Much recent attention has focused on modeling high frequency stock price behavior. On the theoretical side, the blossoming area of market microstructure is providing valuable insights into the trade by trade stock price process. On the empirical side, a wealth of research has focused on capturing salient features of calendar period stock data, including conditional heteroskedasticity in calendar period price changes, or stochastic volatility. We provide a theory based link among asymmetric information, the behavior of market participants, and stochastic volatility through a market microstructure model of securities markets.
Our work follows on from Kelly and Steigerwald (2000), in which the stochastic properties of calendar period trades and squared price changes are derived from a market microstructure model. In the current paper, we make two principle contributions. First, we consider a model in which trade occurs in an options market as well as the stock market. Working from the microstructure model of Easley, OGHara, and Srinivas (1998) we derive the dynamic pattern of trade across markets as well as the stochastic properties of trades and squared price changes for each market. Second, we obtain analytic expressions for the serial correlation in calendar period squared price changes and so can directly relate stochastic volatility to the parameters of the underlying model.