Microstructural Foundation of Rough Log-Normal Volatility Models

Battle Count: 54

The paper provides a rigorous microstructural foundation for the rough Bergomi model, which is widely used in quantitative finance for option pricing and risk management. The weak convergence rates demonstrate that the Poisson-based microstructure model can serve as a viable alternative to classical simulation schemes (Euler, Milstein) with significantly better convergence properties. For H≈0.1, halving the weak error requires only ~2.4x more time steps versus ~1000x for strong errors. However, the paper is primarily theoretical and does not directly propose trading strategies. The practical impact is on improving numerical methods for rough volatility pricing and providing economic interpretation through microstructure.

The paper involves highly advanced mathematical machinery including: C-tightness of cadlag processes, Clark-Ocone formula for Poisson random measures, fractional Brownian motion theory, Volterra process analysis, BDG inequalities, Skorokhod topology, and sophisticated kernel optimization. The numerical implementation of the Poisson simulation scheme with optimized kernels (Equation 4.19) is feasible but requires careful handling of the heavy-tailed kernel singularity at the origin. The theoretical proofs span multiple sections with intricate estimates. For practitioners, implementing the simulation scheme is moderate complexity, but understanding and extending the theory requires deep expertise in stochastic analysis.

The paper is primarily theoretical with complete proofs provided. Numerical simulations are described with parameters (H=0.15, H=0.3, rho=-0.7, M=2*10^7 samples, 5000 time steps for Euler scheme). However, no code repository is provided. The mathematical framework is fully specified with all assumptions, definitions, and proofs included. Reproduction would require implementing the Poisson simulation scheme and the optimized kernel family from Equation (4.19).