Explicit positivity preserving numerical method for linear stochastic volatility models driven by $\hat{I}\pm$-stable process

Abstract

In this paper, we introduce a linear stochastic volatility model driven by $\hat{I}\pm$-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 $1/\hat{I}\pm$. Numerical simulations are presented at the end to verify theoretical results.