DOCSLIB.ORG

Exploring Quantum Computing Use Cases for Financial Services

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Exploring Quantum Computing Use Cases for Financial Services Expert Insights Exploring quantum computing use cases for financial services Experts on this topic Dr. Elena Yndurain Dr. Elena Yndurain leads financial services within the IBM Q consulting team. Elena advises IBM Q Industry Consultant – companies on defining their strategies to get ready Finance, for quantum computing, linking research to IBM Services business. Elena specializes in bringing to market www.yndurain.com solutions based on emerging technologies. She [email protected] is currently focused on quantum computing. Dr. Stefan Woerner Dr. Stefan Woerner is the global leader for quantum finance and optimization at IBM Research in Zurich. Global Leader, Quantum Finance Stefan’s research focuses on the development and and Optimization, analysis of quantum algorithms for optimization IBM Research and machine learning, as well as their practical https://www.linkedin.com/in/ applications, particularly in finance. stefan-woerner/ [email protected] Dr. Daniel J. Egger Dr. Daniel J. Egger is a research staff member in the Quantum Technologies group at IBM Research in Research Staff Member, Quantum Zurich. Daniel’s research focuses on the control of Finance and Optimization, quantum computers and on the practical IBM Research applications of quantum algorithms in finance. https://www.linkedin.com/in/ danieljegger/ [email protected] Contributors The authors thank Francis Lacan, financial markets innovation expert, for his contributions in developing this report. Classical computers limit the potential of machine-learning to solve specific financial services problems, whereas quantum computing promises higher quality solutions.”8 Financial services Talking points and quantum computing Quantum for speed and accuracy Financial services has a history of successfully applying Financial services institutions are exploring physics to help solve its thorniest problems. The Black- Scholes-Merton model, for example, uses the concept of quantum computing to enable calculations Brownian motion to price financial instruments – like that are not possible with traditional European call options – over time.1 computing technology. Applying emerging quantum technology to financial problems—particularly those dealing with uncertainty Experimental systems and constrained optimization—should also prove hugely advantageous for first movers. Imagine being able to Experimental quantum systems are make calculations that reveal dynamic arbitrage already being used to test and develop possibilities that competitors are unable to see. Beyond financial services use cases in such appli- that, greater compliance, employing behavioral data to enhance customer engagement, and faster reaction to cations as targeting and prediction, asset market volatility are some of the specific benefits we trading optimization, and risk profiling, expect quantum computing to deliver. three areas that have been shown to have What gives quantum computing this enormous advantage? the highest potential. The solution space of a quantum computer is orders of magnitude larger than traditional computers—even immensely powerful ones. That’s because doubling the The time is now power of a classical computer requires about double the Engaging now is important, as financial number of transistors working on a problem. The power of a quantum computer can be approximately doubled each institutions that adopt quantum computing time only one qubit is added. early will be able to take advantage of arbitrage potential that is impossible for While broad commercial applications may remain several years away, quantum computing is expected to those who remain solely on traditional produce breakthrough products and services likely to computing. successfully solve very specific business problems within three-to-five years.2 1 Bits and qubits Quantum computing can also enable financial services organizations to re-engineer operational processes, such as: Quantum computers leverage quantum mechanical phenomena to manipulate information, by relying on – Front-office and back-office decisions on client quantum bits, or Qubits. This emerging technology management for “know your customer,” credit computes more efficiently when generating probability origination, and onboarding, distributions, mapping data, testing samples, and iter- – Treasury management, trading and asset management, ating. Quantum computing provides exponential power to mathematically challenging problems, improving – Business optimization, including risk management and accuracy, shortening computation runtimes, and tackling compliance. previously impenetrable calculations. Powerful quantum use cases Quantum computing’s specific use cases for financial services can be classified into three main categories: targeting and prediction, trading optimization, and risk profiling (see Figure 1). We explore potential use cases in each of these categories, providing examples that apply to three main industries in financial services: banking, financial markets, and insurance. Figure 1 Expected quantum computing use cases in financial services Targeting and prediction Trading optimization Risk profiling 2 Because combinatorial optimization problems in trading and portfolio management scale exponentially, quantum computers have the potential to find faster, more cost-effective and better-tailored solutions than classical machines.13 Targeting and prediction Trading optimization Today’s financial services customers demand Complexity in financial markets trading activity is personalized products and services that rapidly anticipate skyrocketing. For example, the valuation adjustments their evolving needs and