Assessing volatility persistence in fractional Heston models with self-exciting jumps

Gilles de Truchis, Bernard Desgraupes and Elena-Ivona Dumitrescu

Econometric Reviews, 2025, vol. 44, issue 3, 275-311

Abstract: We derive a new fractional Heston model with self-exciting jumps. We study volatility persistence and demonstrate that the quadratic variation necessarily exhibits less memory than the integrated variance, which preserves the degree of long-memory of the instantaneous volatility. Focusing on realized volatility measures, we find that traditional long-memory estimators are dramatically downward biased, in particular for low-frequency intraday sampling. Conveniently, our Monte Carlo experiments reveal that some noise-robust local Whittle-type estimators offer good finite sample properties. We apply our theoretical results in a risk forecasting study and show that our frequency-domain forecasting procedure outperforms the traditional benchmark models.

Date: 2025
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DOI: 10.1080/07474938.2024.2409475

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