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.
Simple artificial markets populated by the kinds of trading crowds and market makers we describe are capable of replicating some of the important time series phenomena of real financial markets. For example, the leptokurtic distribution of returns and the persistence of the autocorrelation of absolute returns along with the rapid decay of the autocorrelation of raw returns are important phenomena in financial time series [19]. These phenomena are replicated to some extent in the artificial markets described by Lux [20] and Raberto et al [25] among others, but only with explicit models of opinion propagation and evolutionary behavior in the trading crowd. The fact that our model does not need to postulate such behavior, instead relying on the simple interaction between informed and uninformed traders, may point to an important underlying regularity of such time series phenomena.
In terms of learning, this thesis describes a nonparametric density estimation algorithm that is very successful in the application domain. The importance of smoothness of the density function for good performance is demonstrated by the far superior performance of the algorithm with noisy informed traders (it is worth noting that the gains are not primarily from the noise itself, but are mostly due to the improved estimation – using the perfectly informed estimates with noisy informed traders does not lead to performance as good as that achieved using the noisy estimates). The importance of maintaining a good estimate rather than just increasing the spread is apparent from the success of the “active learning” algorithm that aggressively samples from the distribution in the perfectly informed case.
Contents
1 Introduction
1.1 Background
- 1.1.1 Market Microstructure and Market-Making
1.1.2 Artificial Markets
1.1.3 Multi-Agent Simulations and Machine Learning
1.2 Contributions
1.3 Overview
2 The Market-Making Algorithm
2.1 Market Microstructure Background
2.2 Detailed Market Model
2.3 The Market-Making Algorithm
- 2.3.1 Derivation of Bid and Ask Price Equations
2.3.2 Accounting for Noisy Informed Traders
2.3.3 Approximately Solving the Equations
2.3.4 Updating the Density Estimate
3 Inventory Control, Profit Motive and Transaction Prices
3.1 A Naïve Market-Maker
3.2 Experimental Framework
3.3 Inventory Control
3.4 Profit Motive
- 3.4.1 Increasing the Spread
3.4.2 Active Learning
3.4.3 Competitive Market-Making
3.5 The Effects of Volatility
3.6 Accounting for Jumps
3.7 Time Series Properties of Transaction Prices
4 Conclusions and Future Work
4.1 Summary
4.2 Future Directions
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