behaviors. Twenty-five percent of model for derivatives, the XVA umbrella, has greatly small- and medium-sized financial institutions lose increased in complexity, now including credit (CVA), debit customers due to offerings that don’t prioritize customer (DVA), funding (FVA), capital (KVA) and margin (MVA).10 experience.3 It’s difficult to create analytical models that Due to greater transparency requirements from sift through mounds of behavioral data quickly and regulations, stricter validation processes are applied to accurately enough to target which products are needed by trading, impacting risk-management calculations that specific customers in near real-time. This constrains need to align counterparty credit exposures with credit- financial institutions from providing preemptive product limit utilization of derivatives portfolios.11 Furthermore, recommendations with optimal feature selection in an significant investment frameworks and vehicles have agile manner, missing opportunities to expand current changed. For example, bond exchange traded funds customer share of wallet or reaching the 1.7 billion adults (ETFs) are projected to reach USD 2 trillion by 2024, and worldwide who are unbanked.4 environmental, social and government (ESG) investments are gaining traction, with USD 35 trillion invested in this A similar problem exists in fraud detection. It is estimated asset taxonomy in 2019.12 that financial institutions are losing between USD 10 billion and 40 billion in revenue a year due to fraud and In this complicated trading landscape, investment poor data management practices.5 Fraud detection managers struggle to incorporate real-life constraints, systems remain highly inaccurate, returning 80 percent such as market volatility and customer life-event changes, false positives, causing financial institutions to be overly into portfolio optimization. Ideally, money managers 6 risk averse. To help ensure proper credit scoring, the would like to simulate large numbers of potential customer onboarding process can take as long as 12 scenarios and investment options to validate sensitivities weeks.7 In today’s digital age, where 70 percent of when estimating expected returns. Currently, rebalancing banking takes place digitally, consumers are just not investment portfolios that keep up with market willing to wait that long.9 Financial institutions too slow in movements is significantly constrained by computational engaging effectively with new customers are losing them limitations and transaction costs. to more nimble competitors. Quantum technology could help cut through the For customer targeting and prediction modeling, quantum complexity of today’s trading environments. Quantum computing could be a game changer. The data modeling computing’s combinatorial optimization capabilities may capabilities of quantum computers are expected to prove enable investment managers to improve portfolio superior in finding patterns, performing classifications, diversification, rebalance portfolio investments to more and making predictions that are not possible today precisely respond to market conditions and investor goals, because of the challenges of complex data structures. and more cost-effectively streamline trading settlement processes. 3 Risk profiling In the face of more sophisticated risk-profiling demands and rising regulatory hurdles, the data-processing Financial services institutions are under increasing capabilities of quantum computers may speed up risk pressure to balance risk, hedge positions more effectively, scenario simulations with higher precision, while testing and perform a wider range of stress tests to comply with more outcomes. regulatory requirements. Liquidity management, derivatives pricing, and risk measurement can be complex Benefits of the Quantum Era and calculations difficult to perform, making it hard to properly
Load more

Recommended publications
  • Financial Market Modeling with Quantum Neural Networks Arxiv
    Financial Market Modeling with Quantum Neural Networks Carlos Pedro Gonçalves August 27, 2015 Instituto Superior de Ciências Sociais e Políticas (ISCSP) - University of Lisbon, E-mail: [email protected] Abstract Econophysics has developed as a research field that applies the for- malism of Statistical Mechanics and Quantum Mechanics to address Economics and Finance problems. The branch of Econophysics that applies of Quantum Theory to Economics and Finance is called Quan- tum Econophysics. In Finance, Quantum Econophysics’ contributions have ranged from option pricing to market dynamics modeling, behav- ioral finance and applications of Game Theory, integrating the empir- ical finding, from human decision analysis, that shows that nonlinear update rules in probabilities, leading to non-additive decision weights, can be computationally approached from quantum computation, with resulting quantum interference terms explaining the non-additive prob- abilities. The current work draws on these results to introduce new tools from Quantum Artificial Intelligence, namely Quantum Artifi- arXiv:1508.06586v1 [q-fin.CP] 26 Aug 2015 cial Neural Networks as a way to build and simulate financial market models with adaptive selection of trading rules, leading to turbulence and excess kurtosis in the returns distributions for a wide range of parameters. Keywords: Finance, Econophysics, Quantum Artificial Neural Networks, Quantum Stochastic Processes, Cognitive Science 1 1 Introduction One of the major problems of financial modeling has been to address com- plex financial returns dynamics, in particular, excess kurtosis and volatility- related turbulence which lead to statistically significant deviations from the Gaussian random walk model worked in traditional Financial Theory (Arthur et al., 1997; Voit, 2001; Ilinsky, 2001; Focardi and Fabozzi, 2004).
