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.
Market microstructure, broadly speaking, is the area of economics that deals with the evolution of prices by focusing on the actual trading process [Demsetz (1968), Garman (1976), Amihud and Mendelson (1980), Kyle (1985), Glosten and Milgrom (1985), Easley and OGHara (1987), Easley and OGHara (1992), and Harris and Raviv (1993), among many others]. While market microstructure models come in a wide variety of styles6from inventory and information based models, to batch order and sequential trade models, to strategic behavior and game theoretic models we focus on information based, sequential trade models [Glosten and Milgrom (1985) and Easley and OGHara (1992)]. In particular, information based, sequential trade market microstructure models capture the link between asset prices and informational asymmetries among traders and model the bid ask spread as an adverse selection problem. The raison dVêtre of these models rests in the assertion that trades in a stock are correlated with private information regarding the value of that stock.
In modeling the market microstructure of a stock market, Glosten and Milgrom (1985) allow for fully informed traders, uninformed (liquidity) traders, and a market maker, all of whom are risk neutral and competitive. The market consists of a single stock and the market maker is the asset dealer. The risk neutrality of the market maker eliminates inventory effects. Both the informed and uninformed trade with the market maker and are chosen to transact randomly. The informed receive a signal indicating the true value of the asset, but the uninformed and the market maker do not6thus, there is information asymmetry. The information asymmetry poses an adverse selection problem for the market maker and is the reason for the bid ask spread. Glosten and Milgrom show that the bid ask spread bounds the expected value of the asset via a Bayesian learning process. Easley and OGHara (1992) expand the basic model to take into account event uncertainty by allowing for the possibility that there is no signal regarding the true value of the asset thus in some periods all traders are uninformed. This event uncertainty gives rise to the importance of time in the stock price process: if an information event is not a certainty, then a given traders decision to trade or not to trade may provide information to the market. They examine the time process of the stock price in this less restrictive framework and show that the sequence of bid and ask prices converges to the true value of the asset for a given information event.
We posit that private information is a driving factor in the stock price process, as suggested by French and Roll (1986). It seems reasonable, therefore, that when modeling the stock price the sources of information based trade related to the stock should be considered. Heretofore most market microstructure models considered only the market for a stock but the stock market is not the only medium for information based trade in the stock. Derivative instruments based on the underlying stock such as call and put options6may provide another vehicle through which informed traders can profit from their information. The introduction of the options market is a natural extension of asymmetric information market microstructure models that allows for further sources of information based trade, recognizing the important insight of Black (1975) that the options market may provide a better venue for informed traders and the fact that, when investigating insider trading cases, the Securities and Exchange Commission carefully examines trades in options. Easley, OGHara, and Srinivas (1998) expand the standard market microstructure model to include both a stock market and an options market.
Their sequential trade, asymmetric information model of the stock and options markets demonstrates that both markets can host information based trade. The model is analogous to that of Easley and OGHara (1987), a sequential trade, asymmetric information model of the stock market that allows for multiple trade sizes. In Easley, OGHara, and Srinivas (1998), rather than choosing between stock trade sizes, traders choose between transacting in the stock and options markets. Via equilibrium arguments, they show that informed traders will transact in the options market under certain conditions regarding the depths of the stock and options markets as well as the available leverage offered by the options relative to the stock.
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