Unified Moment-Based Simulation of Multivariate Polynomial Processes and Applications in Financial Engineering

I propose a general simulation scheme for multivariate polynomial processes, a class of stochastic processes for which the calculation of moments up to a fixed order requires only the computation of matrix exponentials. The methodology is based on the approximate computation of conditional moments given joint moments and on performing random sampling given such conditional moments. The general methodology can be adapted to the simulation of many stochastic models of practical relevance in financial engineering. It turns out to be very useful because it can be applied to stochastic volatility models (e.g., the Jacobi model) and commodity price models (e.g., the Pilipović model), for which semi-analytical European option pricing formulas or exact simulation schemes are not available, rendering it necessary to use approximations. I compare the proposed simulation schemes against various benchmarks and find that the new methodology improves the runtime/accuracy performances with respect to existing methods.

This paper was accepted by Ata Baris, stochastic models and simulation.

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.07645.