the two log returns are approximately +0.09531 and −0.09531. Their sample standard deviation is about 0.13479; using 252 periods gives about 213.97% annualized volatility. This deliberately short example illustrates the formula, not a reliable market estimate. Constant proportional returns can have zero sample volatility even while the price trends.
IV requires a model-consistent premium
This implementation assumes no dividends and European exercise. Let D = K × exp(−rT). The call premium must lie from max(S − D, 0) inclusive to S exclusive; the put premium from max(D − S, 0) inclusive to D exclusive. These discounted bounds differ from immediate-exercise intrinsic value. A European put can validly cost less than K − S when rates are positive.
The solver searches 0–1000% volatility and checks the repriced premium. It reports failure instead of returning the last guess. Premiums extremely close to a model bound may not identify a stable IV. Enter the premium per share, spot and strike in the same currency, and a continuously compounded annual rate. Calendar days are divided by 365; expiry at zero days has no IV solution in this tool.
American exercise, dividends, bid/ask spreads and stale quotes can make this simplified model inappropriate for a listed contract. See OIC volatility and model discussion and OIC option-price inputs. A different dividend or exercise assumption can produce a different implied volatility for the same premium.
Calculation questions
What is historical volatility here?
It is the sample standard deviation of consecutive log returns multiplied by the square root of periods per year. Three positive closing prices are the minimum for two returns. Use equally spaced observations, oldest first, and consistent corporate-action adjustments.
Does lookback mean prices or returns?
It means return periods. A 30-period estimate needs 31 closes. If fewer valid closes are supplied, the result identifies the shorter sample actually used; it does not invent prices or silently skip invalid entries.
Which annualization factor should I use?
Use periods per year matching the data frequency. 252 is a common approximation for daily equity observations and 365 for daily calendar observations. An hourly or weekly series needs a different factor. Square-root scaling assumes comparable, uncorrelated return periods and is not a forecast guarantee.
Which options does the IV model cover?
This tool inverts European Black–Scholes with no dividends, a constant continuously compounded annual rate, and calendar days divided by 365. It does not model American early exercise, dividends, discrete events or a full volatility surface. Premium is per share in the same currency as spot and strike.
Why can IV be unavailable or zero?
Invalid inputs, model-bound violations, unstable premiums near a bound or failure to converge produce an error. An exact lower-bound premium is shown as the zero-volatility model limit, not a reliable measurement of traded IV. The search range is 0–1000% annualized volatility.
Related Tools
Implied Volatility Calculator
Solve annualized IV from an entered option premium using a European Black–Scholes model. Review per-share units, input bounds and model limitations.
Bollinger Bands Calculator
Calculate SMA-based Bollinger Bands from user-supplied closing prices.
Crypto Volatility Calculator
Calculate the historical volatility of Bitcoin, Ethereum, and other major cryptocurrencies to assess risk.
Test a volatility rule in TradingView
Use Pineify's paid Coding Agent to draft a Pine Script rule, then inspect the code and test its assumptions in TradingView. These calculator outputs do not establish a profitable strategy.