The Financial Mathematics of Market Liquidity

From Optimal Execution to Market Making
Author: Olivier Gueant
Publisher: CRC Press
ISBN: 1498725481
Category: Business & Economics
Page: 278
View: 9243

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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.

High-Performance Computing in Finance

Problems, Methods, and Solutions
Author: M. A. H. Dempster,Juho Kanniainen,John Keane,Erik Vynckier
Publisher: CRC Press
ISBN: 1315354691
Category: Computers
Page: 614
View: 380

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High-Performance Computing (HPC) delivers higher computational performance to solve problems in science, engineering and finance. There are various HPC resources available for different needs, ranging from cloud computing– that can be used without much expertise and expense – to more tailored hardware, such as Field-Programmable Gate Arrays (FPGAs) or D-Wave’s quantum computer systems. High-Performance Computing in Finance is the first book that provides a state-of-the-art introduction to HPC for finance, capturing both academically and practically relevant problems.

C++ for Financial Mathematics

Author: John Armstrong
Publisher: CRC Press
ISBN: 1498750060
Category: Business & Economics
Page: 410
View: 6276

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If you know a little bit about financial mathematics but don’t yet know a lot about programming, then C++ for Financial Mathematics is for you. C++ is an essential skill for many jobs in quantitative finance, but learning it can be a daunting prospect. This book gathers together everything you need to know to price derivatives in C++ without unnecessary complexities or technicalities. It leads the reader step-by-step from programming novice to writing a sophisticated and flexible financial mathematics library. At every step, each new idea is motivated and illustrated with concrete financial examples. As employers understand, there is more to programming than knowing a computer language. As well as covering the core language features of C++, this book teaches the skills needed to write truly high quality software. These include topics such as unit tests, debugging, design patterns and data structures. The book teaches everything you need to know to solve realistic financial problems in C++. It can be used for self-study or as a textbook for an advanced undergraduate or master’s level course.

Market Microstructure In Practice (Second Edition)

Author: Laruelle Sophie,Lehalle Charles-albert
Publisher: World Scientific
ISBN: 9813231149
Category: Business & Economics
Page: 368
View: 512

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This book exposes and comments on the consequences of Reg NMS and MiFID on market microstructure. It covers changes in market design, electronic trading, and investor and trader behaviors. The emergence of high frequency trading and critical events like the"Flash Crash" of 2010 are also analyzed in depth. Using a quantitative viewpoint, this book explains how an attrition of liquidity and regulatory changes can impact the whole microstructure of financial markets. A mathematical Appendix details the quantitative tools and indicators used through the book, allowing the reader to go further independently. This book is written by practitioners and theoretical experts and covers practical aspects (like the optimal infrastructure needed to trade electronically in modern markets) and abstract analyses (like the use on entropy measurements to understand the progress of market fragmentation). As market microstructure is a recent academic field, students will benefit from the book's overview of the current state of microstructure and will use the Appendix to understand important methodologies. Policy makers and regulators will use this book to access theoretical analyses on real cases. For readers who are practitioners, this book delivers data analysis and basic processes like the designs of Smart Order Routing and trade scheduling algorithms. In this second edition, the authors have added a large section on orderbook dynamics, showing how liquidity can predict future price moves, and how High Frequency Traders can profit from it. The section on market impact has also been updated to show how buying or selling pressure moves prices not only for a few hours, but even for days, and how prices relax (or not) after a period of intense pressure. Further, this edition includes pages on Dark Pools, Circuit Breakers and added information outside of Equity Trading, because MiFID 2 is likely to push fixed income markets towards more electronification. The authors explore what is to be expected from this change in microstructure. The appendix has also been augmented to include the propagator models (for intraday price impact), a simple version of Kyle's model (1985) for daily market impact, and a more sophisticated optimal trading framework, to support the design of trading algorithms. Contents: Monitoring the Fragmentation at Any ScaleUnderstanding the Stakes and the Roots of FragmentationOptimal Organizations for Optimal TradingAppendix A: Quantitative AppendixAppendix B: Glossary Readership: Graduate and research students of financial markets and quantitative finance, Regulators and policy makers, practitioners. Keywords: Market Microstructure;Finance;Financial Markets;Market Liquidity;Financial Regulation;MiFID;Reg NMS;ESMAReview: Reviews of the First Edition: “Lehalle and Laruelle bring [their] experience to bear on every aspect of the discussion, as well as deep quantitative understanding. The resulting book is a unique mixture of real market knowledge and theoretical explanation. There is nothing else out there like it, and this book will be a central resource for many different market participants.” Robert Almgren President and Cofounder of Quantitative Brokers, New York “Charles' and Sophie's book on markets microstructure will improve our knowledge and consequently help us to tweak these potentiometers. In promoting better education, this book is at the roots of restoring trust in the markets.” Philippe Guillot Executive Director, Markets Directorate Autorité des marchés financiers (AMF), Paris “This book pro

