Equilibrium prices under hidden Markov fundamentals

Battle Count: 77

The paper provides a rigorous theoretical foundation for understanding how hidden regime uncertainty and Bayesian learning affect equilibrium asset prices, stock volatility, and option-implied distributions. The belief-dependent volatility mechanism and the state-dependent skewness result (sign determined by the slope of stock volatility with respect to posterior belief) are directly relevant to options trading strategies and risk management. However, the paper is primarily theoretical and does not provide trading signals, backtests, or implementable algorithms. The Fourier pricing representation and the PDE framework could inform quantitative option-pricing models, but significant implementation work would be needed.

The paper involves highly advanced mathematics: continuous-time stochastic calculus, infinite-horizon BSDEs, HJB equations on the probability simplex, degenerate elliptic boundary-value problems, Schauder fixed-point theory, maximum-principle arguments, regularity bootstrapping, Ventcel-type boundary conditions, and Fourier-based option pricing. Implementing the numerical methods (finite-difference solvers for the degenerate ODE, Monte Carlo simulation with log-Euler steps and control variates, Black implied-volatility inversion) requires substantial expertise in both mathematical finance and numerical methods. The theoretical proofs span approximately 20 pages of appendices.

The paper is purely theoretical with complete mathematical proofs provided in Appendices A, B, and C. All numerical illustrations use explicitly stated parameter calibrations (e.g., g1=0.25, g2=0, gamma=0.8, sigma=1.25, lambda12=lambda21=0.04, delta=0.025 for Section 4.4; g1=0.05, g2=-0.05, sigma=0.04, delta=0.06, lambda12=lambda21=0.05, gamma=0.8, theta=0.25, psi=5 for Section 5.5). However, no code or computational scripts are provided. Reproducing the numerical figures would require implementing finite-difference solvers for the degenerate boundary-value problem and Monte Carlo simulation with control variates.