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OPTIMAL HIGH‐FREQUENCY TRADING IN A PRO RATA MICROSTRUCTURE WITH PREDICTIVE INFORMATION
Author(s) -
Guilbaud Fabien,
Pham Huyên
Publication year - 2015
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12042
Subject(s) - high frequency trading , pairs trade , futures contract , limit (mathematics) , order book , stochastic control , market microstructure , trading strategy , context (archaeology) , computer science , algorithmic trading , econometrics , statistical arbitrage , economics , mathematical optimization , optimal control , order (exchange) , mathematics , financial economics , finance , mathematical analysis , alternative trading system , paleontology , capital asset pricing model , arbitrage pricing theory , risk arbitrage , biology
We propose a framework to study optimal trading policies in a one‐tick pro rata limit order book, as typically arises in short‐term interest rate futures contracts. The high‐frequency trader chooses to post either market orders or limit orders, which are represented, respectively, by impulse controls and regular controls. We discuss the consequences of the two main features of this microstructure: first, the limit orders are only partially executed, and therefore she has no control on the executed quantity. Second, the high‐frequency trader faces the overtrading risk, which is the risk of large variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, and we provide the associated numerical resolution procedure and prove its convergence. We propose dimension reduction techniques in several cases of practical interest. We also detail a high‐frequency trading strategy in the case where a (predictive) directional information on the price is available. Each of the resulting strategies is illustrated by numerical tests.