    [Show full text]
  • Quantum Propensity in Economics David Orrell Monireh Houshmand Abstract
    1 Quantum propensity in economics David Orrell1 Monireh Houshmand2 Abstract: This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that rational utility-optimisers drive market prices to a stable equilibrium, subject to external perturbations. While this approach has been highly influential, it has come under increasing criticism following the financial crisis of 2007/8. The quantum approach, in contrast, is inherently probabilistic and dynamic. Decision- makers are described, not by a utility function, but by a propensity function which specifies the probability of transacting. We show how a number of cognitive phenomena such as preference reversal and the disjunction effect can be modelled by using a simple quantum circuit to generate an appropriate propensity function. Conversely, a general propensity function can be quantized to incorporate effects such as interference and entanglement that characterise human decision- making. Applications to some common problems in economics and finance are discussed. Keywords: Quantum economics, quantum finance, quantum cognition, quantum probability, quantum decision theory, quantum computing 1. Introduction Theories of economics always rely on theories of value. In classical economics, it was assumed that value is the product of labour (Smith, 1776). A problem of course is that labour is difficult to measure, and the link with value is not always clear. This became obvious with the development of sophisticated financial markets in the late nineteenth century, where prices for something like a 1 Systems Forecasting, Toronto, Canada 2 Department of Electrical Engineering, Imam Reza International University, Mashhad, Iran.
    [Show full text]
  • The Relationship Between Changes in Cash Dividends and Volatility of Stock Returns
    The Relationship between Changes in Cash Dividends and Volatility of Stock Returns - A Study of the Swedish Stock Market Authors: Cecilia Nylander Sandra Renberg Supervisor: Catherine Lions Student Umeå School of Business and Economics Spring semester 2013 Degree project, 30 hp Acknowledgement We would like to take the opportunity to thank and express our sincere gratitude to everyone who has supported and given us very valuable feedback during the completion of this research. First of all, we would like to give our appreciation to our supervisor Catherine Lions who has, with her knowledge in the field, provided us with continuous feedback on our work, which, has proven to be extremely valuable in the completion of this study. Furthermore, Catherine has been our greatest sounding board and motivator throughout this journey for which we are deeply grateful. Secondly, we would like to thank the statistical department of Umeå University. Especially, we express our gratitude toward Kenny Brännberg and Johan Svensson who guided us in the statistical analysis of this research. Thank you for taking the time to help us and provide us with valuable suggestions on how to best conduct the analysis of the data. Sincerely, Cecilia Nylander and Sandra Renberg I Abstract The dividend policy and the distribution of cash dividend can be of interest to the investors from many angles. Consequently, many theories have been built on the relevance of dividend policy and there are several theories proposing that dividends increase shareholder value. However, the most famous theory on dividend policy might be Miller and Modigliani's dividend irrelevance theory which implies that the dividend policy does not affect shareholder value.
    [Show full text]
  • Application of Theoretical Models to Financial Innovation
    END-OF-DEGREE PAPER Universitat Pompeu Fabra APPLICATION OF THEORETICAL MODELS TO FINANCIAL INNOVATION Gerbert Garcia i Bassa Code: W13 Course: 21279 Degree: International Business Economics GERBERT GARCI A I B ASSA Application of Theoretical Models to Financial Innovation Abstract This paper is aimed at providing a general strategic overview of the potential synergic interactions between science, finance and economics in the context of the emergent econosciences, and presenting some of the existing theoretical models in science that have applications in the field of financial innovation. Thermodynamics, swarm intelligence, and chaos theory are explored, and some of their main applications in finance presented. Financial innovation, along with information, is considered as the centerpiece of the global financial and economic system, and a core strategic and geostrategic asset for corporations and societies throughout the globe. Financial R&D+i centers are briefly described as the main infrastructure to generate, control, defend, and capitalize information and knowledge in today’s technology-based, integrated financial markets. An analytical framework is subsequently suggested as a tool for financial analysis: according to it, the financial system may be modeled as a vector field of forces in an informational space in which subunits (i.e. particles, economic entities) interact according to the laws of thermodynamics and classical mechanics, and constitute a complex system. Finally, an analysis of the effects of financial innovation, along with a proposal to enhance the strategic synergies between science and economics and finance, concludes the paper. © Gerbert Garcia i Bassa, 2013 To my dad, thank you whole-heartedly for helping to build the foundations of a solid conceptual structure.
