High frequency trading in a Markov renewal model
AbstractWe study an optimal high frequency trading problem within a market microstructure model aiming at a good compromise between accuracy and tractability. The stock price is modeled by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock price, and taking into account the adverse selection risk. We apply stochastic control methods in this semi-Markov framework, and show how to reduce remarkably the complexity of the associated Hamilton-Jacobi-Bellman equation by suitable change of variables that exploits the specific symmetry of the problem. We then handle numerically the remaining part of the HJB equation, simplified into an integro-ordinary differential equation, by a bidimensional Euler scheme. Statistical procedures and numerical tests for computing the optimal limit order strategies illustrate our results.
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Date of creation: 27 Sep 2013
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High frequency trading; Markov renewal process; Marked Cox process; adverse selection; integro-ordinary differential equation.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-10-11 (All new papers)
- NEP-MST-2013-10-11 (Market Microstructure)
- NEP-ORE-2013-10-11 (Operations Research)
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