Market Impact Model Research Articles

Do price trajectory data increase the efficiency of market impact estimation?

Market impact is an important problem faced by large institutional investors and active market participants. In this paper, we rigorously investigate whether price trajectory data from the metaorder increases the efficiency of estimation, from the view of the Fisher information, which is directly related to the asymptotic efficiency of statistical estimation. We show that, for popular market impact models, estimation methods based on partial price trajectory data, especially those containing early trade prices, can outperform established estimation methods (e.g. VWAP-based) asymptotically. We discuss theoretical and empirical implications of such phenomenon, and how they could be readily incorporated into practice.

Intraday variation in cross-sectional stock comovement and impact of index-based strategies

We investigate how comovement of S&P 500 stocks changes during a day using a large high-frequency dataset and estimators that are robust under microstructure noise and asynchronicity. We find that, in 2011 to 2021, the stock correlation increases substantially throughout the trading session, while the cross-sectional beta dispersion decreases concurrently. Thus, S&P 500 stocks exhibit stronger comovement near the market close. The time-varying comovement can be explained by the intraday variation in the composition of index-based and firm-based order flows. A cross-section market impact model with time-varying demand from single-stock and index investors generates the intraday patterns we observe.

Economic Consequences of Greylisting by the Financial Action Task Force

This study considers the impact of the FATF’s greylisting process from a market perspective. The results are intended to inform the development of public policy and improvement of market signalling. The study develops a theoretical market impact model and identifies the indicators which may impact banking operations and institutional decisions. It is explicitly market-oriented in that the model seeks to reflect how stakeholders in financial and non-financial markets typically respond to signals sent out by the FATF. The authors find that the FATF’s greylisting signalling has changed over time and distinguish four broad periods reflecting different messaging. The study uses financial, trade, and other variables derived from the World Bank’s ‘World Development Indicators’ databank to explore evidence of impact in each of the different phases of the FATF’s approach to greylisting. The study uses a pooled cross-section and time series approach with fixed effects, based on a sample of 177 countries and 3540 country-years of data from 2000 to 2020. The study examines impacts on net official development assistance, the banking environment (non-performing loans, risk premiums), net foreign assets, indebtedness, and market capitalisation. It finds significant correlations between many financial variables and FATF listing events, including an apparent reduction in development assistance during greylisting periods which endured after the country was delisted. This is of significant concern, as such reductions may impact disproportionately on developing economies.

Cost of trading factor strategies

Recent academic literature claims that style premia are not robust to trading costs. Several papers written by practitioners counter that the assumptions made by academics on how style portfolios rebalance are too conservative. In this paper we analyse the cost of trading factor strategies using a market impact model estimated from actual transactions data, realistic and multiple portfolio construction techniques and up-to-date data. Our results suggest that, for realistic portfolio sizes, the typical costs of rebalancing a single-factor strategy are unlikely to erode the factor premium.
 In addition, by building portfolios across different factors and with alternative portfolio construction techniques, we are able to assess the degree of similarity amongst strategies over time, which can be viewed as a measure of crowding. The properties of our new crowding indicator are illustrated through an extensive empirical investigation. We then assess its relation to volatility, liquidity and market impact and find that increases in our crowding measure tend to be followed by increases in the volatility of a strategy’s returns.

ЗАСТОСУВАННЯ ФУНКЦІЇ ВИТРАТ РИНКОВОГО ВПЛИВУ ДЛЯ ОЦІНКИ ЯКОСТІ БРОКЕРСЬКИХ ПОСЛУГ НА РИНКУ АКЦІЙ

The paper applies the microstructural approach to analyze transaction costs accrued in the process of executing orders on financial exchanges. The extended classification of transaction costs on equity markets is presented. The set of challenges which arise in the analysis of a particular component of transaction costs – market impact – is outlined. It is proposed to apply R. Almgren’s market impact model to normalize observed costs. Normalized values exhibit a lower variance, and therefore, it requires a smaller sample of orders to choose the broker who provides the lowest transaction cost. As a result, the process of assessing broker service quality takes less time. Since, during the period of assessment, the investor has to use broker services to properly evaluate them, a faster process to weed out brokers who deliver higher transaction costs positively impacts investor’s financial results. As part of the larger challenge of reducing transaction costs of trading in financial equity markets, the specific case of market impact cost optimization on the basis of R. Almgren’s model was examined. The suggested methodology focuses on a specific component of market impact, which has lower variance, and could be used to weed out brokers with subpar levels of servicesfaster.

