The Mathematical Foundations Of Barrier Option Pricing Theory

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The Mathematical Foundations of Barrier Option-Pricing Theory

Author : Don R. Rich
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis The Mathematical Foundations of Barrier Option-Pricing Theory by : Don R. Rich

Download or read book The Mathematical Foundations of Barrier Option-Pricing Theory written by Don R. Rich and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Barrier options are one of the most popular first-generation exotic options, yet little theoretical research exists. This paper begins by presenting, in an intuitive and unified framework, the mathematical foundation necessary to value barrier options. Closed-form solutions are derived and comparative statics are presented for European barrier options with a fixed rebate and barrier level. From both a theoretical and hedging perspective, barrier options are shown to be more complex than standard options. Further, it is shown that under certain conditions barrier options are identical in value to standard options, that all valuation solutions are linearly homogeneous of degree one with respect to the underlying asset price, exercise price, barrier level, and rebate, and that barrier options have quite different hedging properties than standard options. Closed-form solutions are also derived for European barrier options with barriers that depend exponentially on time to expiration. Applications discussed in the paper include covered calls, portfolio insurance, options embedded in bonds, and when barrier option prices are more likely to correspond to observed market prices than Black-Scholes option prices.

Mathematical Modeling And Methods Of Option Pricing

Author : Lishang Jiang
Publisher : World Scientific Publishing Company
ISBN 13 : 9813106557
Total Pages : 343 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Mathematical Modeling And Methods Of Option Pricing by : Lishang Jiang

Download or read book Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.

Mathematical Modeling and Methods of Option Pricing

Author : Lishang Jiang
Publisher : World Scientific
ISBN 13 : 9812563695
Total Pages : 344 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Mathematical Modeling and Methods of Option Pricing by : Lishang Jiang

Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.

Introduction to Option Pricing Theory

Author : Gopinath Kallianpur
Publisher : Springer Science & Business Media
ISBN 13 : 1461205115
Total Pages : 266 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Option Pricing Theory by : Gopinath Kallianpur

Download or read book Introduction to Option Pricing Theory written by Gopinath Kallianpur and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.

An Introduction to Exotic Option Pricing

Author : Peter Buchen
Publisher : CRC Press
ISBN 13 : 1498785611
Total Pages : 298 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis An Introduction to Exotic Option Pricing by : Peter Buchen

Download or read book An Introduction to Exotic Option Pricing written by Peter Buchen and published by CRC Press. This book was released on 2012-02-03 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an easy-to-understand, nontechnical yet mathematically elegant manner, An Introduction to Exotic Option Pricing shows how to price exotic options, including complex ones, without performing complicated integrations or formally solving partial differential equations (PDEs). The author incorporates much of his own unpublished work, including ideas

Black Scholes and Beyond: Option Pricing Models

Author : Neil Chriss
Publisher : McGraw Hill Professional
ISBN 13 : 9780786310258
Total Pages : 512 pages
Book Rating : 4.3/5 (12 download)

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Book Synopsis Black Scholes and Beyond: Option Pricing Models by : Neil Chriss

Download or read book Black Scholes and Beyond: Option Pricing Models written by Neil Chriss and published by McGraw Hill Professional. This book was released on 1997 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: An unprecedented book on option pricing! For the first time, the basics on modern option pricing are explained ``from scratch'' using only minimal mathematics. Market practitioners and students alike will learn how and why the Black-Scholes equation works, and what other new methods have been developed that build on the success of Black-Shcoles. The Cox-Ross-Rubinstein binomial trees are discussed, as well as two recent theories of option pricing: the Derman-Kani theory on implied volatility trees and Mark Rubinstein's implied binomial trees. Black-Scholes and Beyond will not only help the reader gain a solid understanding of the Balck-Scholes formula, but will also bring the reader up to date by detailing current theoretical developments from Wall Street. Furthermore, the author expands upon existing research and adds his own new approaches to modern option pricing theory. Among the topics covered in Black-Scholes and Beyond: detailed discussions of pricing and hedging options; volatility smiles and how to price options ``in the presence of the smile''; complete explanation on pricing barrier options.

