Handbook of Price Impact Modeling  book cover
1st Edition

Handbook of Price Impact Modeling

  • Available for pre-order on April 14, 2023. Item will ship after May 5, 2023
ISBN 9781032328225
May 5, 2023 Forthcoming by Chapman & Hall
434 Pages 118 B/W Illustrations

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Book Description

The Handbook of Price Impact Modeling provides practitioners and students with a mathematical framework grounded in academic references to apply price impact models to quantitative trading and portfolio management. Automated trading is now the dominant form of trading across all frequencies. Furthermore, trading algorithm rise introduces new questions professionals must answer, for instance:

  • How do stock prices react to a trading strategy?
  • How to scale a portfolio considering its trading costs and liquidity risk?
  • How to measure and improve trading algorithms while avoiding biases?

Price impact models answer these novel questions at the forefront of quantitative finance. Hence, practitioners and students can use this Handbook as a comprehensive, modern view of systematic trading.

For financial institutions, the Handbook’s framework aims to minimize the firm’s price impact, measure market liquidity risk, and provide a unified, succinct view of the firm’s trading activity to the C-suite via analytics and tactical research.

The Handbook’s focus on applications and everyday skillsets makes it an ideal textbook for a master’s in finance class and students joining quantitative trading desks. Using price impact models, the reader learns how to:

  • Build a market simulator to back test trading algorithms
  • Implement closed-form strategies that optimize trading signals
  • Measure liquidity risk and stress test portfolios for fire sales
  • Analyze algorithm performance controlling for common trading biases
  • Estimate price impact models using public trading tape

Finally, the reader finds a primer on the database kdb+ and its programming language q, which are standard tools for analyzing high-frequency trading data at banks and hedge funds.

Authored by a finance professional, this book is a valuable resource for quantitative researchers and traders.

