Derivative Pricing In Discrete Time

Author : Nigel J. Cutland,Alet Roux
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 47,6 Mb
Release : 2012-09-13
Category : Mathematics
ISBN : 9781447144083

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Derivative Pricing in Discrete Time by Nigel J. Cutland,Alet Roux Pdf

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.

Author : Nigel J. Cutland,Alet Roux
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 54,6 Mb
Release : 2012-09-07
Category : Mathematics
ISBN : 9781447144076

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Derivative Pricing in Discrete Time by Nigel J. Cutland,Alet Roux Pdf

Derivatives are financial entities whose value is derived from the value of other more concrete assets such as stocks and commodities. They are an important ingredient of modern financial markets. 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.

Author : Nicholas H. Bingham,Rudiger Kiesel
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 55,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781447136194

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Risk-Neutral Valuation by Nicholas H. Bingham,Rudiger Kiesel Pdf

With a simple approach accessible to a wide audience, this book aims for the heart of mathematical finance: the fundamental formula of arbitrage pricing theory. This method of pricing discounts everything and takes expected values under the equivalent martingale measure. The authors approach is simple and excludes unnecessary proofs of measure-theoretic probability, instead, it favors techniques and examples of proven interest to financial practitioners.

Author : Ambar Sengupta
Publisher : Unknown
Page : 312 pages
File Size : 50,5 Mb
Release : 2005
Category : Business & Economics
ISBN : IND:30000101575482

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Pricing Derivatives by Ambar Sengupta Pdf

Irwin Library of Investment and Finance Pricing Derivatives provides investors with a clear understanding of derivative pricing models by first focusing on the underlying mathematics and financial concepts upon which the models were originally built. Trading consultant Professor Ambar Sengupta uses short, to-the-point chapters to examine the relation between price and probability as well as pricing structures of all major derivative instruments. Other topics covered include foundations of stochastic models of pricing, along with methods for establishing optimal prices in terms of the max-min principles that underlie game theory.

Author : Martin Baxter,Andrew Rennie
Publisher : Cambridge University Press
Page : 252 pages
File Size : 52,6 Mb
Release : 1996-09-19
Category : Business & Economics
ISBN : 0521552893

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Financial Calculus by Martin Baxter,Andrew Rennie Pdf

A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

Author : T. W. Epps
Publisher : World Scientific
Page : 644 pages
File Size : 40,8 Mb
Release : 2007
Category : Business & Economics
ISBN : 9789812700339

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Pricing Derivative Securities by T. W. Epps Pdf

This book presents techniques for valuing derivative securities at a level suitable for practitioners, students in doctoral programs in economics and finance, and those in masters-level programs in financial mathematics and computational finance. It provides the necessary mathematical tools from analysis, probability theory, the theory of stochastic processes, and stochastic calculus, making extensive use of examples. It also covers pricing theory, with emphasis on martingale methods. The chapters are organized around the assumptions made about the dynamics of underlying price processes. Readers begin with simple, discrete-time models that require little mathematical sophistication, proceed to the basic Black-Scholes theory, and then advance to continuous-time models with multiple risk sources. The second edition takes account of the major developments in the field since 2000. New topics include the use of simulation to price American-style derivatives, a new one-step approach to pricing options by inverting characteristic functions, and models that allow jumps in volatility and Markov-driven changes in regime. The new chapter on interest-rate derivatives includes extensive coverage of the LIBOR market model and an introduction to the modeling of credit risk. As a supplement to the text, the book contains an accompanying CD-ROM with user-friendly FORTRAN, C++, and VBA program components.

Author : Robert E. Brooks,Don M. Chance
Publisher : John Wiley & Sons
Page : 631 pages
File Size : 40,5 Mb
Release : 2024-01-25
Category : Business & Economics
ISBN : 9781394179664

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Foundations of the Pricing of Financial Derivatives by Robert E. Brooks,Don M. Chance Pdf

