an introduction to exotic option pricing

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An Introduction To Exotic Option Pricing

Author : Peter Buchen
ISBN : 9781420091007
Genre : Mathematics
File Size : 74. 45 MB
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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 The author incorporates much of his own unpublished work, including ideas and techniques new to the general quantitative finance community. The first part of the text presents the necessary financial, mathematical, and statistical background, covering both standard and specialized topics. Using no-arbitrage concepts, the Black–Scholes model, and the fundamental theorem of asset pricing, the author develops such specialized methods as the principle of static replication, the Gaussian shift theorem, and the method of images. A key feature is the application of the Gaussian shift theorem and its multivariate extension to price exotic options without needing a single integration. The second part focuses on applications to exotic option pricing, including dual-expiry, multi-asset rainbow, barrier, lookback, and Asian options. Pushing Black–Scholes option pricing to its limits, the author introduces a powerful formula for pricing a class of multi-asset, multiperiod derivatives. He gives full details of the calculations involved in pricing all of the exotic options. Taking an applied mathematics approach, this book illustrates how to use straightforward techniques to price a wide range of exotic options within the Black–Scholes framework. These methods can even be used as control variates in a Monte Carlo simulation of a stochastic volatility model.

Exotic Options And Hybrids

Author : Mohamed Bouzoubaa
ISBN : 047071008X
Genre : Business & Economics
File Size : 24. 78 MB
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The recent financial crisis brought to light many of the misunderstandings and misuses of exotic derivatives. With market participants on both the buy and sell-side having been found guilty of not understanding the products they were dealing with, never before has there been a greater need for clarification and explanation. Exotic Options and Hybrids is a practical guide to structuring, pricing and hedging complex exotic options and hybrid derivatives that will serve readers through the recent crisis, the road to recovery, the next bull market and beyond. Written by experienced practitioners, it focuses on the three main parts of a derivative’s life: the structuring of a product, its pricing and its hedging. Divided into four parts, the book covers a multitude of structures, encompassing many of the most up-to-date and promising products from exotic equity derivatives and structured notes to hybrid derivatives and dynamic strategies. Based on a realistic setting from the heart of the business, inside a derivatives operation, the practical and intuitive discussions of these aspects make these exotic concepts truly accessible. Adoptions of real trades are examined in detail, and all of the numerous examples are carefully selected so as to highlight interesting and significant aspects of the business. The introduction of payoff structures is accompanied by scenario analysis, diagrams and lifelike sample term sheets. Readers learn how to spot where the risks lie to pave the way for sound valuation and hedging of such products. There are also questions and accompanying discussions dispersed in the text, each exploited to illustrate one or more concepts from the context in which they are set. The applications, the strengths and the limitations of various models are highlighted, in relevance to the products and their risks, rather than the model implementations. Models are de-mystified in separately dedicated sections, but their implications are alluded to throughout the book in an intuitive and non-mathematical manner. By discussing exotic options and hybrids in a practical, non-mathematical and highly intuitive setting, this book will blast through the misunderstanding of exotic derivatives, enabling practitioners to fully understand and correctly structure, price and hedge theses products effectively, and stand strong as the only book in its class to make these “exotic” concepts truly accessible.

