Rough Heston model as the scaling limit of bivariate cumulative heavy-tailed INAR processes: Weak-error bounds and option pricing

Yingli Wang, Zhenyu Cui and Lingjiong Zhu

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Abstract: This paper links nearly unstable, heavy-tailed \emph{bivariate cumulative} INAR($\infty$) processes to the rough Heston model via a discrete scaling limit, extending scaling-limit techniques beyond Hawkes processes and providing a microstructural mechanism for rough volatility and leverage effect. Computationally, we simulate the \emph{approximating INAR($\infty$)} sequence rather than discretizing the Volterra SDE, and implement the long-memory convolution with a \emph{divide-and-conquer FFT} (CDQ) that reuses past transforms, yielding an efficient Monte Carlo engine for \emph{European options} and \emph{path-dependent options} (Asian, lookback, barrier). We further derive finite-horizon \emph{weak-error bounds} for option pricing under our microstructural approximation. Numerical experiments show tight confidence intervals with improved efficiency; as $\alpha \to 1$, results align with the classical Heston benchmark, where $\alpha$ is the roughness specification. Using the simulator, we also study the \emph{implied-volatility surface}: the roughness specification ($\alpha

Date: 2025-03, Revised 2025-12
New Economics Papers: this item is included in nep-rmg
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