Alexander Lipton

An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in random fields described by the Kolmogorov and Klein-Kramers equations, the Ornstein-Uhlenbeck and Feller processes, and their generalizations. They are reduced to affine differential and pseudo-differential equations and solved in a unified way by using Kelvin waves and developing a comprehensive math framework for calculating transition probabilities and expectations. Kelvin waves are instrumental for studying the well-known Black-Scholes, Heston, and Stein-Stein models and more complex path-dependent volatility models, as well as the pricing of Asian options, volatility and variance swaps, bonds, and bond options. Kelvin waves help to solve several cutting-edge problems, including hedging the impermanent loss of Automated Market Makers for cryptocurrency trading. This title is also available as Open Access on Cambridge Core.

An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in random fields described by the Kolmogorov and Klein-Kramers equations, the Ornstein-Uhlenbeck and Feller processes, and their generalizations. They are reduced to affine differential and pseudo-differential equations and solved in a unified way by using Kelvin waves and developing a comprehensive math framework for calculating transition probabilities and expectations. Kelvin waves are instrumental for studying the well-known Black-Scholes, Heston, and Stein-Stein models and more complex path-dependent volatility models, as well as the pricing of Asian options, volatility and variance swaps, bonds, and bond options. Kelvin waves help to solve several cutting-edge problems, including hedging the impermanent loss of Automated Market Makers for cryptocurrency trading. This title is also available as Open Access on Cambridge Core.

Get a detailed introduction to quantum computing and quantum machine learning, with a focus on finance-related applications Key Features Find out how quantum algorithms enhance financial modeling and decision-making Improve your knowledge of the variety of quantum machine learning and optimisation algorithms Look into practical near-term applications for tackling real-world financial challenges Purchase of the print or Kindle book includes a free PDF eBook Book DescriptionAs quantum machine learning (QML) continues to evolve, many professionals struggle to apply its powerful algorithms to real-world problems using noisy intermediate-scale quantum (NISQ) hardware. This book bridges that gap by focusing on hands-on QML applications tailored to NISQ systems, moving beyond the traditional textbook approaches that explore standard algorithms like Shor's and Grover's, which lie beyond current NISQ capabilities. You’ll get to grips with major QML algorithms that have been widely studied for their transformative potential in finance and learn hybrid quantum-classical computational protocols, the most effective way to leverage quantum and classical computing systems together. The authors, Antoine Jacquier, a distinguished researcher in quantum computing and stochastic analysis, and Oleksiy Kondratyev, a Quant of the Year awardee with over 20 years in quantitative finance, offer a hardware-agnostic perspective. They present a balanced view of both analog and digital quantum computers, delving into the fundamental characteristics of the algorithms while highlighting the practical limitations of today’s quantum hardware. By the end of this quantum book, you’ll have a deeper understanding of the significance of quantum computing in finance and the skills needed to apply QML to solve complex challenges, driving innovation in your work. What you will learn Familiarize yourself with analog and digital quantum computing principles and methods Explore solutions to NP-hard combinatorial optimisation problems using quantum annealers Build and train quantum neural networks for classification and market generation Discover how to leverage quantum feature maps for enhanced data representation Work with variational algorithms to optimise quantum processes Implement symmetric encryption techniques on a quantum computer Who this book is forThis book is for academic researchers, STEM students, finance professionals in quantitative finance, and AI/ML experts. No prior knowledge of quantum mechanics is needed. Mathematical concepts are rigorously presented, but the emphasis is on understanding the fundamental properties of models and algorithms, making them accessible to a broader audience. With its deep coverage of QML applications for solving real-world financial challenges, this guide is an essential resource for anyone interested in finance and quantum computing.

Learn the principles of quantum machine learning and how to apply themWhile focus is on financial use cases, all the methods and techniques are transferable to other fieldsPurchase of Print or Kindle includes a free eBook in PDFKey FeaturesDiscover how to solve optimisation problems on quantum computers that can provide a speedup edge over classical methodsUse methods of analogue and digital quantum computing to build powerful generative modelsCreate the latest algorithms that work on Noisy Intermediate-Scale Quantum (NISQ) computersBook DescriptionWith recent advances in quantum computing technology, we finally reached the era of Noisy Intermediate-Scale Quantum (NISQ) computing. NISQ-era quantum computers are powerful enough to test quantum computing algorithms and solve hard real-world problems faster than classical hardware.Speedup is so important in financial applications, ranging from analysing huge amounts of customer data to high frequency trading. This is where quantum computing can give you the edge. Quantum Machine Learning and Optimisation in Finance shows you how to create hybrid quantum-classical machine learning and optimisation models that can harness the power of NISQ hardware.This book will take you through the real-world productive applications of quantum computing. The book explores the main quantum computing algorithms implementable on existing NISQ devices and highlights a range of financial applications that can benefit from this new quantum computing paradigm.This book will help you be one of the first in the finance industry to use quantum machine learning models to solve classically hard real-world problems. We may have moved past the point of quantum computing supremacy, but our quest for establishing quantum computing advantage has just begun!What you will learnTrain parameterised quantum circuits as generative models that excel on NISQ hardwareSolve hard optimisation problemsApply quantum boosting to financial applicationsLearn how the variational quantum eigensolver and the quantum approximate optimisation algorithms workAnalyse the latest algorithms from quantum kernels to quantum semidefinite programmingApply quantum neural networks to credit approvalsWho this book is forThis book is for Quants and developers, data scientists, researchers, and students in quantitative finance. Although the focus is on financial use cases, all the methods and techniques are transferable to other areas.

