abaquant.derivatives.simulation.levy

Import path: abaquant.derivatives.simulation.levy

Domain: Derivative pricing, simulation, calibration, diagnostics, and strategy analysis.

Purpose

Levy-style return simulation helpers.

When to use it

This module generates stochastic paths or returns. Reproducible analysis should set the random seed and record time-step, horizon, drift, and volatility conventions.

Public objects

  • function: simulate_vg_nig_returns — Simulate return samples for the implemented Variance-Gamma and NIG parameterizations.

Detailed reference

Levy-style return simulation helpers.

Purpose

The module generates Variance-Gamma and NIG-inspired return samples for comparative diagnostics.

Conventions

Model parameters use the implementation convention. T is in years and n_sim is the number of simulated observations.

References

[ 1 ] Glasserman, P. (2004), Monte Carlo Methods in Financial Mathematics. [ 2 ] Madan, D. B., P. P. Carr, and E. C. Chang (1998), “The Variance Gamma Process and Option Pricing”. [ 3 ] Barndorff-Nielsen, O. E. (1997), “Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling”.

abaquant.derivatives.simulation.levy.simulate_vg_nig_returns(T, vg_sigma, vg_theta, vg_nu, nig_alpha, nig_beta, nig_delta, sigma_bsm, n_sim=50_000, seed=42)

Simulate return samples for the implemented Variance-Gamma and NIG parameterizations.

Parameters:

  • T (float) – Time to maturity in years.

  • vg_sigma (float) – Variance-Gamma diffusion-scale parameter used by the simulation.

  • vg_theta (float) – Variance-Gamma asymmetry parameter used by the simulation.

  • vg_nu (float) – Variance-Gamma activity parameter used by the simulation.

  • nig_alpha (float) – NIG alpha shape parameter under the implemented simulation parameterization.

  • nig_beta (float) – NIG beta skew parameter under the implemented simulation parameterization.

  • nig_delta (float) – NIG delta scale parameter under the implemented simulation parameterization.

  • sigma_bsm (float) – Annualized Black–Scholes volatility used by the comparison simulation.

  • n_sim (int, default=50000) – Number of simulated observations.

  • seed (int | None, default=42) – Optional pseudo-random seed for reproducible simulation.

Returns:

Numeric array ordered consistently with the supplied strikes, time grid, assets, or state labels.

Return type:

numpy.ndarray

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.