Dynamic Hedging

Author : Nassim Taleb
ISBN : 0471152803
Genre : Business & Economics
File Size : 22. 61 MB
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Dynamic Hedging is the definitive source on derivatives risk. Itprovides a real–world methodology for managing portfolioscontaining any nonlinear security. It presents risks from thevantage point of the option market maker and arbitrage operator.The only book about derivatives risk written by an experiencedtrader with theoretical training, it remolds option theory to fitthe practitioner′s environment. As a larger share of marketexposure cannot be properly captured by mathematical models, notedoption arbitrageur Nassim Taleb uniquely covers both on–model andoff–model derivatives risks. The author discusses, in plain English, vital issues,including: The generalized option, which encompasses all instruments withconvex payoff, including a trader′s potential bonus. The techniques for trading exotic options, including binary,barrier, multiasset, and Asian options, as well as methods to takeinto account the wrinkles of actual, non–bellshapeddistributions. Market dynamics viewed from the practitioner′s vantage point,including liquidity holes, portfolio insurance, squeezes, fattails, volatility surface, GARCH, curve evolution, static optionreplication, correlation instability, Pareto–Levy, regime shifts,autocorrelation of price changes, and the severe flaws in the valueat risk method. New tools to detect risks, such as higher moment analysis,topography exposure, and nonparametric techniques. The path dependence of all options hedged dynamically. Dynamic Hedging is replete with helpful tools, market anecdotes,at–a–glance risk management rules distilling years of market lore,and important definitions. The book contains modules in which thefundamental mathematics of derivatives, such as the Brownianmotion, Ito′s lemma, the numeraire paradox, the Girsanov change ofmeasure, and the Feynman–Kac solution are presented in intuitivepractitioner′s language. Dynamic Hedging is an indispensable and definitive reference formarket makers, academics, finance students, risk managers, andregulators. The definitive book on options trading and risk management "If pricing is a science and hedging is an art, Taleb is avirtuoso." –Bruno Dupire, Head of Swaps and Options Research,Paribas Capital Markets "This is not merely the best book on how options trade, it isthe only book." –Stan Jonas, Managing Director, FIMAT–SocietyGARCH "Dynamic Hedging bridges the gap between what the besttraders know and what the best scholars can prove." –WilliamMargrabe, President, The William Margrabe Group, Inc. "The most comprehensive, insightful, intuitive work on thesubject. It is instrumental for both beginning and experiencedtraders."– "A tour de force. That rare find, a book of great practical andtheoretical value. Taleb successfully bridges the gap between theacademic and the real world. Interesting, provocative, wellwritten. Each chapter worth a fortune to any current or prospectivederivatives trader."–Victor Niederhoffer, Chairman, NiederhofferInvestments

Exotic Options

Author : P G Zhang
ISBN : 9789814549400
Genre :
File Size : 41. 4 MB
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This book provides the first systematic classification and treatment to essentially all exotic options currently trading at the Over-the-Counter (OTC) market. It contains exact closed-form pricing formulae and approximated closed-form pricing formulae for all popular exotic options. It includes arguments for and pricing formulae of exotic options with more flexibility than most popular exotic options such as flexible Asian options with flexible weights to various observations in the average, Asian barrier options, correlation digital options, etc. Most of the analyses in this book are within the Black-Scholes environment so that comparisons of each type of exotic options with the Black-Scholes model can be made readily. Emphases have been paid to illustrate the ideas of products clearly and show how to use the pricing expressions conveniently. The book contains many pricing formulae and analyses which do not exist in the literature. The book is suitable for traders, analysts, risk managers, marketers, sales people, professionals in the derivatives industry, and financial professionals in general who have an interest in the concurrent status of the exotic derivatives market. It is also of great interest to professors and graduate students who want to catch up with the ever growing innovation process in the derivatives industry. Scientists, engineers, computer programers, and other professionals may also find the book an efficient way to grasp some financial ideas and connect financial products with mathematical tools. OR This is the first systematic and extensive book on exotic options. The book covers essentially all popular exotic options currently trading in the Over-the-Counter (OTC) market, from digitals, quantos, spread options, lookback options, Asian options, vanilla barrier options, to various types of exotic barrier options and other options. Each type of exotic options is largely written in a separate chapter, beginnning with the basic concepts of the products and then moving on to how to price them in closed-form solutions. Many pricing formulae and analyses which have not previously appeared in the literature are included and illustrated with detailed examples. It will be of great interest to traders, marketers, analysts, risk managers, professors, graduate students, and anyone who is interested in what is going on in the rapidly changing financial market. Contents:From Vanilla Options to Exotic OptionsOption Pricing MethodologyVanilla OptionsAmerican OptionsAsian OptionsApproximating Arithmetic Asian Options with Corresponding Geometric Asian OptionsFlexible Arithmetic Asian OptionsForward-Start OptionsOne-Clique OptionsVanilla Barrier OptionsExotic Barrier OptionsLookback OptionsExchange OptionsOptions Paying the Best/Worst and CashStandard Digital Options and Correlation Digital OptionsQuotient OptionsProduct Options and Foreign Domestic OptionsForeign Equity OptionsEquity-Linked Foreign Exchange OptionsQuanto OptionsRainbow OptionsSpread OptionsSpread Over the RainbowsDual-Strike OptionsOut-Performance OptionsAlternative OptionsBasket OptionsPricing Correlation Options with Uncertain Correlation CoefficientsPackage or Hybrid OptionsNonlinear Payoff OptionsCompound OptionsChooser OptionsContingent Premium OptionsOther Exotic OptionsHedging Exotic OptionsFurther DevelopmentPayoff Functions for Various OptionsTable of Cumulative Function Values of the Standard Normal Distribution Readership: Professionals in the financial industry, interested general readers, and academics. keywords: “Zhang offers quite a few new and elegant results of his own, for example, a unified pricing formula for all sorts of barrier options, a refined approach to approximate arithmetic Asian options, a closed-form solution for spread options, etc … it is the first organized treatment of the valuation of these products … Zhang provides a valuable service to the industry through his collating of extant literature on exotic options and through his own contributions to the valuation of these products. I highly recommend this book for those interested in this growing product area.” Journal of Financial Engineering