This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability.We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.

This textbook focuses on distributed ledger technology (DLT) and its potential impact on society at large. It aims to offer a detailed and self-contained introduction to the founding principles behind DLT accessible to a well-educated but not necessarily mathematically oriented audience. DLT allows solving many complicated problems arising in economics, banking, and finance, industry, trade, and other fields. However, to reap the ultimate benefits, one has to overcome some of its inherent limitations and use it judiciously. Not surprisingly, amid increasing applications of DLT, misconceptions are formed over its use. The book thoroughly dispels these misconceptions via an impartial assessment of the arguments rooted in scientific reasoning.Blockchain and Distributed Ledgers: Mathematics, Technology, and Economics offers a detailed and self-contained introduction to DLT, blockchains, and cryptocurrencies and seeks to equip the reader with an ability to participate in the crypto economy meaningfully.

This textbook focuses on distributed ledger technology (DLT) and its potential impact on society at large. It aims to offer a detailed and self-contained introduction to the founding principles behind DLT accessible to a well-educated but not necessarily mathematically oriented audience. DLT allows solving many complicated problems arising in economics, banking, and finance, industry, trade, and other fields. However, to reap the ultimate benefits, one has to overcome some of its inherent limitations and use it judiciously. Not surprisingly, amid increasing applications of DLT, misconceptions are formed over its use. The book thoroughly dispels these misconceptions via an impartial assessment of the arguments rooted in scientific reasoning.Blockchain and Distributed Ledgers: Mathematics, Technology, and Economics offers a detailed and self-contained introduction to DLT, blockchains, and cryptocurrencies and seeks to equip the reader with an ability to participate in the crypto economy meaningfully.

'Alex Lipton is an absolutely remarkable person. Having joined the field of quantitative finance after a career where he became a world leader in the field of plasma and fusion physics, he has become rightly famous for his beautiful papers on many topics, from the volatility smile to money supply … He's marvellously practical; one is always introduced to the area with a bit of elegant prose and the papers, though very mathematical, never lose the thread of linguistic narrative which makes each one a story which has to be read to the end … Part 4 covers several topics centred around money supply and circulation, and in some ways this is the best part of the book … it's a lovely book and I really enjoyed reading it.'Quantitative FinanceEdited by Alexander Lipton (Quant of the Year, 2000), this volume is a collection of Lipton's important and original papers on financial engineering written over his 20-year career as a preeminent quant working for leading financial institutions in New York, Chicago, and London. The papers cover topics ranging from the volatility smile problem, credit risk, macroeconomics and monetary circuit, and exotic options, summarizing Lipton's fundamental contributions to these areas.In addition to papers published in leading academic and practitioner-oriented journals, this volume contains a detailed introduction and two previously unpublished chapters. Some of the seminal papers in this book cover local-stochastic volatility models, passport options, credit value adjustments for credit default swaps, and asymptotics for exponential Lévy processes and their volatility smile.Alexander Lipton is one of the most respected quants of his generation and the first recipient of the prestigious Quant of the Year award by Risk Magazine.

This comprehensive book presents a systematic and practically oriented approach to mathematical modeling in finance, particularly in the foreign exchange context. It describes all the relevant aspects of financial engineering, including derivative pricing, in detail. The book is self-contained, with the necessary mathematical, economic, and trading background carefully explained. In addition to the lucid treatment of the standard material, it describes many original results.The book can be used both as a text for students of financial engineering, and as a basic reference for risk managers, traders, and academics.

This comprehensive book presents a systematic and practically oriented approach to mathematical modeling in finance, particularly in the foreign exchange context. It describes all the relevant aspects of financial engineering, including derivative pricing, in detail. The book is self-contained, with the necessary mathematical, economic, and trading background carefully explained. In addition to the lucid treatment of the standard material, it describes many original results.The book can be used both as a text for students of financial engineering, and as a basic reference for risk managers, traders, and academics.