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.

Autorentext

Jörg Osterrieder is a quantitative strategist at Goldman Sachs inLondon. Previously, he worked at Merrill Lynch. Dr. Osterriederobtained a PhD in mathematics from ETH Zürich. He was scholar ofnumerous institutions, among them the German National MeritFoundation. His current work focuses on market microstructureand algorithmic trading.

Klappentext

In the first part we study arbitrage opportunities indiverse markets. The construction of such markets isbased on an absolutely continuous but non-equivalentmeasure change which implies the existence ofinstantaneous arbitrage opportunities. In the second part, we look at a model for the limitorder book. Here we deal with the issue of how toconstruct a framework for order arrival, storage,cancellation and execution. It turns out that thelimit order book will be the difference of two doublystochastic Poisson processes at every point in time.We investigate properties of the bid-ask spread, anew type of options, the average order book in thelong-run as well as cancellation of orders usingideas from queuing theory. Finally, we also look atan extension to a large trader model.The third part deals with a dynamic marketmicrostructure model, in which a strategic marketmaker competes with an informed trader. We includethe presence of noise traders and limit order tradersin our setup. The resulting recursive equations leadto various economic interpretations. Our framework isgeneral enough to obtain several well-known models ina straightforward way.