A new analytical solution for option pricing in a nonlinear multi-factor model with correlated regime shifts

This study introduces a nonlinear, multi-factor framework for option pricing by extending the classical Heston-CIR model. Within this framework, both volatility and interest rates are governed by correlated stochastic processes, capturing the full dynamic interdependence among asset returns, volatility, and interest rates in a complex financial environment. To reflect the structural shifts and regime-dependent behaviors observed in real markets, we further incorporate a correlated regime-switching mechanism into these stochastic factors. Despite the increased complexity, the model retains analytical tractability. We derive a generalized moment-generating function under the proposed framework and obtain a closed-form solution for European option prices. Numerical experiments reveal the rich pricing dynamics introduced by the regime-switching structure, while empirical tests demonstrate that the model outperforms the standard Heston-CIR specification, particularly in capturing the nonlinear impacts of correlated economic regimes on option valuation.