Generalized optimal liquidation problems across multiple trading venues

<p style='text-indent:20px;'>In this paper, we generalize the Almgren-Chriss's market impact model to a more realistic and flexible framework and employ it to derive and analyze some aspects of optimal liquidation problem in a security market. We illustrate how a trader's liquidation strategy alters when multiple venues and extra information are brought into the security market and detected by the trader. This study gives some new insights into the relationship between liquidation strategy and market liquidity, and provides a multi-scale approach to the optimal liquidation problem with randomly varying volatility.</p>

An FBSDE approach to market impact games with stochastic parameters

<p style='text-indent:20px;'>In this study, we have analyzed a market impact game between <i>n</i> risk-averse agents who compete for liquidity in a market impact model with a permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has a unique solution, resulting in a unique Nash equilibrium. </p>

Liquidity Stress Testing in Asset Management - Part 2. Modeling the Asset Liquidity Risk

This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers the asset-liability management of the liquidity gap risk (or asset-liability matching). The purpose of this research is to propose a methodological and practical framework in order to perform liquidity stress testing programs, which comply with regulatory guidelines (ESMA, 2019, 2020) and are useful for fund managers. The review of the academic literature and professional research studies shows that there is a lack of standardized and analytical models. The aim of this research project is then to fill the gap with the goal of developing mathematical and statistical approaches, and providing appropriate answers. In this second article focused on asset liquidity risk modeling, we propose a market impact model to estimate transaction costs. After presenting a toy model that helps to understand the main concepts of asset liquidity, we consider a two-regime model, which is based on the power-law property of price impact. Then, we define several asset liquidity measures such as liquidity cost, liquidation ratio and shortfall or time to liquidation in order to assess the different dimensions of asset liquidity. Finally, we apply this asset liquidity framework to stocks and bonds and discuss the issues of calibrating the transaction cost model.

Index-based Investing and Intraday Stock Dynamics

We investigate the implications of index-based investing on intraday stock dynamics using a large high-frequency data set, which consists of trade prices sampled every five seconds for all SP the betas of stocks converge towards one during the day. We show these patterns can be attributed to a ''firm-specific open, index-based close'' intraday trading profile. We theoretically support our findings via a market impact model with time-varying informational shocks and trading demands from single-stock and index investors.

A central bank strategy for defending a currency peg

We consider a central bank strategy for maintaining a two-sided currency target zone, in which an exchange rate of two currencies is forced to stay between two thresholds. To keep the exchange rate from breaking the prescribed barriers, the central bank is generating permanent price impact and thereby accumulating inventory in the foreign currency. Historical examples of failed target zones illustrate that this inventory can become problematic, in particular when there is an adverse macroeconomic trend in the market. We model this situation through a continuous-time market impact model of Almgren–Chriss-type with drift, in which the exchange rate is a diffusion process controlled by the price impact of the central bank’s intervention strategy. The objective of the central bank is to enforce the target zone through a strategy that minimizes the accumulated inventory. We formulate this objective as a stochastic control problem with random time horizon. It is solved by reduction to a singular boundary value problem that was solved by Lasry and Lions (1989). Finally, we provide numerical simulations of optimally controlled exchange rate processes and the corresponding evolution of the central bank inventory.

