A class of hybrid market models: simulation, identification, and estimation

Concerns the modeling of stock market using hybrid processes. By hybrid processes, we mean such processes that involve continuous dynamics and discrete events. The theory developed is based on the hybrid geometric Brownian motion (HGBM). We use both simulation and real market data to demonstrate that the hybrid model better describes the market and is more suitable for applications. Once the generator of the Markov chain is specified, the system is determined. To identify or to estimate the generator, we propose and develop several procedures including nonlinear regression model and stochastic optimization type of procedures.