Hybrid Stock Models and Parameter Estimation

Abstract In this work, we study a class of hybrid models for the stock market to account for the coexistence of continuous dynamics and discrete events. Different from the original geometric Brownian motion models, both the rate of return and the volatility in the hybrid model depend on a continuous-time Markov chain. This model can deal with random volatility by incorporating market trend with other economic factors. To use the models requires being able to estimate the values of elements of the generator of the underlying Markov chain. We develop a stochastic approximation-based algorithm for the estimation task. The asymptotic properties including convergence and rates of convergence of the algorithm are proved. Using the estimated generator, one can then proceed to make equity liquidation decisions.