Lamperti Semi-Discrete method

TL;DR

This paper introduces the Lamperti semi-discrete (LSD) method for numerically approximating solutions to nonlinear stochastic differential equations common in finance and population dynamics, achieving strong convergence without parameter restrictions.

Contribution

The paper proposes the LSD method, a domain-preserving numerical scheme that converges strongly with order 1 for various complex stochastic models.

Findings

LSD method preserves the domain of solutions.

Achieves strong convergence order 1.

Applicable to multiple stochastic models.

Abstract

We study the numerical approximation of numerous processes, solutions of nonlinear stochastic differential equations, that appear in various applications such as financial mathematics and population dynamics. Between the investigated models are the CIR process, also known as the square root process, the constant elasticity of variance process CEV, the Heston $3/2$-model, the A\"it-Sahalia model and the Wright-Fisher model. We propose a version of the semi-discrete method, which we call Lamperti semi-discrete (LSD) method. The LSD method is domain preserving and seems to converge strongly to the solution process with order $1$ and no extra restrictions on the parameters or the step-size.