Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes

Abstract

This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H<1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We present several examples, including EGARCH($\infty$) whose limits give rise to a new class of rough volatility models. Building on this framework, we develop a GPU-accelerated Monte Carlo scheme based on divide-and-conquer fast Fourier transforms, reducing the computational complexity for each path from $\mathcal{O}(N^2)$ to $\mathcal{O}(N{\log }^{2}N)$ for large-scale rough volatility simulation and option pricing.

arXiv commentTo appear in European Journal of Operational Research