    [Show full text]
  • Extending and Simulating the Quantum Binomial Options Pricing Model
    Extending and Simulating the Quantum Binomial Options Pricing Model A thesis presented by Keith Meyer to The Department of Computer Science in partial fulfillment of the requirements for the degree of Master of Science in the subject of Computer Science The University of Manitoba Winnipeg, Manitoba January 2009 c Copyright by Keith Meyer, 2009 Thesis advisor Author Dr. William Kocay Keith Meyer Extending and Simulating the Quantum Binomial Options Pricing Model Abstract Pricing options quickly and accurately is a well known problem in finance. Quan- tum computing is being researched with the hope that quantum computers will be able to price options more efficiently than classical computers. This research extends the quantum binomial option pricing model proposed by Zeqian Chen to European put options and to Barrier options and develops a quantum algorithm to price them. This research produced three key results. First, when Maxwell-Boltzmann statistics are assumed, the quantum binomial model option prices are equivalent to the classical binomial model. Second, options can be priced efficiently on a quantum computer after the circuit has been built. The time complexity is O((N −τ) log2(N −τ)) and it is in the BQP quantum computational complexity class. Finally, challenges extend- ing the quantum binomial model to American, Asian and Bermudan options exist as the quantum binomial model does not take early exercise into account. ii Contents Abstract . ii Table of Contents . iii List of Figures . v List of Tables . vi Acknowledgments . vii Dedication . viii 1 Introduction 1 1.1 Background on Quantum Computing . 3 1.1.1 Computational Complexity .
    [Show full text]
  • Quantum Financial Economics-Risk and Returns
    Quantum Financial Economics - Risk and Returns Carlos Pedro Gonçalves Instituto Superior de Ciências Sociais e Políticas (ISCSP), Technical University of Lisbon E-mail: [email protected] Abstract Financial volatility risk and its relation to a business cycle-related intrinsic time is addressed through a multiple round evolutionary quantum game equilibrium leading to turbulence and multifractal signatures in the financial returns and in the risk dynamics. The model is simulated and the results are compared with actual financial volatility data. Keywords: Quantum Financial Economics, Business Cycle Dynamics, Intrinsic Time, Quantum Chaotic Volatility 1 Introduction Ever since Mandelbrot identified the presence of multifractal turbulence in the arXiv:1107.2562v2 [q-fin.RM] 2 Jan 2012 markets [15, 16, 17], this empirical fact has become a major research problem within financial economics. Mandelbrot [15, 16] hypothesized that financial systems’ dynamics has to be addressed in terms of an intrinsic temporal notion, linked to the economic rhythms and (chaotic) business cycles. Such intrinsic time would not be mea- sured in clock time, but in terms of economic rhythms that would rescale volatil- ity with the usual square root rule that holds for clock-based temporal intervals. In the present work, we return to such a proposal, providing for a quan- tum game theoretical approach to market turbulence with chaotic intrinsic time 1 1 Introduction 2 leading to multifractal signatures in volatility dynamics. The approach followed is that of path-dependent quantum adaptive computation within the framework of quantum game theory, such that a game is divided in rounds and, for each round, an equilibrium condition is formalized in terms of a payoff quantum op- timization problem, subject to: (1) a time-independent Schrödinger equation for the round; (2) an update rule for the Hamiltonian, depending on some evo- lutionary parameter(s)1.
