Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem

Abstract:     
The viability of a market impact model is usually considered to be equivalent to the absence of price manipulation strategies in the sense of Huberman & Stanzl (2004). By analyzing a model with linear instantaneous, transient, and permanent impact components, we discover a new class of irregularities, which we call transaction-triggered price manipulation strategies. We prove that price impact must decay as a convex decreasing function of time to exclude these market irregularities along with standard price manipulation. This result is based on a mathematical theorem on the positivity of minimizers of a quadratic form under a linear constraint, which is in turn related to the problem of excluding the existence of short sales in an optimal Markowitz portfolio.

Number of Pages in PDF File: 24

Keywords: Transient price impact, market impact model, optimal order execution, price manipulation, transaction-triggered price manipulation, Bochner form, positive definite function, no short sales in Markowitz portfolio

JEL Classification: G12, G32

Accepted Paper Series