Table of Contents


1 Introduction to Modeling Price Impact

1.1 The Scope of this Handbook

1.1.1 Introduction

1.1.2 What is Price Impact? Why do Traders care about it?

1.1.3 The Causality Challenge for Price Impact Models

1.1.4 Four Core Modeling Principles

1.1.5 A Brief History of Price Impact Models

1.2 Trading Terminology Used Throughout the Book

1.2.1 Trading Strategies

1.2.2 Trading Data: Fills, Orders and Binned Data

1.2.3 Trading Signals, Alpha Signals

1.2.4 Intended, Predicted and Realized Data

1.2.5 Basic Trading Parameters

1.2.6 Order Slippage, Arrival Price

1.2.7 Alpha Slippage, Slippage Due to Price Impact

1.2.8 Experiments: A-B Testing and Simulations

1.3 Outlining Applications for Various Roles

1.3.1 Transaction Cost Analysis (TCA) for Sell-Side Execution


1.3.2 Portfolio Optimization for Buy-Side Statistical Arbitrage


1.3.3 Liquidity Reports for Risk Management Teams

1.3.4 Portfolio Consolidation Analysis for Senior Management

1.4 Roadmap for the Book

1.4.1 What to Expect from the Book

1.4.2 A Brief Summary of each Chapter

2 Propagator Models for Price Impact

2.1 Mathematical Setup

2.1.1 Defining Price Impact and Instantaneous Transaction


2.1.2 Establishing P&L in Discrete Time

2.1.3 Examples of Microstructure Assumptions

2.1.4 Reduced Form Models

2.2 The Obizhaeva and Wang (OW) Propagator Model

2.2.1 An Optimal Execution Problem

2.2.2 Closed Form Optimal Trading Strategy

2.2.3 Intuition Behind the Optimal Trading Strategy

2.3 Extensions Related to the Objective Function

2.3.1 Alpha Signal

2.3.2 Two-Sided Trading

2.4 Extensions Related to Time

2.4.1 Time Change

2.4.2 Stochastic Push

2.4.3 Linear Propagator Models

2.5 Extensions Related to External Impact

2.5.1 Microstructure Assumptions

2.5.2 Optimal Trading Strategy with External Impact

2.5.3 Local Concavity

2.5.4 Global Concavity

2.6 Summary of Results

2.6.1 Generalized OW Impact Model

2.6.2 Generalized OW Impact Model with External Impact

2.6.3 Control Problems

2.7 Exercises

3 Applications of Price Impact Models

3.1 Optimal Execution

3.1.1 The Case of a Single Day Order

3.1.2 Adding Trading Alphas to Order Instructions

3.1.3 Comparing Orders Using Price Impact and Implied


3.2 Transaction Cost Analysis(TCA)

3.2.1 How to Run Trading Experiments

3.2.2 An Experiment for Automated Trading Systems

3.2.3 An Experiment to Measure Crowding

3.2.4 An Experiment to Evaluate High Touch Trading

3.3 Statistical Arbitrage

3.3.1 Using External Impact as an Alpha Signal

3.3.2 Adjusting Regression Techniques to Liquidity and Price


3.3.3 Using Price Impact for Simulation

3.4 Portfolio and Risk Management

3.4.1 How Price Impact Distorts Accounting P&L and Perceived


3.4.2 General Implications and Actions

3.4.3 Simulating "Fire Sales"

3.5 Combining the Trading Costs of Two Portfolios Together

3.5.1 Why One can’t just Add Up Trading Costs Linearly

3.5.2 Implications for Portfolio Management

3.6 Further Readings

3.7 Exercises

4 Dealing with Biases when Fitting Propagator Models

4.1 Why it Matters to Quants

4.2 A Simple Example: Alpha Bias in Trading Flow

4.2.1 Causality Map for Trading with Alpha

4.2.2 Bias Formula in the Presence of Alpha

4.2.3 Two Actions to Reduce Alpha Bias

4.3 Techniques to Detect and Reduce Biases

4.3.1 Detecting Model Inconsistencies

4.3.2 Selection Bias and Survivorship Bias

4.3.3 General Actions to Reduce Bias

4.4 An Advanced Example: Trading Passively

4.4.1 Causality Map for Passive Trading

4.4.2 Bias Formula for Passive Trading

4.4.3 Actions to Reduce Passive Trading Bias

4.5 Further Readings

4.6 Exercises

5 How to Build Actionable Propagator Models

5.1 Why it Matters to Quants

5.2 A List of Common Practical Pitfalls

5.2.1 Time of Day Effects

5.2.2 Local Concavity

5.2.3 Volume Surprises

5.3 How to Fix Time of Day Effects

5.3.1 Using an Extended OW Model

5.3.2 Using Time-Change

5.4 How to Fix Concavity

5.4.1 Using Local Concavity

5.4.2 Using Global Concavity

5.5 How to Allow Stochastic Pre-Factors

5.5.1 Using an Extended OW Model

5.5.2 Using Anticipative Models

5.6 Martingale Impact Condition

5.7 Further Readings

5.8 Exercises

6 Advanced Fitting Techniques for Propagator Models

6.1 Why it Matters to Quants

6.2 Bayesian Priors, Constraints and Regularization

6.2.1 A Quick Primer on Modified Loss Functions

6.2.2 A Simple Set of Priors and Constraints

6.3 Cofitting, Instrumental Variable Regression

6.3.1 Relationship to the Causality Map

6.3.2 Relationship to Bias-Reduction Actions

6.4 Natural Basis Functions for Non-Parametric Fitting

6.4.1 A Set of Basis Functions for the Time Kernel

6.4.2 A Set of Basis Functions for Concavity

6.5 Generalizing the Model Across a Large Universe of Stocks

6.5.1 How to Normalize Impact Models across Stocks

6.5.2 Cross-Stock Impact

6.6 Further Readings

6.7 Exercises

7 Advanced Optimization Techniques for Propagator Models

7.1 Why it Matters to Quants

7.2 Finding an Approximate Closed-Form Formula

7.2.1 Using an Extended OW Model

7.2.2 Implications for Backtesting Alpha Strategies

7.2.3 Implications for Fitting Propagator Models

7.3 Decoupling Fast and Slow Trading Strategies

7.3.1 The Case of Uncorrelated Strategies

7.3.2 The Case of Correlated Strategies

7.4 Optimizing with Cross-Stock Impact

7.4.1 Implications for Pairs Trading

7.4.2 Implications for Factor Risk-management

7.5 Further Readings

7.6 Exercises

A Using kdb+ for Trading Models

A.1 A Gentle Introduction to kdb+

A.1.1 What is kdb+ and Why Does It Matter to Quants?

A.1.2 First Steps in kdb+

A.1.3 Basic Operations in Q

A.1.4 Setting Up a Small Database

A.2 A Cheat-sheet for Quantitative Trading

A.2.1 "Data Wrangling" in kdb+

A.2.2 Long or Wide Format?

A.2.3 Vectorized Operations and Parallelism in kdb+

A.3 An Efficient Implementation of the Extended OW Model

A.3.1 Key Mathematical Idea

A.3.2 Key Algorithmic Idea

A.3.3 Computing Impact States

A.4 An Efficient Implementation of TCA

A.4.1 Key Algorithmic Idea

A.4.2 Computing TCA Returns

B A Refresher on Advanced Mathematics for Trading

B.1 Why it Matters to Quants

B.2 Basic Mathematical Notation Used Throughout the Book

B.2.1 Conditional Expectations

B.2.2 Stochastic Differential Equations (SDEs)

B.3 Linear Regression

B.3.1 Non-Parametric Models and Basis Functions

B.3.2 Relationship between Bayesian Priors and Regularization

B.4 Optimization Problems

B.4.1 Continuous-Time Setup for Proofs and Intuition

B.4.2 Discrete-Time Setup for Numerical Experiments

B.5 Jacod’s Functional Central Limit Theorem

B.5.1 Goal of the Technique

B.5.2 Detailed Examples

B.6 Further Readings

C Solutions to Exercises

C.1 Solutions to Chapter 2

C.2 Solutions to Chapter 3

C.3 Solutions to Chapter 4

C.4 Solutions to Chapter 5

C.5 Solutions to Chapter 6

C.6 Solutions to Chapter 7

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Dr. Kevin Webster graduated with a PhD from Princeton University Operations Research and Financial Engineering Department (ORFE). At ORFE, he studied mathematical models applied to high-frequency trading, emphasizing price impact, and market-making models. He previously worked at Deutsche Bank and Citadel and is currently a Visiting Assistant Professor (Visiting Reader) in the Department of Mathematics at Imperial College London.

Dr. Webster created and taught the course, ORF 474 High-Frequency Markets: Models and Data Analysis, as a Visiting Lecturer at Princeton in 2015. His publications include, The Self-Financing Equation in High Frequency Markets, Information and Inventories in High Frequency Trading, A Portfolio Manager's Guidebook to Trade Execution, and High Frequency Market Making.