Model-free Hedging

A Martingale Optimal Transport Viewpoint
Author: Pierre Henry-Labordere
Publisher: CRC Press
ISBN: 1351666231
Category: Mathematics
Page: 204
View: 7987

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Model-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.

Financial Modelling with Jump Processes

Author: Peter Tankov
Publisher: CRC Press
ISBN: 1135437947
Category: Mathematics
Page: 552
View: 3199

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WINNER of a Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Lévy processes are beyond their reach. Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by their use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations. Topics covered in this book include: jump-diffusion models, Lévy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms. This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.

Nonlinear Option Pricing

Author: Julien Guyon,Pierre Henry-Labordere
Publisher: CRC Press
ISBN: 1466570342
Category: Business & Economics
Page: 484
View: 6787

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New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.

Analysis, Geometry, and Modeling in Finance

Advanced Methods in Option Pricing
Author: Pierre Henry-Labordère
Publisher: CRC Press
ISBN: 9781420087000
Category: Mathematics
Page: 391
View: 8106

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Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available. Through the problem of option pricing, the author introduces powerful tools and methods, including differential geometry, spectral decomposition, and supersymmetry, and applies these methods to practical problems in finance. He mainly focuses on the calibration and dynamics of implied volatility, which is commonly called smile. The book covers the Black–Scholes, local volatility, and stochastic volatility models, along with the Kolmogorov, Schrödinger, and Bellman–Hamilton–Jacobi equations. Providing both theoretical and numerical results throughout, this book offers new ways of solving financial problems using techniques found in physics and mathematics.

Stochastic Volatility Modeling

Author: Lorenzo Bergomi
Publisher: CRC Press
ISBN: 1482244071
Category: Business & Economics
Page: 506
View: 973

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Packed with insights, Lorenzo Bergomi’s Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including: Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does calibration make sense? This manual covers the practicalities of modeling local volatility, stochastic volatility, local-stochastic volatility, and multi-asset stochastic volatility. In the course of this exploration, the author, Risk’s 2009 Quant of the Year and a leading contributor to volatility modeling, draws on his experience as head quant in Société Générale’s equity derivatives division. Clear and straightforward, the book takes readers through various modeling challenges, all originating in actual trading/hedging issues, with a focus on the practical consequences of modeling choices.

Trades, Quotes and Prices

Financial Markets Under the Microscope
Author: Jean-Philippe Bouchaud,Julius Bonart,Jonathan Donier,Martin Gould
Publisher: Cambridge University Press
ISBN: 1108639062
Category: Science
Page: N.A
View: 1233

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The widespread availability of high-quality, high-frequency data has revolutionised the study of financial markets. By describing not only asset prices, but also market participants' actions and interactions, this wealth of information offers a new window into the inner workings of the financial ecosystem. In this original text, the authors discuss empirical facts of financial markets and introduce a wide range of models, from the micro-scale mechanics of individual order arrivals to the emergent, macro-scale issues of market stability. Throughout this journey, data is king. All discussions are firmly rooted in the empirical behaviour of real stocks, and all models are calibrated and evaluated using recent data from Nasdaq. By confronting theory with empirical facts, this book for practitioners, researchers and advanced students provides a fresh, new, and often surprising perspective on topics as diverse as optimal trading, price impact, the fragile nature of liquidity, and even the reasons why people trade at all.

