Constrained stochastic estimation algorithms for a class of hybrid stock market models
The authors consider the stock market as a hybrid system, in which continuous dynamics and discrete events coexist. The motivation stems from the need for suitable models to better capture the price movement on an individual stock. They model random behavior of equity markets with the help of integrating a hidden, continuous-time Markov chain with a finite state space into the original system equation. This chain has influence on both the return rate and the volatility. A stochastic optimization algorithm for the estimation of the generator of the chain is designed, its convergence is proved, the rate of convergence is derived and its performance using both simulation and real data is examined. The hybrid model is compared to the usual model based on geometric Brownian motion and it is demonstrated that the hybrid geometric Brownian motion model is better in terms of the corresponding least squares error. Also it is shown how to use the estimated generator in making stock liquidation decisions.
scientific article; zbMATH DE number 1981577
scientific article