Rough Heston model as the scaling limit of bivariate heavy-tailed INAR($\infty$) processes and applications

Yingli Wang and Zhenyu Cui

Papers from arXiv.org

Abstract: This paper establishes a novel link between nearly unstable heavy-tailed integer-valued autoregressive (INAR) processes and the rough Heston model via discrete scaling limits. We prove that a sequence of bivariate cumulative INAR($\infty$) processes converge in law to the rough Heston model under appropriate scaling conditions, providing a rigorous mathematical foundation for understanding how microstructural order flow drives rough volatility dynamics. Our theoretical framework extends the scaling limit techniques from Hawkes processes to the INAR($\infty$) setting. Thus we can carry out Monte Carlo simulation of the rough Heston model through simulating the corresponding approximating INAR($\infty$) processes. Extensive numerical experiments illustrate the improved accuracy and efficiency of the proposed simulation method as compared to the literature, in the pricing of not only European options, but also path-dependent options such as arithmetic Asian options, lookback options and barrier options.

Date: 2025-03
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