Volatility

Calculate the Volatility of an investment portfolio or asset’s returns for a given period based on the daily historical prices.

Volatility measures the amount of dispersion or variability in returns. It is the square root of the Variance. A higher Volatility indicates greater variability, while a lower Volatility suggests that returns are closer to the mean.

By default this is the close-to-close Volatility, i.e. the standard deviation of the daily returns. The method parameter selects one of four range-based estimators instead, each of which uses more of the day’s price action than just the close and is therefore more statistically efficient (i.e. needs fewer observations to reach the same precision), at the cost of additional assumptions about how prices move:

• "parkinson" - uses the daily trading range (High vs Low) rather than the close-to-close return, assuming prices follow a continuous geometric Brownian motion with no drift and no overnight jumps.
• "garman_klass" - extends Parkinson by also incorporating the Open and Close, which allows it to account for the opening jump and makes it more efficient still (assuming, as Parkinson does, no drift and no overnight jumps beyond the modeled open).
• "rogers_satchell" - drift-independent, meaning it remains unbiased even when the underlying asset has a non-zero expected return over the period, at the cost of still assuming no overnight jumps.
• "yang_zhang" - a weighted combination of the overnight (close-to-open) Variance, the open-to-close Variance and the Rogers-Satchell Variance. It is both drift-independent and accounts for overnight jumps, which makes it the most statistically efficient of the range-based estimators implemented here.

The formula is as follows (with the default method=”close_to_close”):

Where Std is the sample standard deviation (ddof=1) and the trading days per period are 252 / 52 (weekly), 252 / 12 (monthly), 252 / 4 (quarterly) or 252 (yearly). The range-based estimators take the square root of a daily variance and scale it the same way, with H, L, O and C the daily High, Low, Open and Close, C_(-1) the previous Close, Mean the average and Var the sample variance (ddof=1) over the days in the period:

With rolling, the result is the sample standard deviation of the last rolling returns of the chosen period itself, without scaling.

Also known as: standard deviation of returns. The range-based estimators are also known as Parkinson’s range-based or high-low Volatility, Garman-Klass range-based Volatility, Rogers-Satchell drift-independent Volatility and Yang-Zhang drift-independent overnight-aware Volatility.

For more information about the range-based estimators, see the following papers:

• Parkinson, M. (1980). “The Extreme Value Method for Estimating the Variance of the Rate of Return.” Journal of Business, 53(1), 61-65.
• Garman, M.B., & Klass, M.J. (1980). “On the Estimation of Security Price Volatilities from Historical Data.” Journal of Business, 53(1), 67-78.
• Rogers, L.C.G., & Satchell, S.E. (1991). “Estimating Variance from High, Low and Close Prices.” Annals of Applied Probability, 1(4), 504-512.
• Yang, D., & Zhang, Q. (2000). “Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices.” Journal of Business, 73(3), 477-491.

Volatility in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_volatility as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["EURUSD", "BTCUSD", "^GSPC", "GCUSD"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2021-01-01",
    end_date="2025-12-31",
)

toolkit.risk.get_volatility(period="yearly")

Or, after setting up the Finance Toolkit MCP, ask:

Which returns:

Parameters

get_volatility accepts the following parameters.

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