Exotic Option Pricing And Advanced L Vy Models

Author : Andreas Kyprianou
ISBN : 9780470017203
Genre : Business & Economics
File Size : 49. 85 MB
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Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward

The Mathematics Of Derivatives Securities With Applications In Matlab

Author : Mario Cerrato
ISBN : 9781119973416
Genre : Business & Economics
File Size : 67. 32 MB
Format : PDF
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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.

Exotic Options Trading

Author : Frans de Weert
ISBN : 1119995183
Genre : Business & Economics
File Size : 26. 58 MB
Format : PDF
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Written by an experienced trader and consultant, Frans de Weert’s Exotic Options Trading offers a risk-focused approach to the pricing of exotic options. By giving readers the necessary tools to understand exotic options, this book serves as a manual to equip the reader with the skills to price and risk manage the most common and the most complex exotic options. De Weert begins by explaining the risks associated with trading an exotic option before dissecting these risks through a detailed analysis of the actual economics and Greeks rather than solely stating the mathematical formulae. The book limits the use of mathematics to explain exotic options from an economic and risk perspective by means of real life examples leading to a practical interpretation of the mathematical pricing formulae. The book covers conventional options, digital options, barrier options, cliquets, quanto options, outperformance options and variance swaps, and explains difficult concepts in simple terms, with a practical approach that gives the reader a full understanding of every aspect of each exotic option. The book also discusses structured notes with exotic options embedded in them, such as reverse convertibles, callable and puttable reverse convertibles and autocallables and shows the rationale behind these structures and their associated risks. For each exotic option, the author makes clear why there is an investor demand; explains where the risks lie and how this affects the actual pricing; shows how best to hedge any vega or gamma exposure embedded in the exotic option and discusses the skew exposure. By explaining the practical implications for every exotic option and how it affects the price, in addition to the necessary mathematical derivations and tools for pricing exotic options, Exotic Options Trading removes the mystique surrounding exotic options in order to give the reader a full understanding of every aspect of each exotic option, creating a useable tool for dealing with exotic options in practice. “Although exotic options are not a new subject in finance, the coverage traditionally afforded by many texts is either too high level or overly mathematical. De Weert's exceptional text fills this gap superbly. It is a rigorous treatment of a number of exotic structures and includes numerous examples to clearly illustrate the principles. What makes this book unique is that it manages to strike a fantastic balance between the theory and actual trading practice. Although it may be something of an overused phrase to describe this book as compulsory reading, I can assure any reader they will not be disappointed.” —Neil Schofield, Training Consultant and author of Commodity Derivatives: Markets and Applications “Exotic Options Trading does an excellent job in providing a succinct and exhaustive overview of exotic options. The real edge of this book is that it explains exotic options from a risk and economical perspective and provides a clear link to the actual profit and pricing formulae. In short, a must read for anyone who wants to get deep insights into exotic options and start trading them profitably.” —Arturo Bignardi

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