A Model-Based Synthetic Stock Price Time Series Generation Framework

The Ornstein-Uhlenbeck (OU) process, a mean-reverting stochastic process, has been widely applied as a time series model in various domains. This paper describes the design and implementation of a model-based synthetic time series model based on a multivariate OU process and the Arbitrage Pricing Theory (APT) for generating synthetic pricing data for a complex market of interacting stocks. The objective is to create a group of synthetic stock price time series that reflects the correlation between individual stocks and clusters of stocks in how a real market behaves. We demonstrate the method using the Standard and Poor's (S&P) 500 universe of stocks as an example.