Market Impact: Evidence From the Brazil Stock Market

Market impact risk is a specific type of liquidity risk. It describes the risk of not being able to execute a trade at the currently quoted price because this trade feeds back in an unfavorable manner on the underlying price. This makes market impact modeling a fascinating and active research agenda from a mathematical point of view. Moreover, market impact models are often used in practical applications and it would be desirable to gain a better understanding of their behavior and their stability. Supported by the international empirical evidence, the continuous-time version of the propagator model, discussed by Gatheral (2010), is applied to Brazil stock market. The main finding, based on the False Discovery Rate (FDR), support the adoption of the square-root law of price impact.

Introducing stylized facts on electricity futures through a market impact model

This paper provides an alternative way to introduce the stylized facts on electricity futures. For nonstorable commodities, forward-looking information is not necessarily incorporated in the price history. In contrast to contemporary electricity finance models, we introduce a mechanism based on the trading behavior of market participants and their corresponding market impact by exploiting characteristic initial positions and quantity risk considerations. For long times to maturity we end up with a market influenced by hedging pressure, whereas for short times to maturity quantity risk comes into play and yields an increased volatility. In addition, prices can also be negative. The model is accompanied by an empirical analysis showing that parameters that are typically only relevant on small timescales have a significant dynamic in daily returns over a period of years. This allows us to access the toolbox usually reserved for high-frequency modeling.

A Central Bank Strategy for Defending a Currency Target Zone

We consider a central bank strategy for maintaining a two-sided currency target zone, in which an exchange rate of two currencies is forced to stay between two thresholds. To keep the exchange rate from breaking the prescribed barriers, the central bank is generating permanent price impact and thereby accumulating inventory in the foreign currency. Historical examples of failed target zones illustrate that this inventory can become problematic, in particular when there is an adverse macroeconomic trend in the market. We model this situation through a continuous-time market impact model of Almgren– Chriss-type with drift, in which the exchange rate is a diffusion process controlled by the price impact of the central bank’s intervention strategy. The objective of the central bank is to enforce the target zone through a strategy that minimizes the accumulated inventory. We formulate this objective as a stochastic control problem with random time horizon. It is solved by reduction to a singular boundary value problem that was solved by Lasry and Lions (1989). Finally, we provide numerical simulations of optimally controlled exchange rate processes and the corresponding evolution of the central bank inventory.

Volume-weighted average price tracking: A theoretical and empirical study

The Volume-Weighted Average Price (VWAP) of a security is a key measure of execution quality for large orders often used by institutional investors. We propose a VWAP tracking model with general price and volume dynamics and transaction costs. We find the theoretically optimal VWAP tracking strategy in several special cases. With these solutions we investigate three questions empirically. Do dynamic strategies outperform static strategies? How important is the choice of the market impact model? Does capturing the relationship between trading volume and the variance of stock price returns play an important role in optimal VWAP execution? We find that static strategies are preferable to dynamic ones, that simpler market impact models that assume either constant or linear market impact, perform as well as more sophisticated, nonlinear, market impact models, and that capturing the relationship between trading volume and the variance of stock price returns improves the performance of VWAP execution significantly.

“Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons

We propose a simple non-equilibrium model of a financial market as an open system with a possible exchange of money with an outside world and market frictions (trade impacts) incorporated into asset price dynamics via a feedback mechanism. Using a linear market impact model, this produces a non-linear two-parametric extension of the classical Geometric Brownian Motion (GBM) model, that we call the “Quantum Equilibrium-Disequilibrium” (QED) model.The QED model incorporates non-linear mean-reverting dynamics, broken scale invariance, and corporate defaults. In the simplest one-stock (1D) formulation, our parsimonious model has only one degree of freedom, yet calibrates to both equity returns and credit default swap spreads. Defaults and market crashes are associated with dissipative tunneling events, and correspond to instanton (saddle-point) solutions of the model. When market frictions and inflows/outflows of money are neglected altogether, “classical” GBM scale-invariant dynamics with an exponential asset growth and without defaults are formally recovered from the QED dynamics. However, we argue that this is only a formal mathematical limit, and in reality the GBM limit is non-analytic due to non-linear effects that produce both defaults and divergence of perturbation theory in a small market friction parameter.

