Optimal market making and liquidation strategies in quantitative trading

Abstract

In this thesis, efforts are devoted to developing models for algorithmic trading in market making and execution of large orders. These mathematical models are based on how the electronic markets work, whether the algorithm is trading with better informed traders (adverse selection), and the type of information available to market participants.An event-triggered regime-switching jump-diffusion model is proposed. A novel approach based on regime-switching models is introduced to study the asymmetric information problem in algorithmic trading. The key idea of this approach is to incorporate investors' cognition of the market into the structure of the regime-switching model. A structural model is first extended to an information-based one. Then trading behavior of traders with different types of available information as well as the effect of information delay on market maker's trading behavior are investigated. Dynamic programming approach is adopted to deal with the resulting optimal trading problem. An analytically tractable approximation is obtained and a delicate result of the estimation error is also derived.Optimal pricing model for multiple dealers in a competitive market is considered. Utility-indifference pricing methodology is first used to explore the trigger conditions of a trade. Then focus is placed on the discussion of dealer's trading intensities. Different from traditional single-dealer models, multiple-dealer models incorporate market participants' cross-interactions. To solve the model, the solution concept of Nash equilibrium is adopted and a feasible quoting policy is developed using a linear approximation method and the principle of dynamic programming. Recursive formulas for the bid and ask quotes are obtained to show how a dealer optimally adjusts his/her trading strategy to take into account the market reaction.A Markovian model is proposed, grounded on which, optimal trade scheduling problem is discussed. A compact recursive formula is derived, using the value iterative method, to calculate the optimal execution strategy. In addition, the thesis generalizes the pre-determined time horizon model to a randomly terminated one. The case when the execution process subject to counterparty risk is considered. Viscosity solutions are introduced and employed to analyze the optimal liquidating problem. By verifying the comparison principles for viscosity solutions, we characterize the value function as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. Numerical schedules are proposed to compute the optimal strategy with sufficiently small error, which makes the analysis of liquidating defaultable assets feasible.