Closed-Form Formula for the Conditional Moment-Generating Function Under a Regime-Switching, Nonlinear Drift CEV Process, with Applications to Option Pricing

An analytical derivation of the conditional moment-generating function (MGF) for a regime-switching nonlinear drift constant elasticity of variance process is established. The proposed model incorporates both regime-switching mechanisms and nonlinear drift components to better capture market phenomena such as volatility smiles and leverage effects. Regime-switching models can match the tendency of financial markets to often change their behavior abruptly and the phenomenon that the new behavior of financial variables often persists for several periods after such a change. Closed-form formulas for the MGF under various conditions, which are then applied for option pricing, are also derived. The efficacy and accuracy of the results are validated through a discrete Markov chain simulation. The results obtained from the proposed formulas completely match with those from MC simulations, while requiring significantly less computational time.