Market Impact Model Research Articles

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

The viability of a market impact model is usually considered to be equivalent to the absence of price manipulation strategies. 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 nonincreasing 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.

Market impact measurement of a VWAP trading algorithm

This paper proposes a model for the market impact of algorithmic trades. Usually large orders cannot be executed immediately without significant trading costs. For optimised execution one relies on the help of a VWAP (volume-weighted average price) trading algorithm. It is demonstrated that the VWAP algorithm is the optimal solution of the optimisation problem using the market impact models presented in this paper. The purpose of this work is the empirical market impact analysis of a homogeneous set of algorithmic trades. The underlying data set contains trades resulting from a hedge fund trading strategy. The analysis shows that the participation rate is the most important description variable. Therefore, a linear model and also a concave power law model of the market impact, dependent on the participation rate, are used. The estimated parameters lead to interesting consequences for verifying certain aspects of the market microstructure theory. The results also suggest different behaviour of the various analysed markets. On the one hand the market impact dependency on the participation rate behaves differently for the Japanese market compared to the European, US and Canadian markets. On the other hand, the individualised linear regression results suggest a dependency of the market impact on tick size for the Japanese and US markets.

TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS

We consider the linear‐impact case in the continuous‐time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of Huberman and Stanzl can easily be characterized by means of Bochner’s theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure‐valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko on the nonexistence of transaction‐triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.

Price Manipulation in a Market Impact Model with Dark Pool

For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus on a class of dark-pool models whose market impact at the exchange is described by an Almgren-Chriss model. Conditions for the absence of price manipulation for all Almgren-Chriss models include the absence of temporary cross-venue impact, the presence of full permanent cross-venue impact, and the additional penalization of orders executed in the dark pool. When a particular Almgren-Chriss model has been fixed, we show by a number of examples that the regularity of the dark-pool model hinges in a subtle way on the interplay of all model parameters and on the liquidation time constraint. The paper can also be seen as a case study for the regularity of market impact models in general.

Some Mathematical Aspects of Market Impact Modeling

Market impact models describe the feedback of trading strategies on the underlying asset prices. The resulting feedback effects lead to interesting questions of stability and regularity, which are closely related to the existence and behavior of strategies for optimal order execution. In this paper, we give a survey on some recent results that were obtained in this context. In the first part, we explain in particular the stochastic control approach to the maximization of the expected utility of revenues in the Almgren-Chriss framework. In the second part, we describe stability issues that arise when market impact is allowed to be transient.

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

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.

Optimal Portfolio Liquidation for CARA Investors

We consider the finite-time optimal portfolio liquidation problem for a von Neumann-Morgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuous-time liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by a deterministic strategy, which is explicitly given in terms of an analytic formula. The proof relies on the observation that the corresponding value function solves a degenerate Hamilton-Jacobi-Bellman equation with singular initial condition.