Two essays on modeling financial markets as complex and interactive systems

This dissertation proposes two different approaches to modeling a financial market as a complex and interactive system. The first essay proposes a new asymmetric information modeling framework that provides a theoretical explanation for some of the observed interactions among the key quantities in financial markets: the price impact of a trade, the duration between trades, and the degree of information asymmetry. In my model, the market maker utilizes a non-linear filtering technique to set a competitive price that rationally incorporates multiple sources of information. The price impact of a trade tends to decrease when the duration between trades gets longer. The speed at which the information gets incorporated into the price depends on the quality of the private signal and the trading rate of informed traders. I provide a procedure to estimate the parameters and discuss the sampling distribution of the parameter estimates. In addition, the optimal trading strategy of a monopolistic insider is studied in the limiting model. The second essay takes a microeconomic approach to modeling stock prices in illiquid markets. I propose a model in which the demand curve for stock is constructed from the private valuations of infinitely many interacting investors. Their valuation processes are assumed to be correlated through a common random factor and the stock price. The stock price is expressed as a quantile of the empirical measure of investors' valuations. With a particle representation of the system, I derive a stochastic partial differential equation for the empirical measure whose dynamics characterize the stock price dynamics. Adding a large trader to the pool of small investors, I examine the price impact of a large trade in the context of the option pricing and the optimal trading policy of a large trader. Lastly, under a simple trading rule with transaction costs, the trading rate is quantified in terms of the bid and ask prices, the distribution of investors' valuations, and the interface between owners' and non-owners' valuations.