An accessible and mathematically rigorous resource for masters and PhD students In Foundations of the Pricing of Financial Derivatives: Theory and Analysis two expert finance academics with professional experience deliver a practical new text for doctoral and masters’ students and also new practitioners. The book draws on the authors extensive combined experience teaching, researching, and consulting on this topic and strikes an effective balance between fine-grained quantitative detail and high-level theoretical explanations. The authors fill the gap left by books directed at masters’-level students that often lack mathematical rigor. Further, books aimed at mathematically trained graduate students often lack quantitative explanations and critical foundational materials. Thus, this book provides the technical background required to understand the more advanced mathematics used in this discipline, in class, in research, and in practice. Readers will also find: Tables, figures, line drawings, practice problems (with a solutions manual), references, and a glossary of commonly used specialist terms Review of material in calculus, probability theory, and asset pricing Coverage of both arithmetic and geometric Brownian motion Extensive treatment of the mathematical and economic foundations of the binomial and Black-Scholes-Merton models that explains their use and derivation, deepening readers’ understanding of these essential models Deep discussion of essential concepts, like arbitrage, that broaden students’ understanding of the basis for derivative pricing Coverage of pricing of forwards, futures, and swaps, including arbitrage-free term structures and interest rate derivatives An effective and hands-on text for masters’-level and PhD students and beginning practitioners with an interest in financial derivatives pricing, Foundations of the Pricing of Financial Derivatives is an intuitive and accessible resource that properly balances math, theory, and practical applications to help students develop a healthy command of a difficult subject.

Author : Yue-Kuen Kwok
Publisher : Springer Science & Business Media
Page : 541 pages
File Size : 54,5 Mb
Release : 2008-07-10
Category : Mathematics
ISBN : 9783540686880

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Mathematical Models of Financial Derivatives by Yue-Kuen Kwok Pdf

This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 44,8 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814470636

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Financial Derivatives Pricing by Anonim Pdf

Author : Christophe Chorro,Dominique Guégan,Florian Ielpo
Publisher : Springer
Page : 202 pages
File Size : 52,7 Mb
Release : 2014-12-04
Category : Business & Economics
ISBN : 9783662450376

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A Time Series Approach to Option Pricing by Christophe Chorro,Dominique Guégan,Florian Ielpo Pdf

The current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.

Author : Ambrose Lo
Publisher : CRC Press
Page : 427 pages
File Size : 55,7 Mb
Release : 2018-07-04
Category : Mathematics
ISBN : 9781315301211

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Derivative Pricing by Ambrose Lo Pdf

The proliferation of financial derivatives over the past decades, options in particular, has underscored the increasing importance of derivative pricing literacy among students, researchers, and practitioners. Derivative Pricing: A Problem-Based Primer demystifies the essential derivative pricing theory by adopting a mathematically rigorous yet widely accessible pedagogical approach that will appeal to a wide variety of audience. Abandoning the traditional "black-box" approach or theorists’ "pedantic" approach, this textbook provides readers with a solid understanding of the fundamental mechanism of derivative pricing methodologies and their underlying theory through a diversity of illustrative examples. The abundance of exercises and problems makes the book well-suited as a text for advanced undergraduates, beginning graduates as well as a reference for professionals and researchers who need a thorough understanding of not only "how," but also "why" derivative pricing works. It is especially ideal for students who need to prepare for the derivatives portion of the Society of Actuaries Investment and Financial Markets Exam. Features Lucid explanations of the theory and assumptions behind various derivative pricing models. Emphasis on intuitions, mnemonics as well as common fallacies. Interspersed with illustrative examples and end-of-chapter problems that aid a deep understanding of concepts in derivative pricing. Mathematical derivations, while not eschewed, are made maximally accessible. A solutions manual is available for qualified instructors. The Author Ambrose Lo is currently Assistant Professor of Actuarial Science at the Department of Statistics and Actuarial Science at the University of Iowa. He received his Ph.D. in Actuarial Science from the University of Hong Kong in 2014, with dependence structures, risk measures, and optimal reinsurance being his research interests. He is a Fellow of the Society of Actuaries (FSA) and a Chartered Enterprise Risk Analyst (CERA). His research papers have been published in top-tier actuarial journals, such as ASTIN Bulletin: The Journal of the International Actuarial Association, Insurance: Mathematics and Economics, and Scandinavian Actuarial Journal.

Author : Jamil Baz,George Chacko
Publisher : Cambridge University Press
Page : 128 pages
File Size : 41,8 Mb
Release : 2004-01-12
Category : Business & Economics
ISBN : 9781107268739

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Financial Derivatives by Jamil Baz,George Chacko Pdf

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.

