EGARCH Volatility Model

Calculates the conditional variance (sigma_t^2) of the returns with an EGARCH(1, 1) model fitted to them. Take the square root for the conditional volatility, and see get_egarch_forecast for the variance forecast.

EGARCH models the log of the conditional variance, which avoids having to constrain the parameters to keep the variance positive and, like GJR-GARCH, lets negative and positive shocks of the same size have a different impact on volatility (the leverage effect).

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

• Nelson, D.B. (1991). “Conditional Heteroskedasticity in Asset

Returns: A New Approach.” Econometrica, 59(2), 347-370.

The formula is as follows:

• ln sigma_t^2 = Omega + Alpha * (|z_(t-1)| - √(2 / π)) + Gamma * z_(t-1) + Beta * ln sigma_(t-1)^2
• z_t = r_t / sigma_t
• ln sigma_1^2 = Omega + Beta * ln(Backcast)

Where r_t are the returns (not demeaned), √(2 / π) is the expected |z| of a standard normal shock, the log variance is kept within [-20, 20] and the Backcast is the same as in get_garch. The parameters maximize the Gaussian log-likelihood with |Beta| < 1 (see get_egarch_parameters).

Also known as: exponential GARCH, log-GARCH.

EGARCH Volatility Model in Python

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_egarch as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["AMZN", "TSLA"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2021-01-01",
    end_date="2025-12-31",
)

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

Which returns:

Parameters

get_egarch accepts the following parameters.

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