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

This paper investigates whether long-memory fiscal policy, implemented through tax-rate volatility, can contribute to preserving stock market efficiency. Focusing on the CAC 40 index during its historically efficient period (1999–2000), we incorporate a fractional Brownian motion structure into a Heston–Nandi volatility framework to model the dynamics of fiscal variance. Tax-rate volatility is interpreted as a dynamic policy instrument operating under martingale pricing conditions and reflecting market expectations. We formulate and solve a nonlinear optimization problem subject to moment and smoothness constraints to identify optimal fiscal variance trajectories. The model is empirically calibrated using a fiscal–market variance proxy derived from observed CAC 40 dynamics. The results indicate that when the tax-variance process exhibits strong persistence, characterized by a Hurst exponent close to 0.9, the model closely reproduces the observed relationship ( \mathrm{Var}(\tau_{t+1}) = \lambda^{2}\mathrm{Var}(h_{t+1}) + 1 ). These findings suggest that persistent and well-structured fiscal volatility may reinforce, rather than undermine, informational efficiency in equity markets.