High Frequency Trading in a Markov Renewal Model

26 Pages Posted: 1 Oct 2013 Last revised: 2 Oct 2013

See all articles by Pietro Fodra

Pietro Fodra

Université Paris VII Denis Diderot

Huyên Pham

Université Paris VII Denis Diderot

Date Written: September 27, 2013

Abstract

We study an optimal high frequency trading problem within a market micro-structure 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 bi-dimensional Euler scheme. Statistical procedures and numerical tests for computing the optimal limit order strategies illustrate our results.

Keywords: High frequency trading – Markov renewal process, Marked Cox process, adverse selection, integro-ordinary differential equation

JEL Classification: G10, C51

Suggested Citation

Fodra, Pietro and Pham, Huyen, High Frequency Trading in a Markov Renewal Model (September 27, 2013). Available at SSRN: https://ssrn.com/abstract=2333752 or http://dx.doi.org/10.2139/ssrn.2333752

Pietro Fodra

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Huyen Pham (Contact Author)

Université Paris VII Denis Diderot ( email )

Batiment Sophie Germain 5 rue Thomas Mann
Paris, 75205
France

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