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The Financial Mathematics of Market Liquidity

From Optimal Execution to Market Making

Olivier Gueant (Universite Paris Diderot, France)

$158.00

Hardback

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Productivity Press
01 April 2016
Investment & securities; Mathematical modelling
This book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problems-inspired from the Almgren-Chriss approach-and then demonstrates the use of that framework across a wide range of areas.

The book introduces the classical tools of optimal execution and market making, along with their practical use. It also demonstrates how the tools used in the optimal execution literature can be used to solve classical and new issues where accounting for liquidity is important. In particular, it presents cutting-edge research on the pricing of block trades, the pricing and hedging of options when liquidity matters, and the management of complex share buy-back contracts.

What sets this book apart from others is that it focuses on specific topics that are rarely, or only briefly, tackled in books dealing with market microstructure. It goes far beyond existing books in terms of mathematical modeling-bridging the gap between optimal execution and other fields of Quantitative Finance.

The book includes two appendices dedicated to the mathematical notions used throughout the book. Appendix A recalls classical concepts of mathematical economics. Appendix B recalls classical tools of convex analysis and optimization, along with central ideas and results of the calculus of variations.

This self-contained book is accessible to anyone with a minimal background in mathematical analysis, dynamic optimization, and stochastic calculus. Covering post-electronification financial markets and liquidity issues for pricing, this book is an ideal resource to help investment banks and asset managers optimize trading strategies and improve overall risk management.
By:   Olivier Gueant (Universite Paris Diderot France)
Imprint:   Productivity Press
Country of Publication:   United States
Volume:   33
Dimensions:   Height: 235mm,  Width: 156mm,  Spine: 20mm
Weight:   567g
ISBN:   9781498725477
ISBN 10:   1498725473
Series:   Chapman & Hall/CRC Financial Mathematics Series
Pages:   278
Publication Date:   01 April 2016
Audience:   College/higher education ,  Professional and scholarly ,  Professional and scholarly ,  Primary ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
I: INTRODUCTION General Introduction A Brief History of Quantitative Finance Optimal Execution and Market Making in the Extended Market Microstructure Literature Conclusion Organization of Markets Introduction Stock Markets Bond Markets Conclusion II: OPTIMAL LIQUIDATION The Almgren-Chriss Framework Introduction A Generalized Almgren-Chriss Model in Continuous Time The Model in Discrete Time Conclusion Optimal Liquidation with Different Benchmarks Introduction: the Different Types of Orders Target Close Orders POV Orders VWAP Orders Conclusion Extensions of the Almgren-Chriss Framework A More Complex Price Dynamics Adding Participation Constraints Portfolio Liquidation Conclusion Numerical Methods The Case of Single-Stock Portfolios The Case of Multi-Asset Portfolios Conclusion Beyond Almgren-Chriss Overview of the Literature Optimal Execution Models in Practice Conclusion III: LIQUIDITY IN PRICING MODELS Block Trade Pricing Introduction General Definition of Block Trade Prices and Risk-Liquidity Premium The Specific Case of Single-Stock Portfolios A Simpler Case with POV Liquidation Guaranteed VWAP Contracts Conclusion Option Pricing and Hedging with Execution Costs and Market Impact Introduction The Model in Continuous Time The Model in Discrete Time Numerical Examples Conclusion Share Buy-Back Introduction The Model Optimal Management of an ASR Contract Numerical Methods and Examples Conclusion IV: MARKET MAKING Market Making: From Avellaneda-Stoikov to Gueant-Lehalle, and Beyond Introduction The Avellaneda-Stoikov Model Generalization of the Avellaneda-Stoikov Model Market Making on Stock Markets Conclusion Appendices: Mathematical Economics The Expected Utility Theory Utility Functions and Risk Aversion Certainty Equivalent and Indifference Pricing Convex Analysis and Variational Calculus Basic Notions of Convex Analysis Calculus of Variation

Olivier Gueant is Professor of Quantitative Finance at Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE), where he teaches many aspects of financial mathematics-from classical asset pricing to advanced option pricing theory, to new topics about execution, market making, and high-frequency trading. Before joining ENSAE, Olivier was Associate Professor of Applied Mathematics at Universite Paris-Diderot, where he taught applied mathematics and financial mathematics to both undergraduate and graduate students. He joined Universite Paris-Diderot after finishing his PhD on mean field games, under the supervision of Pierre-Louis Lions. He progressively moved to Quantitative Finance through the publication of research papers on optimal execution and market making. Olivier is also a renowned scientific and strategy consultant, who has taken on projects for many hedge funds, brokerage companies, and investment banks, including Credit Agricole, Kepler-Cheuvreux, BNP Paribas, and HSBC. His main current research interests include optimal execution, market making, and the use of big data methods in Finance.

Reviews for The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making

This excellent monograph covers the mathematical theory of market microstructure with particular emphasis in models of optimal execution and market making. Gueant's book is a superb introduction to these topics for graduate students in mathematical finance or quants who want to work in execution algorithms or market-making strategies. -Jose A. Scheinkman, Charles and Lynn Zhang Professor of Economics, Columbia University, and Theodore Wells '29 Professor of Economics Emeritus, Princeton University This is a very timely book that cuts across various fields (applied mathematics, operations research, and quantitative finance). Execution costs due to market illiquidity can significantly reduce returns on investment strategies and, for this reason, affect asset prices. It is therefore important to design trading strategies minimizing these costs and to account for their effect on prices. In the last decade, 'quants' and researchers in quantitative finance have made considerable progress on these issues, integrating in their models changes in the way financial markets work (e.g., the development of continuous limit order books, market fragmentation, dark pools, the automation of trading, etc.). Olivier Gueant's book takes stock of this effort by providing a rigorous and expert presentation of mathematical tools, models, and numerical methods developed in this area. I strongly recommend it for researchers and graduate students interested in how illiquidity costs affect trading strategies and should be accounted for in asset valuation problems. -Thierry Foucault, HEC Foundation Chair Professor of Finance, HEC, Paris This book is a must-have for quantitative analysts working at algorithmic trading desks. Olivier Gueant could have written a sophisticated book dedicated to cutting-edge research. He rather decided to put his talent at the service of a far more difficult task: deliver a clear view of modern algorithmic trading to strats or quants having decent scientific training. Scientists will find here all the needed keys to control the intraday risk of their trading models, improving their overall efficiency. Covering brokerage algorithms, market making, hedging, and share buyback techniques, this book is the definitive reference for algorithm builders. Moreover, Olivier links algorithmic trading with market microstructure during the first chapter of the book, including interesting thoughts on corporate bonds trading. On the other hand, he provides a nice introduction to mathematical economics in the Appendix. This book is resolutely more than a bunch of equations thrown on blank pages. I consider it an important step forward in the building of the mathematics of market microstructure. -Charles-Albert Lehalle, Senior Research Advisor, Capital Fund Management


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