This thesis comprises of five chapters. The first chapter gives a brief introduction on the existing literature about the optimal trading order execution problem, the concept of limit order book, market impact models and their underlying market microstructure. We will also provide some brief review on the regularity problem of market impact model and the resilience effect of the LOB market. Some notions about the limit order book trading will also be introduced in this chapter. The second chapter, a game theoretical model given by Rosu [74] is introduced and the same side and opposite side resilience are reinterpreted for this model. The solution structure of a Markov equilibrium of this model is obtained for the same side resilience by providing a rigourous mathematical analysis. We also provide a sufficient condition for the existence of real-valued solutions under this situation. We also reproduce the results in Rosu [74] about the opposite side resilience in this LOB model. In the third chapter, we extend the LOB market impact model in Obizhaeva and Wang [65] by introducing two sides resilience and a general LOB shape function. Two existing LOB market impact models are then replicated by our extended model, allowing the cross-impact resilience rate going to zero and infinity respectively. In the last two chapters, we conduct two applications of our extended market impact model. These two applications are able to help us study the optimal execution problem and the market regularity issues. We find out that the minimum cost of the zero-spread LOB model is a lower bound of the minimum cost of our extended market impact LOB model and those models with zero bid-ask spread have weaker regularity conditions than those with a non-zero bid-ask spread.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:644943 |
| Date | January 2015 |
| Creators | Geng, Xin |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/67146/ |
Page generated in 0.0019 seconds