Fits a GARCH(1, 1) model to the historical returns and returns the estimated Omega, Alpha and Beta parameters for each asset.

GARCH (Generalized autoregressive conditional heteroskedasticity) is a stochastic model for time series, used to model volatility clustering. A GARCH(1, 1) model expresses the conditional variance sigma_t^2 as:

\[\sigma_{t} ^{2} = \text{Omega} + \text{Alpha} \cdot \operatorname{u\_}(t-1) ^{2} + \text{Beta} \cdot \operatorname{sigma\_}(t-1) ^{2}\]

With the constraints Omega, Alpha, Beta > 0 and Alpha + Beta < 1. The parameters are estimated via simulated annealing, maximizing the GARCH log-likelihood function.

Unlike get_garch and get_garch_forecast, which return a (forecasted) volatility path, this method returns the fitted parameters themselves. This is useful when the parameters are needed directly, for example to seed a separate volatility simulation.

For more information about the method, see the following book:

  • Finance Compact Plus Band 1, by Yvonne Seler Zimmerman and Heinz Zimmerman; ISBN: 978-3-907291-31-1

Also known as: GARCH weights, GARCH coefficients, conditional variance parameters.

No programming experience? With the Finance Toolkit MCP server, AI assistants such as Claude and ChatGPT can calculate the GARCH Parameters for you. Just ask in plain English.

Calculate the GARCH Parameters in Python

The GARCH Parameters is available in the Risk module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_garch_parameters as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(["AMZN", "TSLA"], api_key="FINANCIAL_MODELING_PREP_KEY")

toolkit.risk.get_garch_parameters(period="quarterly")

Which returns:

  AMZN TSLA Benchmark
Omega 0.0191 0.1379 0.0011
Alpha 0.0038 0.143 0.1528
Beta 0.278 0.0677 0.6939

Parameters

get_garch_parameters accepts the following parameters:

  • period (str, optional): The data frequency for returns (daily, weekly, monthly, quarterly, or yearly). Defaults to “quarterly” if the Toolkit is initialised with quarterly=True, otherwise “yearly”.
  • optimization_t (int, optional): Time steps of the returns series to use for the optimization. Defaults to the full length of the returns series.
  • rounding (int | None, optional): The number of decimals to round the results to. Defaults to None.
Hurst Exponent Marginal Value at Risk (mVaR) Component Value at Risk (cVaR) CoVaR Value at Risk Backtest Acerbi-Szekely Test GJR-GARCH Volatility Model GJR-GARCH Volatility Forecast GJR-GARCH Parameters EGARCH Volatility Model EGARCH Volatility Forecast EGARCH Parameters

The Risk module page introduces the module, and the sidebar lists all of its functions.

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