    [Show full text]
  • Quantum Algorithms for Portfolio Management
    FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO Quantum Algorithms for Portfolio Management Duarte Frazão Mestrado Integrado em Engenharia Informática e Computação Supervisor: Koen Bertels Second Supervisor: José Matos July 19, 2021 Quantum Algorithms for Portfolio Management Duarte Frazão Mestrado Integrado em Engenharia Informática e Computação Approved in oral examination by the committee: Chair: Prof. João Paulo Fernandes External Examiner: Prof. Imran Ashraf Supervisor: Prof. Koen Bertels July 19, 2021 Abstract Quantum Computing is the process of leveraging quantum phenomena such as superposition and entanglement to solve problems that are intractable for classical computers. These properties al- low quantum computers to process an exponential amount of states in parallel in relation to the number of quantum bits, which is the main limitation of classical computing. With recent suc- cessful innovation on building more powerful quantum computers, the research community has started to explore different areas that will be disrupted when operational error-corrected quantum computers become a reality. One recent area of research is Quantum Finance, intended to be the bridge between Quantum Computing and Finance. The focus lies on understanding which problems in this area will be impacted by quantum computers. These can either be problems that can be solved more efficiently or problems that have never been solved due to classical computer limitations. Finance is one of the largest industries in the world, impacting every citizen in many ways, from our savings and investments to the companies that we rely upon to live our lives. Port- folio Management is the sub-field of Finance that tries to find the optimal investment portfolio for each individual investor.
    [Show full text]
  • Econophysics and the Complexity of Financial Markets
    D. RICKLES ECONOPHYSICS AND THE COMPLEXITY OF FINANCIAL MARKETS ABSTRACT: In this chapter we consider economic systems, and in particular financial systems, from the perspec- tive of the physics of complex systems (i.e. statistical physics, the theory of critical phenomena, and their cognates). This field of research is known as econophysics—alternative names are ‘financial physics’ and ‘statistical phynance.’ This title was coined in 1995 by Eugene Stanley, and since then its researchers have attempted to forge it as an independent and important field, one that stands in opposition to standard (‘Neo-Classical’) economic theory. Econophysicists argue that the empirical data is best explained in terms flowing out of statistical physics, according to which the (stylized) facts of economics are best understood as emergent properties of a complex system. However, some economists argue that the methods used by econophysics are not sufficient to prove the existence of underlying complexity in economic systems. The complexity claim can nonetheless be defended as a good example of an inference to the best explanation rather than a definitive deduction. To appear in J. Collier and C. Hooker (eds.), Handbook of the Philosophy of Science, Vol.10: Philoso- phy of Complex Systems. North Holland: Elsevier. 1 INTRODUCTION Within the ‘complexity science’ camp there are two broadly distinct ways of mod- eling the properties and behavior of socioeconomic systems1: • ‘Econobiology’ (‘evolutionary economics’) perspective: uses the lessons of evolutionary biology to explain economic phenomena—economic complex- ity is viewed as analogous to, or grounded in, biological complexity. • ‘Econophysics’ perspective: applies to economic phenomena various mod- els and concepts associated with the physics of complex systems—e.g.
    [Show full text]
  • Ubiquitous Quantum Structure
    Ubiquitous Quantum Structure Andrei Khrennikov Ubiquitous Quantum Structure From Psychology to Finance 123 Prof. Andrei Khrennikov University of Vaxj¨ o¨ International Center for Mathematical Modeling in Physics and Cognitive Science Vejdes Plats 7 SE-351 95 Vaxj¨ o¨ Sweden [email protected] ISBN 978-3-642-05100-5 e-ISBN 978-3-642-05101-2 DOI 10.1007/978-3-642-05101-2 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009943303 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface The aim of this book is to demonstrate that quantum-like (QL) models, i.e., models based on the mathematical formalism of quantum mechanics (QM) and its general- izations, can be successfully applied to cognitive science, psychology, genetics, the economy, finances, and game theory.
