Designing Optimal Fiscal Intervention in the CAC 40: A Fractional Memory Approach to Tax-Rate Volatility

Designing Optimal Fiscal Intervention in the CAC 40: A Fractional Memory Approach to Tax-Rate Volatility | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Designing Optimal Fiscal Intervention in the CAC 40: A Fractional Memory Approach to Tax-Rate Volatility houssam boughabi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7132953/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper explores whether a long-memory fiscal policy, specifically in the form of tax-rate volatility, can help preserve stock market efficiency. Focusing on the CAC 40 index during its historically efficient phase (1999–2000), we embed a fractional Brownian motion structure into a Heston–Nandi volatility framework to model the evolution of fiscal variance. The tax process is treated as a dynamic control mechanism subject to martingale pricing conditions, reflecting market expectations. We formulate and solve a nonlinear optimization system with moment and smoothness constraints to identify the optimal sequences of fiscal variance parameters. The model is calibrated empirically using a fiscal-market variance proxy derived from observed CAC 40 dynamics. Results show that when the tax variance process exhibits strong memory effects (Hurst exponent $H \approx 0.9$), the model closely aligns with the observed relationship $\operatorname{Var}(t_{t+1}) = \lambda^2 \operatorname{Var}(h_{t+1}) + 1$, suggesting that persistent and well-structured tax volatility can support, rather than disrupt, informational efficiency in equity markets. JEL Classification. C58, E62, G18, H21, H30 Macroeconomics Tax policy market efficiency fractional volatility CAC 40 FIGARCH model Full Text Additional Declarations The authors declare no competing interests. Supplementary Files Codearticle.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Focusing on the CAC 40 index during its historically efficient phase (1999–2000), we embed a fractional Brownian motion structure into a Heston–Nandi volatility framework to model the evolution of fiscal variance. The tax process is treated as a dynamic control mechanism subject to martingale pricing conditions, reflecting market expectations. We formulate and solve a nonlinear optimization system with moment and smoothness constraints to identify the optimal sequences of fiscal variance parameters. The model is calibrated empirically using a fiscal-market variance proxy derived from observed CAC 40 dynamics. Results show that when the tax variance process exhibits strong memory effects (Hurst exponent $H \\approx 0.9$), the model closely aligns with the observed relationship $\\operatorname{Var}(t_{t+1}) = \\lambda^2 \\operatorname{Var}(h_{t+1}) + 1$, suggesting that persistent and well-structured tax volatility can support, rather than disrupt, informational efficiency in equity markets.\u003c/p\u003e\n\u003cp\u003eJEL Classification. 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