The major contribution of this thesis is the presentation of an algorithm for market-making under conditions of asymmetric information in markets with informed and uninformed traders. Glosten and Milgrom derive the basic concept of setting bid and ask prices to be the conditional expectations of the true value given that a sell or buy order is received, but do not extend the concept beyond toy problems [15]. On the other side of the spectrum, Chan and Shelton develop a reinforcement learning algorithm for market-making that is fairly complex and attempts to deal with multiple objectives like profit and inventory control simultaneously, but needs many training episodes and has a hard time approaching profitability, even in markets simpler than the ones we study here [6]. The price setting equations of our market making algorithm are theoretically grounded in the work of Glosten and Milgrom, and the density estimation technique is essentially explicit Bayesian learning. Modules for inventory control and for increasing profit by increasing the spread can be added to the algorithm after solution of the expected value equations for price-setting.
Our market-making algorithm displays many qualities that one would expect from any reasonable market-maker. It increases the spread when it is more uncertain about the true value (for example, following a jump in the underlying value) and tends to maintain a higher spread in more volatile markets. Our market-maker also allows us to gain insights into the structure of simple markets. For example, in markets with large numbers of noisy informed traders, increasing the spread is counterproductive beyond a point even in the absence of competition because it no longer allows the market-maker to make profits from the errant estimates of the noisy informed traders. In competitive dealer markets, as one would expect, market-makers who execute more trades tend to benefit even if they make less profit per trade, because their quotes are on the inside more often.