Historical Volatility & ATR Calculator

About the Historical Volatility & ATR Calculator

Paste a list of closing prices, or load a price file with opens, highs, lows and closes, and see how much the price really moved: close-to-close volatility (the standard deviation of daily log returns, annualised), and from the bars’ ranges the Parkinson, Garman–Klass, Rogers–Satchell and Yang–Zhang estimates, with ATR and the average daily range.

You also get a rolling volatility chart, and the size of a one-standard-deviation move over a day and a week at the last price — in price units, as a percentage and, for currency pairs, in pips. Choose the periods a year (252 trading days, 365 calendar days for markets that trade every day, 52 weeks, 12 months) or let the tool read it from the dates.

It works for shares, indices, futures, currency pairs and coins in any market. The figures are historical: they describe how your prices moved, not how they will move. Your prices stay in your browser.

Common uses

• Size a stop or a position from how far your instrument really moves in a day or a week.
• Compare realized volatility with the implied volatility of an option on the same underlying.
• Express a currency pair’s typical daily move in pips.
• See whether volatility rose or fell over the period of your file.

The formulas

• Close to close: σ = the sample standard deviation of ln(Cₜ ÷ Cₜ₋₁), × √(periods a year).
• Parkinson: σ² = Σ ln(H ÷ L)² ÷ (4n ln 2), from each bar’s high and low (Parkinson, The Journal of Business).
• Garman–Klass: σ² = (1/n) Σ [½ ln(H ÷ L)² − (2 ln 2 − 1) ln(C ÷ O)²] (Garman and Klass, The Journal of Business).
• Rogers–Satchell: σ² = (1/n) Σ [ln(H ÷ C) ln(H ÷ O) + ln(L ÷ C) ln(L ÷ O)], which allows for a drift in the price (Rogers and Satchell, The Annals of Applied Probability).
• Yang–Zhang: σ² = σ²(overnight: ln(Oₜ ÷ Cₜ₋₁)) + k σ²(open to close: ln(Cₜ ÷ Oₜ)) + (1 − k) σ²(Rogers–Satchell), k = 0.34 ÷ (1.34 + (n + 1) ÷ (n − 1)) (Yang and Zhang, The Journal of Business).
• ATR is Wilder’s average true range (ATR); the average daily range is the mean of high − low over the rolling window, and as a percentage the mean of (high − low) ÷ close.
• The 1σ move over t years ≈ the last close × σ × √t (a normal approximation): a day is 1/252 of a year (1/365 for 365-day data), a week 1/52.

Reading the results

• Close to close uses only closes; the range-based estimates use what happened inside each bar too, so they are steadier with few bars. Garman–Klass and Parkinson assume no drift; Rogers–Satchell and Yang–Zhang allow for it, and Yang–Zhang also counts the jump from one close to the next open.
• Annualised figures assume the moves add up independently over a year; the periods a year must match your data (252 for trading days, 365 for markets that trade every day).
• A 1σ move is a size, not a forecast: in a normal distribution about two days in three move less than it, and real prices have fatter tails.
• Intraday files: the bars are counted per day to annualise, and the average daily range is the range of each whole day, not of a single bar.

What it leaves out

Anything that is not in your prices: dividends and splits (unless the prices are adjusted), gaps between sessions in a closes-only list, and moves inside a bar that its high and low do not show. Volatility changes over time; the rolling chart shows how much it did in your file.

Limitations

• The range-based estimates need opens, highs and lows; a pasted list of closes gives close to close only.
• Rows with a high below the low, or an open or close outside the range, leave the range estimates out until the file is fixed.
• Historical figures describe the past prices in your file, not future ones.

Privacy

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.