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

This paper links nearly unstable, heavy-tailed bivariate cumulative INAR () 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 approximating INAR () sequence rather than discretizing the Volterra SDE, and implement the long-memory convolution with a divide-and-conquer FFT (CDQ) that reuses past transforms, yielding an efficient Monte Carlo engine for European options and path-dependent options (Asian, lookback, barrier). We further derive finite-horizon weak-error bounds for option pricing under our microstructural approximation. Numerical experiments show tight confidence intervals with improved efficiency; as α 1, results align with the classical Heston benchmark, where α is the roughness specification. Using the simulator, we also study the implied-volatility surface: the roughness specification (α<1) reproduces key empirical features -- most notably the steep short-maturity ATM skew with power-law decay -- whereas the classical model produces a much flatter skew.