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Author: Anatoliy Swishchuk
Publisher: Springer
ISBN: 331932408X
Category : Mathematics
Languages : en
Pages : 140
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Book Description
This book is devoted to the history of Change of Time Methods (CTM), the connections of CTM to stochastic volatilities and finance, fundamental aspects of the theory of CTM, basic concepts, and its properties. An emphasis is given on many applications of CTM in financial and energy markets, and the presented numerical examples are based on real data. The change of time method is applied to derive the well-known Black-Scholes formula for European call options, and to derive an explicit option pricing formula for a European call option for a mean-reverting model for commodity prices. Explicit formulas are also derived for variance and volatility swaps for financial markets with a stochastic volatility following a classical and delayed Heston model. The CTM is applied to price financial and energy derivatives for one-factor and multi-factor alpha-stable Levy-based models. Readers should have a basic knowledge of probability and statistics, and some familiarity with stochastic processes, such as Brownian motion, Levy process and martingale.
Author: Anatoliy Swishchuk
Publisher: Springer
ISBN: 331932408X
Category : Mathematics
Languages : en
Pages : 140
Get Book Here
Book Description
This book is devoted to the history of Change of Time Methods (CTM), the connections of CTM to stochastic volatilities and finance, fundamental aspects of the theory of CTM, basic concepts, and its properties. An emphasis is given on many applications of CTM in financial and energy markets, and the presented numerical examples are based on real data. The change of time method is applied to derive the well-known Black-Scholes formula for European call options, and to derive an explicit option pricing formula for a European call option for a mean-reverting model for commodity prices. Explicit formulas are also derived for variance and volatility swaps for financial markets with a stochastic volatility following a classical and delayed Heston model. The CTM is applied to price financial and energy derivatives for one-factor and multi-factor alpha-stable Levy-based models. Readers should have a basic knowledge of probability and statistics, and some familiarity with stochastic processes, such as Brownian motion, Levy process and martingale.
Author: Ole E Barndorff-nielsen
Publisher: World Scientific Publishing Company
ISBN: 9813108002
Category : Business & Economics
Languages : en
Pages : 323
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Book Description
Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance. It is invaluable as a textbook for graduate-level courses and students or a handy reference for researchers and practitioners in financial mathematics and econometrics.
Author: Cornelis W Oosterlee
Publisher: World Scientific
ISBN: 1786347962
Category : Business & Economics
Languages : en
Pages : 1310
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Book Description
This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.
Author: Gianluca Fusai
Publisher: Springer Science & Business Media
ISBN: 3540499598
Category : Business & Economics
Languages : en
Pages : 606
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Book Description
This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.
Author: Ioannis Karatzas
Publisher: Springer Science & Business Media
ISBN: 0387948392
Category : Business & Economics
Languages : en
Pages : 427
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Book Description
This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion- driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options. Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.
Author: Joel Gibbons
Publisher: Routledge
ISBN: 1351521012
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
This book presents a novel approach to characterizing markets in quantitative terms. The examples cut across the world of interest rates, price of gold, stock market and corporate worlds that the stock market rests on, and the pricing of options on financial instruments. The emphasis is on methods of inquiry, methods that can just as easily be applied to other markets and other economic phenomena as well. The goal is to make the methods available to the widest possible audience of quantitative analysts and to the trading desks and investment plans they feed.Quantitative research and modeling in finance and economics have a long history going back to Frank Ramsey, mathematician, logician, and economist, who pioneered the application of dynamic models in economics in the 1920s, and to his theory of the Ramsey Tax, which is a rule for apportioning tax rates in a way that raises the maximum tax revenues while impacting the decisions of taxpayers as little as possible. The opposite would be a tax so inefficient that it causes people to avoid doing whatever it is that subjects them to the tax.These experiments yield valuable insight into economic affairs, but they are only a stepping-stone for others—a starting point for discovery. Foremost among them is locating usable statistical findings to the investment world. Gibbons' intention is not to provide investment advice, it is to provide education. These data are subject to changing results, but that should not diminish their educational value. This is a proactive fusion of business economics and sound social science methods.
