2019/07/13 by Aditi Dandapani, Dandapani, Aditi, Paul Jusselin +3 · 1 citation
Mathematics · #FOS: Economics and business #Point processes and geometric inequalities #Statistical Finance (q-fin.ST) #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.1907.06151
openalex publication_date 2019/07/13 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Using microscopic price models based on Hawkes processes, it has been shown\nthat under some no-arbitrage condition, the high degree of endogeneity of\nmarkets together with the phenomenon of metaorders splitting generate rough\nHeston-type volatility at the macroscopic scale. One additional important\nfeature of financial dynamics, at the heart of several influential works in\neconophysics, is the so-called feedback or Zumbach effect. This essentially\nmeans that past trends in returns convey significant information on future\nvolatility. A natural way to reproduce this property in microstructure modeling\nis to use quadratic versions of Hawkes processes. We show that after suitable\nrescaling, the long term limits of these processes are refined versions of\nrough Heston models where the volatility coefficient is enhanced compared to\nthe square root characterizing Heston-type dynamics. Furthermore the Zumbach\neffect remains explicit in these limiting rough volatility models.\n