| Summary: | This thesis studies the modeling of irregularly spaced tick data using intensity mod- els, and the optimal trading strategy for executing orders based on these models. It is divided into five chapters: Time-deformation modeling of FX returns, Modeling the inten- sity of trades using order book information, Optimal execution with Hawkes market impact functions, A dynamic adaptive strategy, and Applications of dynamic adaptive strategy. Time-deformation modeling of FX returns. We model trade arrival rates using a Hawkes process in an FX market. We show that the Hawkes process produces a good fit and is able to capture the empirical characteristics of the trade arrival data. Using a wavelet jump detection method we separate the data into two components and employ Hawkes processes to model each individually. An intensity-based volatility estimator is proposed and tested with market data, and compared with realized volatility measures in a forecasting exercise. The intensity-based volatility is derived from a structural volatility model and we show that it is able to forecast volatility with great precision. Modeling the intensity of trades using order book information. Using information from the limit order book, the proposed framework takes into account measures of aggregated market activity and order imbalance in the bid and ask queue to model intensity. Empirical analysis shows that the inclusion of covariates in the Hawkes model improves the fit of the intensity model and provides a better volatility forecast. In addition we show how order book resiliency can be measured using estimates of the Hawkes process. Optimal execution with Hawkes market impact functions. We derive the optimal execu- tion strategy without imposing the assumption of a pure buy strategy. The optimal solution is obtained by finding a trade-o¤ between the market impact costs of trading and the price risk of slow execution. We derive the optimal solution in closed form in a variety of settings and study their properties. A dynamic adaptive strategy. We modify the strategy derived in chapter 4 to a dynamic adaptive strategy by admitting only a pure buy strategy. We study the dynamic adaptive strategy in various situations such as including a positive or negative drift in the price process and a risk aversion coefficient. The strategy allows for adaption to changes of market conditions. We test it using simulated data and compare it with commonly use practical execution strategies such as VWAP and POV. Applications of the dynamic adaptive strategy. We examine the optimal execution strat- egy where the market resiliency function is specified by a Hawkes process with a power law decay function and then implement the optimal trading strategy using real market data.
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