Handbooks in Operations Research and Management Science: Financial Engineering

Author : John R. Birge
Publisher : Elsevier
ISBN 13 : 9780080553252
Total Pages : 1026 pages
Book Rating : 4.5/5 (532 download)

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Book Synopsis Handbooks in Operations Research and Management Science: Financial Engineering by : John R. Birge

Download or read book Handbooks in Operations Research and Management Science: Financial Engineering written by John R. Birge and published by Elsevier. This book was released on 2007-11-16 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.

Introduction to Option Pricing Theory

Author : G. Kallianpur
Publisher :
ISBN 13 : 9783764341084
Total Pages : 268 pages
Book Rating : 4.3/5 (41 download)

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Book Synopsis Introduction to Option Pricing Theory by : G. Kallianpur

Download or read book Introduction to Option Pricing Theory written by G. Kallianpur and published by . This book was released on 2000 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure." "Introduction to Option Pricing Theory is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Derivatives

Author : Espen Gaarder Haug
Publisher : John Wiley & Sons
ISBN 13 : 1118836820
Total Pages : 400 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Derivatives by : Espen Gaarder Haug

Download or read book Derivatives written by Espen Gaarder Haug and published by John Wiley & Sons. This book was released on 2013-10-18 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

American-Type Options

Author : Dmitrii S. Silvestrov
Publisher : Walter de Gruyter
ISBN 13 : 3110329824
Total Pages : 520 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis American-Type Options by : Dmitrii S. Silvestrov

Download or read book American-Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter. This book was released on 2013-11-27 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.

Modular Pricing of Options

Author : Jianwei Zhu
Publisher : Springer Science & Business Media
ISBN 13 : 3662043092
Total Pages : 181 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Modular Pricing of Options by : Jianwei Zhu

Download or read book Modular Pricing of Options written by Jianwei Zhu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a technical point of view, the celebrated Black and Scholes option pricing formula was originally developed using a separation of variables technique. However, already Merton mentioned in his seminal 1973 pa per, that it could have been developed by using Fourier transforms as well. Indeed, as is well known nowadays, Fourier transforms are a rather convenient solution technique for many models involving the fundamental partial differential equation of financial economics. It took the community nearly another twenty years to recognize that Fourier transform is even more useful, if one applies it to problems in financial economics without seeking an explicit analytical inverse trans form. Heston (1993) probably was the first to demonstrate how to solve a stochastic volatility option pricing model quasi analytically using the characteristic function of the problem, which is nothing else than the Fourier transform of the underlying Arrow /Debreu-prices, and doing the inverse transformation numerically. This opened the door for a whole bunch of new closed form solutions in the transformed Fourier space and still is one of the most active research areas in financial economics.

Foreign Exchange Option Pricing

Author : Iain J. Clark
Publisher : John Wiley & Sons
ISBN 13 : 1119978602
Total Pages : 308 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Foreign Exchange Option Pricing by : Iain J. Clark

Download or read book Foreign Exchange Option Pricing written by Iain J. Clark and published by John Wiley & Sons. This book was released on 2011-10-20 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers foreign exchange options from the point of view of the finance practitioner. It contains everything a quant or trader working in a bank or hedge fund would need to know about the mathematics of foreign exchange—not just the theoretical mathematics covered in other books but also comprehensive coverage of implementation, pricing and calibration. With content developed with input from traders and with examples using real-world data, this book introduces many of the more commonly requested products from FX options trading desks, together with the models that capture the risk characteristics necessary to price these products accurately. Crucially, this book describes the numerical methods required for calibration of these models – an area often neglected in the literature, which is nevertheless of paramount importance in practice. Thorough treatment is given in one unified text to the following features: Correct market conventions for FX volatility surface construction Adjustment for settlement and delayed delivery of options Pricing of vanillas and barrier options under the volatility smile Barrier bending for limiting barrier discontinuity risk near expiry Industry strength partial differential equations in one and several spatial variables using finite differences on nonuniform grids Fourier transform methods for pricing European options using characteristic functions Stochastic and local volatility models, and a mixed stochastic/local volatility model Three-factor long-dated FX model Numerical calibration techniques for all the models in this work The augmented state variable approach for pricing strongly path-dependent options using either partial differential equations or Monte Carlo simulation Connecting mathematically rigorous theory with practice, this is the essential guide to foreign exchange options in the context of the real financial marketplace.

