Modeling high frequency stock market data by using stochastic models

Abstract The main task of this paper is to model the dependency and effects of the Lehman Brothers financial collapse event using a superposed and coupled Ornstein-Uhlenbeck type system of stochastic differential equations driven by a Lévy process. The development of these types of efficient models to correctly quantify and predict the sample paths of these kinds of time series is essential since it helps prevent losses or maximize profits in the field of financial modeling. The results obtained from this study suggest that the solutions of the stochastic models provide a good fit to the high frequency financial stock market data since it captures realistic dependence structures. In addition, the estimated model parameters are useful for making inferences and predicting these types of events.