COMMENTARY: Beyond the Black Box Revisited: Algorithmic Trading and TCA Analysis Using Excel

In this paper we revisit techniques from “Creating Dynamic Pre-Trade Models: Beyond the Black Box” (Kissell, 2011) which was awarded The Journal of Trading’s Best Paper of the Year Award in 2011. We provide investors a pre-trade of pre-trade modeling technique that can be used to decipher broker and vendor models, and to calibrate a customized investor specific market impact model. We also provide a suite of Excel TCA Add-In functions that can incorporate investor specific market impact parameters and allow investors to perform TCA analysis on their own desktops within Excel, and with the added level of security and comfort that their investment decision process will not be reverse engineered because they do not need to upload or transmit any of their proprietary information and valuable trade information to a third-party website or API for analysis. Techniques in this paper enable investors to create their own customized TCA analyses within Excel to assist with both trading decisions and portfolio analysis and optimization.

A Stackelberg Order Execution Game

We study a sequential order execution differential game over a finite time horizon in the Stackelberg duopoly framework, in contrast to the simultaneous Nash game investigated by Carlin et al (2007). In our game, there are two players, one leader and one follower, who maximize their expected trading payoffs respectively by trading a single risky asset whose price dynamics follows the linear-price market impact model of Almgren & Chriss (2001). We derive a closed-form solution for the unique open-loop Stackelberg equilibrium. We then develop new and complementary managerial insights by looking at both players' equilibrium behavior in terms of trading speeds, inventory positions, price dynamics, and first mover's advantage. We also quantify different behavioral metrics of the same players under our sequential game and the aforementioned simultaneous Nash game of Carlin et al (2007).

Beyond th Black Box Revisited: Algorithmic Trading and TCA Analysis using Excel

In this paper we revisit techniques from Creating Dynamic Pre-Trade Models: Beyond the Black Box (Kissell, 2011) which was awarded the Journal of Trading's Best Paper of the Year Award in 2011. We provide investors a pre-trade of pre-trade modeling technique that can be used to decipher broker and vendor models, and can be used to calibrate a customized investor specific market impact model. We also provide a suite of Excel TCA Add-In functions that can incorporate investor specific market impact parameters and allow investors to perform TCA analysis on their own desktops within Excel, and with the added level of security and comfort that their investment decision process will not be reverse engineered because they do not need to upload or transmit any of their proprietary information and valuable trade information to a third-party website or API for analysis. Techniques in this paper enable investors to create their own customized TCA analyses within Excel to assist with both trading decisions and portfolio analysis and optimization.

A Market Impact Game Under Transient Price Impact

We consider a Nash equilibrium between two high-frequency traders (HFTs) in a simple market impact model with transient price impact and additional quadratic transaction costs. We prove existence a...

'Quantum Equilibrium-Disequilibrium': Asset Price Dynamics, Symmetry Breaking, and Defaults as Dissipative Instantons

We propose a simple non-equilibrium model of a financial market as an open system with a possible exchange of money with an outside world and market frictions (trade impacts) incorporated into asset price dynamics via a feedback mechanism. Using a linear market impact model, this produces a non-linear two-parametric extension of the classical Geometric Brownian Motion (GBM) model, that we call the ”Quantum Equilibrium-Disequilibrium” (QED) model. The QED model gives rise to non-linear mean-reverting dynamics, broken scale invariance, and corporate defaults. In the simplest one-stock (1D) formulation, our parsimonious model has only one degree of freedom, yet calibrates to both equity returns and credit default swap spreads. Defaults and market crashes are associated with dissipative tunneling events, and correspond to instanton (saddle-point) solutions of the model. When market frictions and inflows/outflows of money are neglected altogether, ”classical” GBM scale-invariant dynamics with an exponential asset growth and without defaults are formally recovered from the QED dynamics. However, we argue that this is only a formal mathematical limit, and in reality the GBM limit is non- analytic due to non-linear effects that produce both defaults and divergence of perturbation theory in a small market friction parameter.