    [Show full text]
  • The Commercial Prospects for Quantum Computing Issue 1, December 2016 Rupesh Srivastava, Iris Choi, Tim Cook NQIT User Engagement Team
    The Commercial Prospects for Quantum Computing Issue 1, December 2016 Rupesh Srivastava, Iris Choi, Tim Cook NQIT User Engagement Team Networked Quantum Information Technologies NQIT (Networked Quantum Information Technologies) is funded by the Engineering and Physical Sciences Research Council and is a part of the UK National Quantum Technologies Programme Authors: Rupesh Srivastava, Iris Choi, Tim Cook NQIT User Engagement Team Design & layout: Hannah Rowlands, based on a design by Hunts If you have relevant information that should be added to this report, or suggested corrections to its content, please contact the authors so we can include them in future editions: [email protected] 2 Table of Contents 1: Overview of Quantum Computing 4 1.1 Quantum Computing – from the unthinkable to the inevitable 4 2: Current Commercial Activity 6 2.1 Commercial Investment 6 2.2 Open Source Activity 12 2.3 Patent Activity 14 3: Market Status 17 3.1 Introduction 17 3.2 Established Firms in the Quantum Computing Space 19 3.3 Strategic Partnerships and Initiatives 19 3.4 The Road Ahead 20 4: Research Status 21 5: Public Perceptions 25 5.1 Quantum Confusion 25 5.2 Unrealistic Expectations about Quantum Computing 26 5.3 Breaking Encryption 26 5.4 Responsible Innovation 27 6: Potential Market Segments 28 6.1 Health 28 6.2 Finance 30 6.3 Machine Learning 31 6.4 Simulation 32 6.5 Logistics 34 6.6 Software Verification & Validation 35 Appendix 36 Commercial Investment Timeline 36 Open Source Software 40 References 41 3 1: Overview of Quantum Computing 1.1 Quantum Computing – from the unthinkable to the inevitable With the promise of performing previously impossible computing tasks, quantum computing has gained substantial research momentum over the last decade in the race to realise the world’s first universal quantum computing machine.
    [Show full text]
  • D-Fine from Physics to Finance.Pdf
    From Physics to Finance XXXVII Heidelberg Physics Graduate Days Heidelberg, October 10th, 2016 © d- fine© d- —fine All — rights All rights reserved reserved | 0 The opinions expressed in this presentation and on the following slides are solely those of the authors and not necessarily those of d-fine GmbH. d-fine GmbH does not guarantee the accuracy or reliability of the information provided herein. The slides in this presentation were prepared as basis for the XXXVII Heidelberg Physics Graduate Days. It is therefore possible that key substantive elements were delivered only orally and are not present on the slides. The slides in this presentation are provided for information purposes only. Any and all information contained herein is not intended to constitute technical or legal advice and shall not be the initial position for taking actions based on this content. We do not guarantee or warrant the accuracy of this information or any results and further assume no liability in connection with this presentation, including any information, methods, or suggestions contained herein. Without the express prior written consent of the authors, the presentation and any information contained within may not be used for any purpose other than personal information. © d- fine© d- —fine All — rights All rights reserved reserved | 1 Agenda » The banks’ role in the economy 3 » Time series in finance – non-linearity and prediction of the future 12 » The mechanics of the balance sheet – an engineers approach 68 » The costs of the crisis 76 » Is the financial
    [Show full text]
  • QUANTUM FINANCE: Path Integrals and Hamiltonians for Options And
    This page intentionally left blank QUANTUM FINANCE Path Integrals and Hamiltonians for Options and Interest Rates This book applies the mathematics and concepts of quantum mechanics and quan- tum field theory to the modelling of interest rates and the theory of options. Particular emphasis is placed on path integrals and Hamiltonians. Financial mathematics at present is almost completely dominated by stochastic calculus. This book is unique in that it offers a formulation that is completely independent of that approach. As such many new results emerge from the ideas developed by the author. This pioneering work will be of interest to physicists and mathematicians work- ing in the field of finance, to quantitative analysts in banks and finance firms, and to practitioners in the field of fixed income securities and foreign exchange. The book can also be used as a graduate text for courses in financial physics and financial mathematics. BELAL E. BAAQUIE earned his B.Sc. from Caltech and Ph.D. in theoretical physics from Cornell University. He has published over 50 papers in leading inter- national journals on quantum field theory and related topics, and since 1997 has regularly published papers on applying quantum field theory to both the theoretical and empirical aspects of finance. He helped to launch the International Journal of Theoretical and Applied Finance in 1998 and continues to be one of the editors. QUANTUM FINANCE Path Integrals and Hamiltonians for Options and Interest Rates BELAL E. BAAQUIE National University of Singapore CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Informationonthistitle:www.cambridge.org/9780521840453 © B.
    [Show full text]