Derivative Securities and Difference Methods

Author: You-lan Zhu,Xiaonan Wu,I-Liang Chern,Zhi-zhong Sun

Publisher: Springer Science & Business Media

ISBN: 1461473063

Category: Mathematics

Page: 647

View: 6224

This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts. In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods in financial derivatives. For this new edition, the book has been updated throughout with many new problems added. More details about numerical methods for some options, for example, Asian options with discrete sampling, are provided and the proof of solution-uniqueness of derivative security problems and the complete stability analysis of numerical methods for two-dimensional problems are added. Review of first edition: “...the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS

Pricing Financial Instruments

The Finite Difference Method

Author: Domingo Tavella,Curt Randall

Publisher: John Wiley & Sons

ISBN: 9780471197607

Category: Business & Economics

Page: 256

View: 3088

Pricing Financial Instruments Numerical methods for the solution of financial instrument pricing equations are fast becoming essential for practitioners of modern quantitative finance. Among the most promising of these new computational finance techniques is the finite difference method-yet, to date, no single resource has presented a quality, comprehensive overview of this revolutionary quantitative approach to risk management. Pricing Financial Instruments, researched and written by Domingo Tavella and Curt Randall, two of the chief proponents of the finite difference method, presents a logical framework for applying the method of finite difference to the pricing of financial derivatives. Detailing the algorithmic and numerical procedures that are the foundation of both modern mathematical finance and the creation of financial products-while purposely keeping mathematical complexity to a minimum-this long-awaited book demonstrates how the techniques described can be used to accurately price simple and complex derivative structures. From a summary of stochastic pricing processes and arbitrage pricing arguments, through the analysis of numerical schemes and the implications of discretization-and ending with case studies that are simple yet detailed enough to demonstrate the capabilities of the methodology-Pricing Financial Instruments explores areas that include: * Pricing equations and the relationship between European and American derivatives * Detailed analyses of different stability analysis approaches * Continuous and discrete sampling models for path dependent options * One-dimensional and multi-dimensional coordinate transformations * Numerical examples of barrier options, Asian options, forward swaps, and more With an emphasis on how numerical solutions work and how the approximations involved affect the accuracy of the solutions, Pricing Financial Instruments takes us through doors opened wide by Black, Scholes, and Merton-and the arbitrage pricing principles they introduced in the early 1970s-to provide a step-by-step outline for sensibly interpreting the output of standard numerical schemes. It covers the understanding and application of today's finite difference method, and takes the reader to the next level of pricing financial instruments and managing financial risk.

Implementing Models in Quantitative Finance: Methods and Cases

Author: Gianluca Fusai,Andrea Roncoroni

Publisher: Springer Science & Business Media

ISBN: 9783540499596

Category: Business & Economics

Page: 607

View: 9603

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.

Numerical Methods in Finance with C++

Author: Maciej J. Capiński,Tomasz Zastawniak

Publisher: Cambridge University Press

ISBN: 1139536273

Category: Business & Economics

Page: N.A

View: 368

Driven by concrete computational problems in quantitative finance, this book provides aspiring quant developers with the numerical techniques and programming skills they need. The authors start from scratch, so the reader does not need any previous experience of C++. Beginning with straightforward option pricing on binomial trees, the book gradually progresses towards more advanced topics, including nonlinear solvers, Monte Carlo techniques for path-dependent derivative securities, finite difference methods for partial differential equations, and American option pricing by solving a linear complementarity problem. Further material, including solutions to all exercises and C++ code, is available online. The book is ideal preparation for work as an entry-level quant programmer and it gives readers the confidence to progress to more advanced skill sets involving C++ design patterns as applied in finance.

Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

Author: Christophe Profeta,Bernard Roynette,Marc Yor

Publisher: Springer Science & Business Media

ISBN: 9783642103957

Category: Mathematics

Page: 270

View: 4589

Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ?

The Econometrics of Financial Markets

Author: John Y. Campbell,Andrew W. Lo,A. Craig MacKinlay

Publisher: Princeton University Press

ISBN: 1400830214

Category: Business & Economics

Page: 632

View: 5656

The past twenty years have seen an extraordinary growth in the use of quantitative methods in financial markets. Finance professionals now routinely use sophisticated statistical techniques in portfolio management, proprietary trading, risk management, financial consulting, and securities regulation. This graduate-level textbook is intended for PhD students, advanced MBA students, and industry professionals interested in the econometrics of financial modeling. The book covers the entire spectrum of empirical finance, including: the predictability of asset returns, tests of the Random Walk Hypothesis, the microstructure of securities markets, event analysis, the Capital Asset Pricing Model and the Arbitrage Pricing Theory, the term structure of interest rates, dynamic models of economic equilibrium, and nonlinear financial models such as ARCH, neural networks, statistical fractals, and chaos theory. Each chapter develops statistical techniques within the context of a particular financial application. This exciting new text contains a unique and accessible combination of theory and practice, bringing state-of-the-art statistical techniques to the forefront of financial applications. Each chapter also includes a discussion of recent empirical evidence, for example, the rejection of the Random Walk Hypothesis, as well as problems designed to help readers incorporate what they have read into their own applications.

