Handbook of Price Impact Modeling

© 2023, Chapman & Hall/CRC

Price impact—the adverse effect large trades have on execution prices—is a key concern for the design and implementation of systematic trading strategies. Indeed, impact is the major source of ‘slippage’ for sizable funds and, if not accounted for in an appropriate manner, quickly turns strategies that appear to be profitable in paper trading into losing ones. As a consequence, understanding the nature of price impact and its consequences for optimal trading are central practical problems.

Kevin Webster has written a remarkable textbook that studies these problems in a uniquely comprehensive manner. To wit, he covers theory, empirics, and implementation by bringing together insights developed in a number of different research communities, ranging from Industry Practitioners, Financial Economists, Econophysicists, to Applied Mathematicians. In doing so, Kevin develops the underlying theory in a very accessible manner. He also presents important practical applications beyond optimal trading (such as risk management), which showcase that a good grasp of the mechanics of price impact is an essential part of any modern financial engineer's toolkit.

Let me now describe the contents of the handbook in some more detail. The theory part of the book (‘Acting on Price Impact ’) introduces the model of Obizhaeva and Wang (2013) as a concrete example for a parsimonious yet flexible price impact model. Using an observation of Fruth et al. (2013), it is shown how optimal trading problems in this context can be solved without appealing to sophisticated techniques such as stochastic control.¹ Indeed, after switching control variables from positions held to the corresponding impact caused, many (risk-neutral) trading problems become simple pointwise maximizations that can be solved directly. In the handbook, the powerful implications of this approach are explored by bringing it to bear on important extensions of the baseline model such as general alpha signals, stochastic liquidity parameters, or nonlinear impact functions. Remarkably, all these advanced features remain straightforward to study and their effects remain easy to interpret when studied in ‘impact space’. Whence, the handbook opens the door to teaching these advanced concepts in a self-contained manner in an MSc-level course.

Another important contribution of the chapter ‘Acting on Price Impact’ is to showcase a number of situations where price impact plays a key role beyond the optimal execution and optimal trading problems that have taken center stage in most academic literature. These range from transaction cost analysis (TCA), alpha research based on external flows, to risk management accounting for liquidity risk.

The empirical part of the handbook (‘Measuring Price Impact ’) then delves into how to estimate price impact from price and trade data. This leads to subtle identification problems, for example, most trading strategies are based on price predictions, so if a strategy buys and the price rises it is crucially important to disentangle whether the strategy indeed successfully predicted an exogenous price change, or whether the price just went up mechanically due to price impact. The handbook proposes to study problems of thus kind through the lens of causal inference. This has become increasingly important in machine learning, but is still an emerging tool in financial applications.² The handbook presents the basic formalism and elements of the corresponding ‘do-calculus’ in a self-contained manner. The general concepts and tools are then applied to a range of live trading experiments that can be run to identify causal relationships.

Equipped with this toolbox, the handbook then presents a detailed empirical analysis of the price impact models studied in the theoretical part of the book. This analysis is based on high-frequency limit-order book data from the LOBSTER database and stands out for fitting and comparing a range of different models on the same dataset. This includes nonlinear impact functions, time-dependent parameters (such as time-of-day effects), as well as universal models across several stocks. The toolbox developed here again is accessible enough to be taught in an MSc-level course, yet nevertheless encompasses many of the key features needed to make models competitive in practice.

Finally, in the appendix, the handbook also contains an implementation part (‘Using Kdb+ for Trading Models ’) that outlines how Kdb+ can be used to implement trading models. This part covers the competitive advantages that make Kdb+ widely used by quantitative researchers and traders. It then presents a concise introduction of the main concepts, illustrated by the implementation of the Obizhaeva–Wang price impact model.

In summary, this is a fantastic book that provides new insights for a number of different audiences. For practitioners, it provides a consistent and systematic overview of modeling, analysis and inference in this context. For academics, it contains a wealth of practical insights and problems that are rarely discussed in the academic literature.³ For students in quantitative MSc programs, the handbook is a comprehensive yet very accessible introduction to price impact modeling and its applications, which the author has used for very popular MSc courses at Columbia University of New York and Imperial College London.

Additional information

Notes on contributors

Johannes Muhle-Karbe

Johannes Muhle-Karbe is the Head of the Mathematical Finance Section at Imperial College London.

Notes

1 Stochastic control approaches to price impact models are covered in detail by Cartea et al. (2015) as well as Guéant (2016).

2 De-Prado (2023) discusses the challenges of causal inference in the context of factor investing.

3 Isichenko (2021) is another notable reference in this spirit.