Nonlinearity in high-frequency finance and optimal execution

Market microstructure theory continues to evolve due to the rapid development of algorithmic and electronic trading. In this book we consider two problems regarding this research field: the analysis and modeling of high frequency financial data and the optimal execution of large orders. The first problem is analyzed empirically within the context of the dynamics of limit order books. We model NASDAQ high frequency financial time series. Such context imposes a discrete modeling approach about the variables of interest, like prices and bid-ask spreads. The price dynamics and bid-ask spread dynamics are coupled using a double chain Markov model. The second problem, instead, is analyzed theoretically within the context of a price model which allows for a nonlinear-transient market impact. In this context the optimal strategy is described by bursts of trading. A higher trading speed can determine a lower execution cost. Such strategies can be regularized by adding bid-ask spread costs. This volume can be of interest to scholars interested in the study of price manipulations and practitioners interested in the development of new trading strategies.