Optimal Liquidation with Self-Exciting Order Flow and Market Microstructure

Summary

This research models the discrete-time liquidation of a large position in an illiquid market, where incoming orders arrive with a stochastic, self-exciting intensity. Price impact is modeled as a linear function of that evolving order-flow process. The liquidation task is formulated as a Markov decision process with a piecewise deterministic state process, allowing the strategy to account for changing order activity and market structure.

Numerical results indicate that the optimal policy depends on the market’s microstructure. In the described case where sufficiently large orders do not arrive, the strategy takes offers at lower levels of the limit order book to reduce the chance of leaving inventory unsold and incurring end-of-horizon costs. The excerpt does not specify the tested market settings, parameter choices, or comparisons, which limits how broadly the numerical finding can be applied.

Key ideas

• Order arrivals are modeled as a stochastic process with self-exciting intensity.
• Price impact is linked linearly to the evolving order-flow process.
• The liquidation problem is framed as a discrete-time Markov decision process.
• Optimal behavior varies with market microstructure and may use lower book offers to reduce leftover inventory risk.

Tags

# Optimum Liquidation Problem Associated with the Poisson Cluster Process


# Optimum Liquidation Problem Associated with the Poisson Cluster Process









In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a point process with stochastic intensity. We model the price impact as a linear function of a self-exciting dynamic process. We formulate the liquidation problem as a discrete-time Markov Decision Processes, where the state process is a Piecewise Deterministic Markov Process (PDMP). The numerical results indicate that an optimal trading strategy is dependent on characteristics of the market microstructure. When no orders above certain value come the optimal solution takes offers in the lower levels of the limit order book in order to prevent not filling of orders and facing final inventory costs.

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