Author: Jan W Dash
Publisher: World Scientific Publishing Company
ISBN: 9814571253
Category : Business & Economics
Languages : en
Pages : 1008
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Book Description
Written by a physicist with extensive experience as a risk/finance quant, this book treats a wide variety of topics. Presenting the theory and practice of quantitative finance and risk, it delves into the 'how to' and 'what it's like' aspects not covered in textbooks or papers. A 'Technical Index' indicates the mathematical level for each chapter.This second edition includes some new, expanded, and wide-ranging considerations for risk management: Climate Change and its long-term systemic risk; Markets in Crisis and the Reggeon Field Theory; 'Smart Monte Carlo' and American Monte Carlo; Trend Risk — time scales and risk, the Macro-Micro model, singular spectrum analysis; credit risk: counterparty risk and issuer risk; stressed correlations — new techniques; and Psychology and option models.Solid risk management topics from the first edition and valid today are included: standard/advanced theory and practice in fixed income, equities, and FX; quantitative finance and risk management — traditional/exotic derivatives, fat tails, advanced stressed VAR, model risk, numerical techniques, deals/portfolios, systems, data, economic capital, and a function toolkit; risk lab — the nuts and bolts of risk management from the desk to the enterprise; case studies of deals; Feynman path integrals, Green functions, and options; and 'Life as a Quant' — communication issues, sociology, stories, and advice.
Author: Maria Cristina Mariani
Publisher: John Wiley & Sons
ISBN: 1118629884
Category : Business & Economics
Languages : en
Pages : 513
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Book Description
Presents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, and some generic pseudo-algorithms to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field. The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. We also present some useful finance concepts used throughout the book. In part two of the book we present the classical Black-Scholes-Merton model in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are also discussed. Next, solutions to Partial Differential Equations (PDE), wavelets and Fourier transforms are presented. Several methodologies for pricing options namely, tree methods, finite difference method and Monte Carlo simulation methods are also discussed. We conclude this part with a discussion on stochastic differential equations (SDE’s). In the third part of this book, several new and advanced models from current literature such as general Lvy processes, nonlinear PDE's for stochastic volatility models in a transaction fee market, PDE's in a jump-diffusion with stochastic volatility models and factor and copulas models are discussed. In part four of the book, we conclude with a solid presentation of the typical topics in fixed income securities and derivatives. We discuss models for pricing bonds market, marketable securities, credit default swaps (CDS) and securitizations. Classroom-tested over a three-year period with the input of students and experienced practitioners Emphasizes the volatility of financial analyses and interpretations Weaves theory with application throughout the book Utilizes R and MATLAB software programs Presents pseudo-algorithms for readers who do not have access to any particular programming system Supplemented with extensive author-maintained web site that includes helpful teaching hints, data sets, software programs, and additional content Quantitative Finance is an ideal textbook for upper-undergraduate and beginning graduate students in statistics, financial engineering, quantitative finance, and mathematical finance programs. It will also appeal to practitioners in the same fields.
Author: Cheng-Few Lee
Publisher: Springer Science & Business Media
ISBN: 0387771174
Category : Business & Economics
Languages : en
Pages : 1700
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Book Description
Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.
Author: Espen Gaarder Haug
Publisher: John Wiley & Sons
ISBN: 1118836820
Category : Business & Economics
Languages : en
Pages : 400
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Book Description
Derivatives Models on Models takes a theoretical and practical look at some of the latest and most important ideas behind derivatives pricing models. In each chapter the author highlights the latest thinking and trends in the area. A wide range of topics are covered, including valuation methods on stocks paying discrete dividend, Asian options, American barrier options, Complex barrier options, reset options, and electricity derivatives. The book also discusses the latest ideas surrounding finance like the robustness of dynamic delta hedging, option hedging, negative probabilities and space-time finance. The accompanying CD-ROM with additional Excel sheets includes the mathematical models covered in the book. The book also includes interviews with some of the world’s top names in the industry, and an insight into the history behind some of the greatest discoveries in quantitative finance. Interviewees include: Clive Granger, Nobel Prize winner in Economics 2003, on Cointegration Nassim Taleb on Black Swans Stephen Ross on Arbitrage Pricing Theory Emanuel Derman the Wall Street Quant Edward Thorp on Gambling and Trading Peter Carr the Wall Street Wizard of Option Symmetry and Volatility Aaron Brown on Gambling, Poker and Trading David Bates on Crash and Jumps Andrei Khrennikov on Negative Probabilities Elie Ayache on Option Trading and Modeling Peter Jaeckel on Monte Carlo Simulation Alan Lewis on Stochastic Volatility and Jumps Paul Wilmott on Paul Wilmott Knut Aase on Catastrophes and Financial Economics Eduardo Schwartz the Yoga Master of Quantitative Finance Bruno Dupire on Local and Stochastic Volatility Models
