Abstract

http://ssrn.com/abstract=1871969
 
 

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Optimal High Frequency Trading with Limit and Market Orders


Fabien Guilbaud


Université Paris VII Denis Diderot

Huyên Pham


Université Paris VII Denis Diderot; National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST)

2011


Abstract:     
We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for getting the execution order priority, which is a crucial issue in high frequency trading. By trading with limit orders, the agent faces an execution risk since her orders are executed only when they meet counterpart market orders, which are modelled by Cox processes with intensities depending on the spread and on her limit prices. By holding non-zero positions on the risky asset, the agent is also subject to the inventory risk related to price volatility. Then the agent can also choose to trade with market orders, and therefore get immediate execution, but at a least favorable price because she has to cross the bid-ask spread.

The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables.

Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders.

Number of Pages in PDF File: 22

Keywords: Market making, limit order book, inventory risk, point process, stochastic control

JEL Classification: G11

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Date posted: June 24, 2011  

Suggested Citation

Guilbaud, Fabien and Pham, Huyên, Optimal High Frequency Trading with Limit and Market Orders (2011). Available at SSRN: http://ssrn.com/abstract=1871969 or http://dx.doi.org/10.2139/ssrn.1871969

Contact Information

Fabien Guilbaud (Contact Author)
University of Paris 7 Denis Diderot ( email )
2, place Jussieu
Paris, 75005
France
Huyên Pham
University of Paris 7 Denis Diderot ( email )
Batiment Sophie Germain, 5 rue Thomas Mann
Paris, 75205
France
National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST) ( email )
15 Boulevard Gabriel Peri
1 92245
France
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