Optimal Execution with Poisson and Hawkes Order Flow and Price Impact

Summary

The document studies optimal execution in a linear price impact model that includes orders from other liquidity takers. Those external orders are modeled either as Poisson arrivals or as a Hawkes process, which allows order flow to be self-exciting. The authors solve the execution problem explicitly and derive a closed-form strategy that describes how an executing trader should respond to other traders’ orders.

The analysis also uses the model to examine market viability and price manipulation. It finds that Poisson order arrivals can permit robust price manipulation strategies under the Huberman–Stanzl notion. In contrast, a particular set of conditions for Hawkes order flow balances self-excitation against price resilience, excludes such strategies, and yields some market stability. The document does not provide the exact formulas or parameter conditions in its summary, so readers cannot assess their practical range from this text alone. Its conclusions are tied to the stated linear-impact model and should not be read as universal claims about execution markets.

Key ideas

• The execution model includes linear price impact and orders from other liquidity takers.
• External order arrivals are represented by either a Poisson process or a self-exciting Hawkes process.
• The optimal strategy is solved in closed form and responds to other traders’ orders.
• Poisson arrivals can support price manipulation, while specific Hawkes conditions can prevent it and support stability.

Tags

# Dynamic optimal execution in a mixed-market-impact Hawkes price model


# Dynamic optimal execution in a mixed-market-impact Hawkes price model









We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal strategy describes in particular how one should react to the orders of other traders. This result enables us to discuss the viability of the market. It is shown that Poissonian arrivals of orders lead to quite robust Price Manipulation Strategies in the sense of Huberman and Stanzl. Instead, a particular set of conditions on the Hawkes model balances the self-excitation of the order flow with the resilience of the price, excludes Price Manipulation Strategies and gives some market stability.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.