High frequency trading and asymptotics for small risk aversion in a Markov renewal model - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Financial Mathematics Year : 2015

High frequency trading and asymptotics for small risk aversion in a Markov renewal model

, (1)
1

Abstract

We study an optimal high frequency trading problem within a market microstructure model designed to be a good compromise between accuracy and tractability. The stock price is driven by a Markov renewal process (MRP), as described in [P. Fodra and H. Pham, Appl. Math. Finance, to appear], while market orders arrive in the limit order book via a point process correlated with the stock price itself. In this framework, we can reproduce the adverse selection risk, appearing in two different forms: the usual form due to big market orders impacting the stock price and penalizing the agent, and the weak form due to small market orders and reducing the probability of a profitable execution. We solve the market making problem by stochastic control techniques in this semi-Markov model. In the no risk-aversion case, we provide an explicit formula for the optimal controls and characterize the value function as a simple linear PDE. In the general case, we derive the optimal controls and the value function in terms of the previous result and illustrate how the risk aversion influences the trader strategy and her expected gain. Finally, by using a perturbation method, approximate optimal controls for small risk aversions are explicitly computed in terms of two simple PDEs, drastically reducing the computational cost and enlightening the financial interpretation of the results.

Dates and versions

hal-01261362 , version 1 (25-01-2016)

Identifiers

Cite

P. Fodra, H. Pham. High frequency trading and asymptotics for small risk aversion in a Markov renewal model. SIAM Journal on Financial Mathematics, 2015, 6 (1), pp.656-684. ⟨10.1137/140976005⟩. ⟨hal-01261362⟩
43 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More