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X-WR-CALDESC:Events for Mathematical Finance
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DTSTART;TZID=America/Chicago:20250912T140000
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SUMMARY:Rough Heston model as the scaling limit of bivariate cumulative heavy-tailed INAR( ∞) processes and applications
DESCRIPTION:Speaker: Prof. Zhenyu Cui\, School of Business\, Stevens Institute of Technology\, Hoboken NJ \nAbstract: We establish a novel link between nearly unstable cumulative 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(∞) 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 macroscopic prices following rough volatility dynamics. Our theoretical framework extends the scaling limit techniques from Hawkes processes to the INAR(∞) setting.\n     Hence\, we can carry out efficient Monte Carlo simulation of the rough Heston model through simulating the corresponding approximating INAR(∞) processes\, which provides an alternative discrete-time simulation method to the Euler-Maruyama method.  Extensive numerical experiments illustrate the improved accuracy and efficiency of the proposed simulation scheme as compared to the literature\, in the valuation of European options\, and also path-dependent options such as arithmetic Asian options\, lookback options and barrier options.
URL:https://www.math.ttu.edu/mathematicalfinance/event/seminar-date-reserved-4/
LOCATION:via Zoom
CATEGORIES:Fall 2025
ATTACH;FMTTYPE=image/jpeg:https://www.math.ttu.edu/mathematicalfinance/wp-content/uploads/2025/07/Cui.jpg
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