Arbitrage, Market Microstructure and the Limit Order Book

In the first part we study arbitrage opportunities in§diverse markets. The construction of such markets is§based on an absolutely continuous but non-equivalent§measure change which implies the existence of§instantaneous arbitrage opportunities. §In the second part, we look at a model for the limit§order book. Here we deal with the issue of how to§construct a framework for order arrival, storage,§cancellation and execution. It turns out that the§limit order book will be the difference of two doubly§stochastic Poisson processes at every point in time.§We investigate properties of the bid-ask spread, a§new type of options, the average order book in the§long-run as well as cancellation of orders using§ideas from queuing theory. Finally, we also look at§an extension to a large trader model.§The third part deals with a dynamic market§microstructure model, in which a strategic market§maker competes with an informed trader. We include§the presence of noise traders and limit order traders§in our setup. The resulting recursive equations lead§to various economic interpretations. Our framework is§general enough to obtain several well-known models in§a straightforward way.