Multivariate Jacobi process with application to smooth transitions

We introduce the multivariate Jacobi process as a representation for the dynamics of a stochastic discrete probability distribution. Its domain of application is dynamic analysis of switching regimes in asset return volatility, business cycle and corporate credit ratings. The paper shows how the multivariate Jacobi process is derived from the multivariate Cox–Ingersoll–Ross (CIR) model by time deformation and presents the main distributional properties. For illustration, selected continuous time models of prices and returns on financial assets are extended to smooth transitions processes featuring regimes of different volatilities and persistence. In this framework the effects of transitions between the regimes on derivative prices and long memory are examined.