Stochastic optimal control for market making on coupled Ornstein-Uhlenbeck processes

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Stochastic optimal control for market making on coupled Ornstein-Uhlenbeck processes

 

Author: Yuen, Yui Chi Peter
Title: Stochastic optimal control for market making on coupled Ornstein-Uhlenbeck processes
Degree: M.Sc.
Year: 2015
Subject: Stochastic processes.
Finance -- Mathematical models.
Hong Kong Polytechnic University -- Dissertations
Department: Dept. of Applied Mathematics
Pages: ix, 71 leaves : color illustrations ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b2800770
URI: http://theses.lib.polyu.edu.hk/handle/200/7907
Abstract: Automated quantitative trading activity (including algorithmic trading, high-frequency trading and statistical arbitrage) now constitute the bulk of trading volume (over 60%) in global stock exchanges. Of that, a large portion of such trading can be classified as high frequency market making, in which an automated dealer places both bids and offers for a stock on an electronic exchange in order to make profit from the bid-ask spread. Previous studies examined a market-making model where the underlying asset was a single Brownian or Ornstein-Uhlenbeck process and a stochastic control was devised in order to model a market-maker who adjusts bid and offer quotes via limit orders with the goal of maximizing expected terminal profit while minimizing risk. This study extends the literature by examining the situation where the market-maker trades two coupled processes whose price difference obeys an Ornstein-Uhlenbeck process but whose average price obeys an arithmetic Brownian motion. While a closed-form optimal solution to the Hamilton-Jacobi-Bellman PDE is not given in this study, we present a computationally-simple sub-solution and some properties of the solution are discussed. Furthermore simulations of the strategy are performed and compared against both a naive “mid-point market maker and the Brownian-motion based strategy presented in previous literature. It is shown that the proposed control has superior risk / reward (Sharpe) characteristics.

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