ajdmom: A Python Package for Deriving Moment Formulas of Affine Jump Diffusion Processes

TL;DR

ajdmom is a Python package that automatically derives explicit moment formulas and their derivatives for affine jump diffusion processes, facilitating model analysis and sensitivity studies.

Contribution

It introduces a modular, open-source tool that simplifies deriving moments and derivatives for affine jump diffusion models, enhancing research efficiency.

Findings

Produces explicit closed-form moment formulas

Computes derivatives of moments with respect to parameters

Enhances usability of affine jump diffusion models

Abstract

We introduce ajdmom, a Python package designed for automatically deriving moment formulae for the well-established affine jump diffusion processes with state-independent jump intensities. ajdmom can produce explicit closed-form expressions for conditional and unconditional moments of any order, significantly enhancing the usability of these models. Additionally, ajdmom can compute partial derivatives of these moments with respect to the model parameters, offering a valuable tool for sensitivity analysis. The package's modular architecture makes it easy for adaptation and extension by researchers. ajdmom is open-source and readily available for installation from GitHub or the Python package index (PyPI).