Moate Simulation of Stochastic Processes

TL;DR

The paper introduces Moate Simulation, a new numerical method for accurately and efficiently evolving probability distributions of stochastic processes, offering a faster alternative to Monte Carlo methods with flexible distribution modification capabilities.

Contribution

It presents the Moate Simulation approach, a novel numerical technique for simulating probability distributions of stochastic differential equations with improved accuracy and speed over traditional Monte Carlo methods.

Findings

Provides highly accurate distribution simulations

Achieves faster computation compared to Monte Carlo

Enables distribution modification during simulation

Abstract

A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are specified. Where the variables of stochastic differential equations may be transformed via It\^o-Doeblin calculus into stochastic differentials with a constant diffusion term, the probability distribution function for these variables can be simulated in discrete time steps. The drift is applied directly to a volume element of the distribution while the stochastic diffusion term is applied through the use of convolution techniques such as Fast or Discrete Fourier Transforms. This allows for highly accurate distributions to be efficiently simulated to a given time horizon and may be employed in one, two or higher dimensional expectation integrals, e.g. for pricing of financial derivatives. The Moate Simulation approach forms a more accurate and considerably faster alternative to Monte Carlo Simulation for many applications while retaining the opportunity to alter the distribution in mid-simulation.