Author : T. Kariya,Regina Liu
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 40,8 Mb
Release : 2011-06-27
Category : Business & Economics
ISBN : 9781441992307

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Asset Pricing by T. Kariya,Regina Liu Pdf

1. Main Goals The theory of asset pricing has grown markedly more sophisticated in the last two decades, with the application of powerful mathematical tools such as probability theory, stochastic processes and numerical analysis. The main goal of this book is to provide a systematic exposition, with practical appli cations, of the no-arbitrage theory for asset pricing in financial engineering in the framework of a discrete time approach. The book should also serve well as a textbook on financial asset pricing. It should be accessible to a broad audi ence, in particular to practitioners in financial and related industries, as well as to students in MBA or graduate/advanced undergraduate programs in finance, financial engineering, financial econometrics, or financial information science. The no-arbitrage asset pricing theory is based on the simple and well ac cepted principle that financial asset prices are instantly adjusted at each mo ment in time in order not to allow an arbitrage opportunity. Here an arbitrage opportunity is an opportunity to have a portfolio of value aat an initial time lead to a positive terminal value with probability 1 (equivalently, at no risk), with money neither added nor subtracted from the portfolio in rebalancing dur ing the investment period. It is necessary for a portfolio of valueato include a short-sell position as well as a long-buy position of some assets.

Author : Peter M. Knopf,John L. Teall
Publisher : Elsevier
Page : 348 pages
File Size : 40,9 Mb
Release : 2015-07-29
Category : Business & Economics
ISBN : 9780128017272

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Risk Neutral Pricing and Financial Mathematics by Peter M. Knopf,John L. Teall Pdf

Risk Neutral Pricing and Financial Mathematics: A Primer provides a foundation to financial mathematics for those whose undergraduate quantitative preparation does not extend beyond calculus, statistics, and linear math. It covers a broad range of foundation topics related to financial modeling, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, and term structure models, along with related valuation and hedging techniques. The joint effort of two authors with a combined 70 years of academic and practitioner experience, Risk Neutral Pricing and Financial Mathematics takes a reader from learning the basics of beginning probability, with a refresher on differential calculus, all the way to Doob-Meyer, Ito, Girsanov, and SDEs. It can also serve as a useful resource for actuaries preparing for Exams FM and MFE (Society of Actuaries) and Exams 2 and 3F (Casualty Actuarial Society). Includes more subjects than other books, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, term structure models, valuation, and hedging techniques Emphasizes introductory financial engineering, financial modeling, and financial mathematics Suited for corporate training programs and professional association certification programs

Author : Ser-Huang Poon,Richard Stapleton
Publisher : OUP Oxford
Page : 156 pages
File Size : 50,8 Mb
Release : 2005-01-13
Category : Business & Economics
ISBN : 9780191533891

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Asset Pricing in Discrete Time by Ser-Huang Poon,Richard Stapleton Pdf

Relying on the existence, in a complete market, of a pricing kernel, this book covers the pricing of assets, derivatives, and bonds in a discrete time, complete markets framework. It is primarily aimed at advanced Masters and PhD students in finance. — Covers asset pricing in a single period model, deriving a simple complete market pricing model and using Stein's lemma to derive a version of the Capital Asset Pricing Model. — Looks more deeply into some of the utility determinants of the pricing kernel, investigating in particular the effect of non-marketable background risks on the shape of the pricing kernel. — Derives the prices of European-style contingent claims, in particular call options, in a one-period model; derives the Black-Scholes model assuming a lognormal distribution for the asset and a pricing kernel with constant elasticity, and emphasizes the idea of a risk-neutral valuation relationship between the price of a contingent claim on an asset and the underlying asset price. — Extends the analysis to contingent claims on assets with non-lognormal distributions and considers the pricing of claims when risk-neutral valuation relationships do not exist. — Expands the treatment of asset pricing to a multi-period economy, deriving prices in a rational expectations equilibrium. — Uses the rational expectations framework to analyse the pricing of forward and futures contracts on assets and derivatives. — Analyses the pricing of bonds given stochastic interest rates, and then uses this methodology to model the drift of forward rates, and as a special case the drift of the forward London Interbank Offer Rate in the LIBOR Market Model.