Numerical Methods in Finance

Author : L. C. G. Rogers
Publisher : Cambridge University Press
ISBN 13 : 9780521573542
Total Pages : 348 pages
Book Rating : 4.5/5 (735 download)

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Book Synopsis Numerical Methods in Finance by : L. C. G. Rogers

Download or read book Numerical Methods in Finance written by L. C. G. Rogers and published by Cambridge University Press. This book was released on 1997-06-26 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.

Nonlinear Option Pricing

Author : Julien Guyon
Publisher : CRC Press
ISBN 13 : 1466570334
Total Pages : 486 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Nonlinear Option Pricing by : Julien Guyon

Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.

Implementing Models in Quantitative Finance: Methods and Cases

Author : Gianluca Fusai
Publisher : Springer Science & Business Media
ISBN 13 : 3540499598
Total Pages : 606 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Implementing Models in Quantitative Finance: Methods and Cases by : Gianluca Fusai

Download or read book Implementing Models in Quantitative Finance: Methods and Cases written by Gianluca Fusai and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Options on Foreign Exchange

Author : David F. DeRosa
Publisher : John Wiley & Sons
ISBN 13 : 9780471316411
Total Pages : 256 pages
Book Rating : 4.3/5 (164 download)

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Book Synopsis Options on Foreign Exchange by : David F. DeRosa

Download or read book Options on Foreign Exchange written by David F. DeRosa and published by John Wiley & Sons. This book was released on 2000-01-18 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your A to Z Guide to the World's Largest Option Market "A clearly written manual that flows smoothly. Whether you have 20 years of experience in the FX options markets or none, you will learn something interesting from reading this book. Highly recommended for both traders and non-traders." * Adam Kreysar, Global Head FX Options Warburg Dillon Read "DeRosa presents technical material with a minimum of technical fuss. Filtered through his scholarship and practical trading experience, up-to-date topics such as exotic options, forward volatilities, and the volatility smile become accessible. The book will be extremely useful to asset managers and risk managers." * Allan M. Malz, Partner The RiskMetrics Group "This new edition of Options on Foreign Exchange provides an exhaustive review of the literature on currency options, in addition to covering the practical aspects of the business. It is greatly pedagogical and well written-as can be expected from David DeRosa." * Nassim Taleb, President Empirica Capital LLC

Structured Finance

Author : Umberto Cherubini
Publisher : John Wiley & Sons
ISBN 13 : 9780470512722
Total Pages : 298 pages
Book Rating : 4.5/5 (127 download)

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Book Synopsis Structured Finance by : Umberto Cherubini

Download or read book Structured Finance written by Umberto Cherubini and published by John Wiley & Sons. This book was released on 2007-04-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structured Finance: The Object Orientated Approach is aimed at both the finance and IT professionals involved in the structured finance business with the intention of sharing common concepts and language within the industry. The financial community (structurers, pricers and risk managers) view structured products as collections of objects under the so-called replicating portfolio paradigm. The IT community use object oriented programming (OOP) techniques to improve the software updating and maintenance process. For them structured products are collections of objects as well. Despite use of the same object concept, it looks like communication between these different professional functions has been problematic. Recently, construction of standard data structures known as FpML has begun to lay out a common definition of objects, at least for plain vanilla derivatives, both between IT and financial people and across different market players. Along this line, this book builds upon the concept of object to provide frontier treatment of structured finance issues relevant to both communities engaged in building, pricing and hedging products and people engaged in designing and up-dating the corresponding software. Structured Finance: The Object Orientated Approach will enable you to: decompose a structured product in elementary constituent financial objects and risk factors (replicating portfolio) understand the basics of object oriented programming (OOP) applied to the design of structured cash flows objects build your own objects and to understand FpML data structures available for standard products gauge risk exposures of the objects in structured products to: risk factors, their volatilities and the correlation among them (which factor are you long/short? Are you long/short volatility? Are you long/short correlation?) update your risk management system to accommodate structured products with non linear exposures and to design objects to represent, price and hedge, counterparty risk