GJR-GARCH Parameters
Fits a GJR-GARCH(1, 1, 1) model to the historical returns and returns the estimated Omega, Alpha, Gamma and Beta parameters for each asset.
A positive Gamma indicates the presence of a leverage effect (negative shocks raise volatility by more than positive ones of the same size), which symmetric GARCH cannot represent.
For more information about the method, see the following paper:
- Glosten, L.R., Jagannathan, R., and Runkle, D.E. (1993). “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” The Journal of Finance, 48(5), 1779-1801.
Also known as: GJR-GARCH weights, GJR-GARCH coefficients, leverage parameters.
GJR-GARCH Parameters in Python
get_gjr_garch_parameters is part of the Risk module of the open-source Finance Toolkit. Install it with:
pip install financetoolkit -U
Then call get_gjr_garch_parameters as shown below.
from financetoolkit import Toolkit
toolkit = Toolkit(["AMZN", "TSLA"], api_key="FINANCIAL_MODELING_PREP_KEY")
toolkit.risk.get_gjr_garch_parameters(period="quarterly")
Which returns:
| AMZN | TSLA | Benchmark | |
|---|---|---|---|
| Omega | 0.0074 | 0.138 | 0.0045 |
| Alpha | 0 | 0.1492 | 0.0699 |
| Gamma | 0.0428 | -0.0828 | 1 |
| Beta | 0.7156 | 0.0711 | 0 |
Parameters
get_gjr_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 initialized 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.