Finite-Series Solutions of Hybrid PDE Systems for Conditional Moments of Regime-Switching Extended CEV Processes with Applications in Finance

Thispaper develops finite-series solutions of a hybrid system of interconnected partial differential equations for computing the conditional moments of regime-switching extended constant elasticity of variance processes with generalized drift and diffusion coefficients. The regime-switching mechanism is modeled by a continuous-time, finite-state, irreducible Markov chain with m regimes, for any integer m≥1. For any real γ>0, we identify a tractable class of processes where the γth conditional moment admits an explicit finite power series representation in the initial state, arising from the polynomial structure. The analytical framework is derived via a Feynman–Kac representation adapted for regime-switching diffusions and validated for accuracy and efficiency using Monte Carlo simulations. In addition, we investigate the asymptotic behavior of the first conditional moment for a two-state regime-switching constant elasticity of variance process with nonlinear drift, emphasizing the effects of symmetry in the Markov intensity matrix and comparisons with the corresponding linear-drift case. Applications in futures pricing demonstrate the framework’s relevance for derivative pricing and risk management.