Automatic trading using stochastic methods

In this thesis, we develop algorithms for automatic trading and execution strategies for institutional investors. In the first part, we develop optimal execution strategies for traders who trade continuously using only market orders and account for stochastic trading impact. There are a great variety of impacts in the electronic trading market which may affect the performance of trading strategies in a direct or indirect manner. To understand the way of measuring and taking control of the effects potentially caused by these impacts, some of traders opt to simulate the impacts by using mathematical models such as stochastic control theories. These attempts help traders to find solutions, such as how to develop an optimal execution strategy by solving Hamilton-Jacobi-Bellman equations and how these strategies affect trading. In the second part, we focus on a new market, the cryptocurrencies' market, and find out the pairs trading strategies for the buy-side investors. We introduce the traditional trading model, Almgren-Chriss model in Chapter 2, and use it to benchmark the performance of the strategies we proposed. Chapters 3 and 4 illustrate how agents or sell-side traders interact in the market when stochastic market impacts and latency impact are modelled. We also explore the numerical methods and closed-form expression to obtain the optimal execution strategy. In Chapter 5, we analyse how to execute by using co-integrated pairs trading as a buy-side trader in the cryptocurrencies' market. We consider how to trade 'BTC/USD' and 'ETH/USD' by using the quantitative trading methods and find out the optimal weight for each cryptocurrency.