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Mathematics of Derivative Securities
Author: Stanley R. Pliska
Publisher: Cambridge University Press
ISBN: 0521584248
Pages: 582
Year: 1997-10-13
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During 1995 the Isaac Newton Institute for the Mathematical Sciences at Cambridge University hosted a six month research program on financial mathematics. During this period more than 300 scholars and financial practitioners attended to conduct research and to attend more than 150 research seminars. Many of the presented papers were on the subject of financial derivatives. The very best were selected to appear in this volume. They range from abstract financial theory to practical issues pertaining to the pricing and hedging of interest rate derivatives and exotic options in the market place. Hence this book will be of interest to both academic scholars and financial engineers.
Derivative Securities and Difference Methods
Author: You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
Publisher: Springer Science & Business Media
ISBN: 1461473063
Pages: 647
Year: 2013-07-04
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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
An Introduction to the Mathematics of Financial Derivatives
Author: Ali Hirsa, Salih N. Neftci
Publisher: Academic Press
ISBN: 0123846838
Pages: 454
Year: 2013-12-18
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An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learning Presented intuitively, breaking up complex mathematics concepts into easily understood notions Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching
Pricing Derivatives
Author: Ambar Sengupta
Publisher:
ISBN:
Pages: 282
Year: 2005
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Irwin Library of Investment and FinancePricing Derivatives provides investors with a clear understandingof derivative pricing models by first focusing on the underlyingmathematics and financial concepts upon which themodels were originally built. Trading consultant ProfessorAmbar Sengupta uses short, to-the-point chapters to examinethe relation between price and probability as well as pricingstructures of all major derivative instruments. Other topicscovered include foundations of stochastic models of pricing,along with methods for establishing optimal prices in terms ofthe max-min principles that underlie game theory.
Financial Derivatives
Author: Jamil Baz, George Chacko
Publisher: Cambridge University Press
ISBN: 052181510X
Pages: 338
Year: 2004-01-12
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This book offers a complete, succinct account of the principles of financial derivatives pricing. The first chapter provides readers with an intuitive exposition of basic random calculus. Concepts such as volatility and time, random walks, geometric Brownian motion, and Ito's lemma are discussed heuristically. The second chapter develops generic pricing techniques for assets and derivatives, determining the notion of a stochastic discount factor or pricing kernel, and then uses this concept to price conventional and exotic derivatives. The third chapter applies the pricing concepts to the special case of interest rate markets, namely, bonds and swaps, and discusses factor models and term structure consistent models. The fourth chapter deals with a variety of mathematical topics that underlie derivatives pricing and portfolio allocation decisions such as mean-reverting processes and jump processes and discusses related tools of stochastic calculus such as Kolmogorov equations, martingale techniques, stochastic control, and partial differential equations.
Derivatives in Financial Markets with Stochastic Volatility
Author: Jean-Pierre Fouque, George Papanicolaou, K. Ronnie Sircar
Publisher: Cambridge University Press
ISBN: 0521791634
Pages: 201
Year: 2000-07-03
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This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
A Course in Derivative Securities
Author: Kerry Back
Publisher: Springer Science & Business Media
ISBN: 3540279008
Pages: 356
Year: 2006-03-30
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"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
Integral, Measure and Derivative
Author: G. E. Shilov, B. L. Gurevich
Publisher: Courier Corporation
ISBN: 0486165612
Pages: 256
Year: 2013-05-13
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This treatment examines the general theory of the integral, Lebesque integral in n-space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.
American-Style Derivatives
Author: Jerome Detemple
Publisher: CRC Press
ISBN: 1420034863
Pages: 248
Year: 2005-12-09
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While the valuation of standard American option contracts has now achieved a fair degree of maturity, much work remains to be done regarding the new contractual forms that are constantly emerging in response to evolving economic conditions and regulations. Focusing on recent developments in the field, American-Style Derivatives provides an extensive treatment of option pricing with an emphasis on the valuation of American options on dividend-paying assets. The book begins with a review of valuation principles for European contingent claims in a financial market in which the underlying asset price follows an Ito process and the interest rate is stochastic and then extends the analysis to American contingent claims. In this context the author lays out the basic valuation principles for American claims and describes instructive representation formulas for their prices. The results are applied to standard American options in the Black-Scholes market setting as well as to a variety of exotic contracts such as barrier, capped, and multi-asset options. He also reviews numerical methods for option pricing and compares their relative performance. The author explains all the concepts using standard financial terms and intuitions and relegates proofs to appendices that can be found at the end of each chapter. The book is written so that the material is easily accessible not only to those with a background in stochastic processes and/or derivative securities, but also to those with a more limited exposure to those areas.