A Course in Derivative Securities

Introduction to Theory and Computation

Author: Kerry Back

Publisher: Springer Science & Business Media

ISBN: 3540279008

Category: Business & Economics

Page: 356

View: 971

"Deals with pricing and hedging financial derivatives.... Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book. This is valuable since computer simulation can help readers understand the theory....The book...succeeds in presenting intuitively advanced derivative modelling... it provides a useful bridge between introductory books and the more advanced literature." --MATHEMATICAL REVIEWS

Quantitative Methods in Derivatives Pricing

An Introduction to Computational Finance

Author: Domingo Tavella

Publisher: John Wiley & Sons

ISBN: 9780471274797

Category: Business & Economics

Page: 304

View: 4596

This book presents a cogent description of the main methodologies used in derivatives pricing. Starting with a summary of the elements of Stochastic Calculus, Quantitative Methods in Derivatives Pricing develops the fundamental tools of financial engineering, such as scenario generation, simulation for European instruments, simulation for American instruments, and finite differences in an intuitive and practical manner, with an abundance of practical examples and case studies. Intended primarily as an introductory graduate textbook in computational finance, this book will also serve as a reference for practitioners seeking basic information on alternative pricing methodologies. Domingo Tavella is President of Octanti Associates, a consulting firm in risk management and financial systems design. He is the founder and chief editor of the Journal of Computational Finance and has pioneered the application of advanced numerical techniques in pricing and risk analysis in the financial and insurance industries. Tavella coauthored Pricing Financial Instruments: The Finite Difference Method. He holds a PhD in aeronautical engineering from Stanford University and an MBA in finance from the University of California at Berkeley.

Modeling Derivatives in C++

Author: Justin London

Publisher: John Wiley & Sons

ISBN: 047168189X

Category: Business & Economics

Page: 840

View: 2255

This book is the definitive and most comprehensive guide to modeling derivatives in C++ today. Providing readers with not only the theory and math behind the models, as well as the fundamental concepts of financial engineering, but also actual robust object-oriented C++ code, this is a practical introduction to the most important derivative models used in practice today, including equity (standard and exotics including barrier, lookback, and Asian) and fixed income (bonds, caps, swaptions, swaps, credit) derivatives. The book provides complete C++ implementations for many of the most important derivatives and interest rate pricing models used on Wall Street including Hull-White, BDT, CIR, HJM, and LIBOR Market Model. London illustrates the practical and efficient implementations of these models in real-world situations and discusses the mathematical underpinnings and derivation of the models in a detailed yet accessible manner illustrated by many examples with numerical data as well as real market data. A companion CD contains quantitative libraries, tools, applications, and resources that will be of value to those doing quantitative programming and analysis in C++. Filled with practical advice and helpful tools, Modeling Derivatives in C++ will help readers succeed in understanding and implementing C++ when modeling all types of derivatives.

Risk Management, Speculation, and Derivative Securities

Author: Geoffrey Poitras

Publisher: Academic Press

ISBN: 9780125588225

Category: Business & Economics

Page: 601

View: 8457

Presenting an integrated explanation of speculative trading and risk management from the practitioner's point of view, "Risk Management, Speculation, and Derivative Securities" is a standard text on financial risk management that departs from the perspective of an agent whose main concerns are pricing and hedging derivatives.

The World of Risk Management

Author: H. Gifford Fong

Publisher: World Scientific

ISBN: 9812565175

Category: Business & Economics

Page: 218

View: 4105

Risk management is a foundation discipline for the prudent conduct of investment management. Being effective requires ongoing evolution and adaptation. In The World of Risk Management, an expert team of contributors addresses the important issues arising in the practice of risk management. A common thread among these distinguished articles is a rigorous theoretical or conceptual basis as well as their practical significance. The topics include not only broad policy considerations but also detailed how-to prescriptions.

Financial Markets

Author: Jeff Madura

Publisher: SAGE Publications Limited

ISBN: N.A

Category: Business & Economics

Page: 1656

View: 9850

This landmark work illustrates the progress that has been made in financial markets and assesses innovations that provide solutions to dilemmas and increase efficiency. These articles break down the complex web of relationships between the financial intermediary, the managers of corporations, shareholders, creditors, analysts and regulators. If complete information was disseminated to all participants, and all participants were ethical and competent, there would be less need for research on financial markets. Given the numerous conflicts of interest, the research included in these volumes attacks existing problems in financial markets in search of a solution. The research also identifies problems that have gone unnoticed. Research on financial markets identifies more problems in financial markets than it solves. Nevertheless, the research findings can help one use financial markets to one's advantage, rather than be used by them. This new edition to the SAGE Library in Business and Management discloses relevant research about the environment and behaviour within each of several financial markets so that participants can make informed decisions. It also hints at some of the unresolved issues in financial markets that are likely to receive more attention in future financial research.

Foundations and Trends in Finance

Author: John H. Cochrane

Publisher: Now Publishers Inc

ISBN: 9781933019154

Category: Finance

Page: 103

View: 3951

What are the real, macroeconomic risks that drive asset prices? This question is centrally important to macroeconomics. Where better to learn about the risks of recessions and depressions than by understanding the prices of assets such as stocks that carry macroeconomic risks? The question is also at the core of finance. For example, finance has long wondered if asset prices are "rational" or not. The only meaning of that term is whether asset prices are properly connected to macroeconomic risks. Financial Markets and the Real Economy reviews the current academic literature on the macroeconomics of finance. It starts by collecting the important facts such as the equity premium, size and value effects, and the predictability of returns. It then reviews the equity premium puzzle, which is the most basic challenge to the connection between asset prices and macroeconomics. Next, it surveys the current state of consumption-based models, and some of their surprising recent successes. It covers production and general-equilibrium models that tie asset returns to more cyclically important output and investment. Finally, it surveys the potential importance of labor income and idiosyncratic risk in understanding asset markets. This is the most current and comprehensive review on the subject and will be of interest to both macroeconomists and financial economists.

Hedging with trees

advances in pricing and risk managing derivatives

Author: Mark Nathan Broadie,Paul Glasserman

Publisher: N.A

ISBN: 9781899332021

Category: Business & Economics

Page: 262

View: 9438

An insightful collection of 35+ articles encapsulating advances in financial derivatives, selected by two well-respected academics.