Explicit positivity preserving numerical method for linear stochastic volatility models driven by $\alpha$-stable process

TL;DR

This paper develops a positivity-preserving numerical method for linear stochastic volatility models driven by alpha-stable processes, ensuring positive solutions and analyzing convergence properties.

Contribution

It introduces a modified Euler-Maruyama scheme that maintains positivity and achieves a convergence order of 1/alpha for such models.

Findings

The scheme preserves positivity of solutions.

Achieves strong convergence order of 1/alpha.

Numerical simulations verify theoretical convergence.

Abstract

In this paper, we introduce a linear stochastic volatility model driven by $\alpha$-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its numerical properties. The scheme achieves a strong convergence order of $1/\alpha$. Numerical simulations are presented at the end to verify theoretical results.