Market Microstructure

Confronting Many Viewpoints
Author: Frédéric Abergel,Jean-Philippe Bouchaud,Thierry Foucault,Charles-Albert Lehalle,Mathieu Rosenbaum
Publisher: John Wiley & Sons
ISBN: 1119952786
Category: Business & Economics
Page: 416
View: 1470

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The latest cutting-edge research on market microstructure Based on the December 2010 conference on market microstructure, organized with the help of the Institut Louis Bachelier, this guide brings together the leading thinkers to discuss this important field of modern finance. It provides readers with vital insight on the origin of the well-known anomalous "stylized facts" in financial prices series, namely heavy tails, volatility, and clustering, and illustrates their impact on the organization of markets, execution costs, price impact, organization liquidity in electronic markets, and other issues raised by high-frequency trading. World-class contributors cover topics including analysis of high-frequency data, statistics of high-frequency data, market impact, and optimal trading. This is a must-have guide for practitioners and academics in quantitative finance.

Algorithmic and High-Frequency Trading

Author: Álvaro Cartea,Sebastian Jaimungal,José Penalva
Publisher: Cambridge University Press
ISBN: 1316453650
Category: Mathematics
Page: N.A
View: 8171

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The design of trading algorithms requires sophisticated mathematical models backed up by reliable data. In this textbook, the authors develop models for algorithmic trading in contexts such as executing large orders, market making, targeting VWAP and other schedules, trading pairs or collection of assets, and executing in dark pools. These models are grounded on how the exchanges work, whether the algorithm is trading with better informed traders (adverse selection), and the type of information available to market participants at both ultra-high and low frequency. Algorithmic and High-Frequency Trading is the first book that combines sophisticated mathematical modelling, empirical facts and financial economics, taking the reader from basic ideas to cutting-edge research and practice. If you need to understand how modern electronic markets operate, what information provides a trading edge, and how other market participants may affect the profitability of the algorithms, then this is the book for you.

Optimal Mean Reversion Trading

Mathematical Analysis and Practical Applications
Author: Tim Leung (Professor of industrial engineering),X. I. N. LI
Publisher: World Scientific
ISBN: 9814725927
Category: Business & Economics
Page: 220
View: 3319

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"Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives. This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature. This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments."--

Handbook of High Frequency Trading

Author: Greg N. Gregoriou
Publisher: Academic Press
ISBN: 0128023627
Category: Business & Economics
Page: 494
View: 7796

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This comprehensive examination of high frequency trading looks beyond mathematical models, which are the subject of most HFT books, to the mechanics of the marketplace. In 25 chapters, researchers probe the intricate nature of high frequency market dynamics, market structure, back-office processes, and regulation. They look deeply into computing infrastructure, describing data sources, formats, and required processing rates as well as software architecture and current technologies. They also create contexts, explaining the historical rise of automated trading systems, corresponding technological advances in hardware and software, and the evolution of the trading landscape. Developed for students and professionals who want more than discussions on the econometrics of the modelling process, The Handbook of High Frequency Trading explains the entirety of this controversial trading strategy. Answers all questions about high frequency trading without being limited to mathematical modelling Illuminates market dynamics, processes, and regulations Explains how high frequency trading evolved and predicts its future developments

High Frequency Trading and Limit Order Book Dynamics

Author: Ingmar Nolte,Mark Salmon,Chris Adcock
Publisher: Routledge
ISBN: 1317570766
Category: Business & Economics
Page: 320
View: 4887

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This book brings together the latest research in the areas of market microstructure and high-frequency finance along with new econometric methods to address critical practical issues in these areas of research. Thirteen chapters, each of which makes a valuable and significant contribution to the existing literature have been brought together, spanning a wide range of topics including information asymmetry and the information content in limit order books, high-frequency return distribution models, multivariate volatility forecasting, analysis of individual trading behaviour, the analysis of liquidity, price discovery across markets, market microstructure models and the information content of order flow. These issues are central both to the rapidly expanding practice of high frequency trading in financial markets and to the further development of the academic literature in this area. The volume will therefore be of immediate interest to practitioners and academics. This book was originally published as a special issue of European Journal of Finance.

