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import numpy as np
from arch.univariate.volatility import VolatilityProcess
from qf_lib.common.utils.volatility.volatility_forecast import VolatilityForecast
from qf_lib.containers.dataframe.qf_dataframe import QFDataFrame
[docs]class RobustCovariance:
"""
Creates a class used for vol forecasting and covariance matrix estimation
NOTE: this method has a tendency to make decrease the volatility
Parameters
----------
simple_returns: QFDataFrame
QFDataFrame of simple returns of the assets
"""
def __init__(self, simple_returns: QFDataFrame):
self.returns = simple_returns
[docs] def calculate_covariance(self, vol_process: VolatilityProcess, horizon: int, method: str = 'analytic') -> QFDataFrame:
"""
Calculates the covariance matrix using foretasted volatility for each asset and
rank correlation between the assets. Covariance matrix contains NOT annualised values.
They are expressed in the frequency of the input returns
Parameters
-----------
vol_process: VolatilityProcess
volatility proces used for forecats calculation. For example EGARCH(p=p, o=o, q=q)
horizon: int
horizon for the volatility forecast. It is expressed in the frequency of the returns provided
method (optional): str
method of the volatility forecast calculation. Possible: 'analytic', 'simulation' or 'bootstrap'
'analytic' is the fastest but is not available for EGARCH and possibly some other models.
For details check arch documentation
Returns
----------
QFDataFrame
cov_matrix of the assets.
"""
vol_forecast_array = self._calculate_expected_volatilities(vol_process, horizon, method)
# use spearman rank correlation instead of simple pearson correlation
corr_matrix = self.returns.corr(method='spearman')
cov_matrix = corr_matrix.copy()
for i, _ in enumerate(vol_forecast_array):
for j, _ in enumerate(vol_forecast_array):
cov_matrix.iloc[i, j] = corr_matrix.iloc[i, j] * vol_forecast_array[i] * vol_forecast_array[j]
return cov_matrix
def _calculate_expected_volatilities(self, vol_process, horizon, method):
vol_forecast_array = np.zeros(self.returns.shape[1]) # size = nr o assets
for i, asset in enumerate(self.returns):
asset_returns = self.returns[asset]
vol_forecast = VolatilityForecast(asset_returns, vol_process, method, horizon, annualise=False)
vol_forecast_array[i] = vol_forecast.calculate_single_forecast()
return vol_forecast_array