On a Stationarity Theory for Stochastic Volterra Integral Equations with Affine Drift

Battle Count: 79

Highly relevant for quantitative finance, particularly for rough volatility modeling. The paper provides a theoretical foundation for stabilized rough Heston-type models that can capture both short- and long-maturity volatility behavior within a single coherent framework. This addresses a well-known limitation of classical Heston and rough Heston models. The fake stationary regime ensures constant mean and variance of volatility, which is desirable for consistent option pricing and risk management across the full term structure. However, the paper is primarily theoretical and does not provide direct trading strategies or empirical backtests.

The theoretical framework is highly sophisticated, requiring expertise in stochastic analysis, Volterra equations, Laplace transforms, and fractional calculus. Numerical implementation involves: (1) computing the resolvent R_λ and its derivative f_λ via Neumann series or Laplace inversion, (2) solving the stabilizer functional equation (E_{λ,c}) numerically using triangular Volterra discretization, (3) implementing the semi-integrated Euler-Maruyama scheme with Cholesky decomposition of the covariance matrix for correlated Gaussian increments. The simulation scheme in Appendix A is well-described but computationally intensive for large grids.

The paper is primarily theoretical with proofs provided in appendices. Numerical illustrations (Figures 3-9) include specific parameter values and simulation details (number of steps, sample sizes). The semi-integrated Euler-Maruyama scheme is described in Appendix A with sufficient detail for implementation. However, no code repository is provided. The theoretical results are fully self-contained with complete proofs.