Quantitative Trading

Algorithms, Analytics, Data, Models, Optimization
Author: Xin Guo,Tze Leung Lai,Howard Shek,Samuel Po-Shing Wong
Publisher: CRC Press
ISBN: 1315354357
Category: Business & Economics
Page: 379
View: 3415

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The first part of this book discusses institutions and mechanisms of algorithmic trading, market microstructure, high-frequency data and stylized facts, time and event aggregation, order book dynamics, trading strategies and algorithms, transaction costs, market impact and execution strategies, risk analysis, and management. The second part covers market impact models, network models, multi-asset trading, machine learning techniques, and nonlinear filtering. The third part discusses electronic market making, liquidity, systemic risk, recent developments and debates on the subject.

The Microstructure Approach to Exchange Rates

Author: Richard K. Lyons
Publisher: Mit Press
Category: Business & Economics
Page: 333
View: 6245

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Explaining the puzzling behavior of exchange rates using models from microstructure finance and data from electronic trading.

Quantitative Trading with R

Understanding Mathematical and Computational Tools from a Quant’s Perspective
Author: Harry Georgakopoulos
Publisher: Springer
ISBN: 1137437472
Category: Business & Economics
Page: 272
View: 5432

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Quantitative Finance with R offers a winning strategy for devising expertly-crafted and workable trading models using the R open source programming language, providing readers with a step-by-step approach to understanding complex quantitative finance problems and building functional computer code.

Computational Methods in Finance

Author: Ali Hirsa
Publisher: CRC Press
ISBN: 1466576049
Category: Business & Economics
Page: 444
View: 1039

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As today’s financial products have become more complex, quantitative analysts, financial engineers, and others in the financial industry now require robust techniques for numerical analysis. Covering advanced quantitative techniques, Computational Methods in Finance explains how to solve complex functional equations through numerical methods. The first part of the book describes pricing methods for numerous derivatives under a variety of models. The book reviews common processes for modeling assets in different markets. It then examines many computational approaches for pricing derivatives. These include transform techniques, such as the fast Fourier transform, the fractional fast Fourier transform, the Fourier-cosine method, and saddlepoint method; the finite difference method for solving PDEs in the diffusion framework and PIDEs in the pure jump framework; and Monte Carlo simulation. The next part focuses on essential steps in real-world derivative pricing. The author discusses how to calibrate model parameters so that model prices are compatible with market prices. He also covers various filtering techniques and their implementations and gives examples of filtering and parameter estimation. Developed from the author’s courses at Columbia University and the Courant Institute of New York University, this self-contained text is designed for graduate students in financial engineering and mathematical finance as well as practitioners in the financial industry. It will help readers accurately price a vast array of derivatives.

Market Risk and Financial Markets Modeling

Author: Didier Sornette,Sergey Ivliev,Hilary Woodard
Publisher: Springer Science & Business Media
ISBN: 3642279317
Category: Business & Economics
Page: 268
View: 7891

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The current financial crisis has revealed serious flaws in models, measures and, potentially, theories, that failed to provide forward-looking expectations for upcoming losses originated from market risks. The Proceedings of the Perm Winter School 2011 propose insights on many key issues and advances in financial markets modeling and risk measurement aiming to bridge the gap. The key addressed topics include: hierarchical and ultrametric models of financial crashes, dynamic hedging, arbitrage free modeling the term structure of interest rates, agent based modeling of order flow, asset pricing in a fractional market, hedge funds performance and many more.