Derivative Pricing in Discrete Time
Author: Nigel J. Cutland, Alet Roux
Publisher: Springer Science & Business Media
ISBN: 1447144082
Pages: 325
Year: 2012-09-13
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This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative. To keep the mathematics as simple as possible, while explaining the basic principles, only discrete time models with a finite number of possible future scenarios are considered. The theory examines the simplest possible financial model having only one time step, where many of the fundamental ideas occur, and are easily understood. Proceeding slowly, the theory progresses to more realistic models with several stocks and multiple time steps, and includes a comprehensive treatment of incomplete models. The emphasis throughout is on clarity combined with full rigour. The later chapters deal with more advanced topics, including how the discrete time theory is related to the famous continuous time Black-Scholes theory, and a uniquely thorough treatment of American options. The book assumes no prior knowledge of financial markets, and the mathematical prerequisites are limited to elementary linear algebra and probability. This makes it accessible to undergraduates in mathematics as well as students of other disciplines with a mathematical component. It includes numerous worked examples and exercises, making it suitable for self-study.
Inequalities Involving Functions and Their Integrals and Derivatives
Author: Dragoslav S. Mitrinovic, J. Pecaric, A.M Fink
Publisher: Springer Science & Business Media
ISBN: 9401135622
Pages: 587
Year: 2012-12-06
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The Mathematics of Derivatives Securities with Applications in MATLAB
Author: Mario Cerrato
Publisher: John Wiley & Sons
ISBN: 1119973414
Pages: 248
Year: 2012-02-24
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Quantitative Finance is expanding rapidly. One of the aspects of the recent financial crisis is that, given the complexity of financial products, the demand for people with high numeracy skills is likely to grow and this means more recognition will be given to Quantitative Finance in existing and new course structures worldwide. Evidence has suggested that many holders of complex financial securities before the financial crisis did not have in-house experts or rely on a third-party in order to assess the risk exposure of their investments. Therefore, this experience shows the need for better understanding of risk associate with complex financial securities in the future. The Mathematics of Derivative Securities with Applications in MATLAB provides readers with an introduction to probability theory, stochastic calculus and stochastic processes, followed by discussion on the application of that knowledge to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility and an introduction to interest rates modelling. The book begins with an overview of MATLAB and the various components that will be used alongside it throughout the textbook. Following this, the first part of the book is an in depth introduction to Probability theory, Stochastic Processes and Ito Calculus and Ito Integral. This is essential to fully understand some of the mathematical concepts used in the following part of the book. The second part focuses on financial engineering and guides the reader through the fundamental theorem of asset pricing using the Black and Scholes Economy and Formula, Options Pricing through European and American style options, summaries of Exotic Options, Stochastic Volatility Models and Interest rate Modelling. Topics covered in this part are explained using MATLAB codes showing how the theoretical models are used practically. Authored from an academic’s perspective, the book discusses complex analytical issues and intricate financial instruments in a way that it is accessible to postgraduate students with or without a previous background in probability theory and finance. It is written to be the ideal primary reference book or a perfect companion to other related works. The book uses clear and detailed mathematical explanation accompanied by examples involving real case scenarios throughout and provides MATLAB codes for a variety of topics.
Risk Management and Financial Derivatives
Author: Satyajit Das
Publisher: McGraw-Hill
ISBN:
Pages: 799
Year: 1998
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"Risk Management and Financial Derivatives: A Guide to the Mathematics meets the demand for a simple, nontechnical explanation of the methodology of risk management and financial derivatives." "Risk Management and Financial Derivatives provides clear, concise explanations of the mathematics behind today's complex financial risk management topics. An ideal introduction for those new to the subject, it will also serve as an indispensable reference for those already experienced in the field."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
All About Derivatives Second Edition
Author: Michael Durbin
Publisher: McGraw Hill Professional
ISBN: 0071743529
Pages: 272
Year: 2010-12-03
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EVERYTHING YOU NEED TO KNOW ABOUT DERIVATIVES All About Derivatives, Second Edition, presents the complex subject of financial derivatives with a clarity and coherence you won’t find in other books. Using real-world examples and simple language, it lucidly illustrates what derivatives are and why they are so powerful. This second edition of All About Derivatives provides a rock-solid foundation on: The most common contracts available to you in today's market Key concepts such as cost of carry, settlement, valuation, and payoff Proven methods for establishing fair value How leverage can work for you--and against you The various derivative contracts traded today, including forwards, futures, swaps, and options Pricing methods and mathematics for determining fair value Hedging strategies for managing and reducing different types of risk INCLUDES A BRAND-NEW CHAPTER ON THE ROLE DERIVATIVES PLAYED IN THE 2008 FINANCIAL MELTDOWN
Options, Futures, and Other Derivatives
Author: John C. Hull
Publisher: Pearson
ISBN: 0134631498
Pages: 864
Year: 2017-01-09
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This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. For courses in business, economics, and financial engineering and mathematics. The definitive guide to derivatives markets, updated with contemporary examples and discussions Known as “the bible” to business and economics professionals and a consistent best-seller, Options, Futures, and Other Derivatives gives readers a modern look at derivatives markets. By incorporating the industry’s hottest topics, such as the securitization and credit crisis, author John C. Hull helps bridge the gap between theory and practice. The 10th Edition covers all of the latest regulations and trends, including the Black-Scholes-Merton formulas, overnight indexed swaps, and the valuation of commodity derivatives.