Copula Simulation

Calibrate a bivariate copula (see get_copula_parameters) between ticker_a and ticker_b, and simulate joint scenarios from it.

When ticker_a/ticker_b are not given, every unique pair among the Toolkit’s tickers is calibrated and simulated instead, as columns grouped under a top-level (Ticker A, Ticker B) column per pair.

This is what a copula-based portfolio Monte Carlo simulation needs: draws that preserve the calibrated dependence structure – including tail dependence, for the “student-t”, “clayton” and “gumbel” families – rather than the (typically understated) joint crash risk a plain multivariate gaussian simulation would produce.

Also known as: copula Monte Carlo, dependence simulation, scenario generation.

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Calculate the Copula Simulation in Python

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

pip install financetoolkit -U

Then call get_copula_simulation as shown below.

from financetoolkit import Toolkit

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

toolkit.risk.get_copula_simulation(
    "AAPL", "MSFT", copula="clayton", period="weekly", n_simulations=5000
).describe()

Which returns:

Parameters

get_copula_simulation accepts the following parameters:

• ticker_a (str, optional): The first asset. Defaults to None, meaning every unique pair of tickers in the Toolkit instance is used (requires ticker_b to also be None).
• ticker_b (str, optional): The second asset. Defaults to None, see ticker_a.
• copula (str, optional): The copula family to fit and simulate from, one of “gaussian”, “student-t”, “clayton”, “gumbel” or “frank”. Defaults to “gaussian”.
• period (str, optional): The data frequency (daily, weekly, monthly, quarterly, or yearly). Defaults to “daily”, since a dependence estimate needs far more observations than a lower frequency provides – at “yearly” a decade of history is only ten observations.
• column (str, optional): The historical data column to use. Defaults to “Return”.
• n_simulations (int, optional): The number of joint draws to simulate. Defaults to 10,000.
• random_state (int, optional): The seed for the random number generator. Defaults to 42.
• empirical_margins (bool, optional): Whether to map the simulated pseudo-observations back to realistic returns via each asset’s own empirical (historical) quantile function. Defaults to True. When False, the raw pseudo-observations (each in (0, 1)) are returned instead.
• rounding (int | None, optional): The number of decimals to round the results to. Defaults to None.

Related Risk Metrics

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