Parametric Sampling

Parametric distributions can be either normal (mean-variance assumption) or lognormal (Black-Scholes assumption). When moments=’deterministic’ (default), the algorithm from Simulations with Exact Means and Covariances is applied to the discrete or log returns.

simulate_multivariate_normal(mean, covariance_matrix, S, distribution='normal', moments='deterministic', seed=None)

Function for simulating from a multivariate normal or lognormal distribution.

Parameters:

• mean (ndarray) – np.ndarray with shape (I,) containing the means of the normal distribution.

• covariance_matrix (ndarray) – Covariance matrix with shape (I, I) containing the covariances of the normal distribution.

• S (int) – Number of simulation scenarios (must be an even number for moments=’deterministic’).

• distribution (str) – {‘normal’, ‘lognormal’}. Default: ‘normal’.

• moments (str) – {‘deterministic’, ‘stochastic’}. Default: ‘deterministic’.

• seed (int) – Random seed for the simulation.

Return type:

ndarray

Returns:

Simulation with shape (S, I).

Raises:

• ValueError – If there is a mismatch between mean and covariance_matrix dimensions.

• ValueError – If covariance_matrix is not a square two-dimensional matrix.

• TypeError – If S is not an integer.

• ValueError – If distribution is not in {‘normal’, ‘lognormal’}.

• ValueError – If moments are not in {‘deterministic’, ‘stochastic’}.

• ValueError – If S is not an even integer for moments=’deterministic’.

• TypeError – If seed is not an integer.