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

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 ≈ 0.9), the model closely aligns with the observed relationship Var(tₜ₊₁) = λ² Var(hₜ₊₁) + 1, suggesting that persistent and well-structured tax volatility can support, rather than disrupt, informational efficiency in equity markets. JEL Classification.