Exotic Option Pricing and Advanced Lévy Models

Exotic Option Pricing and Advanced Lévy Models
Author: Andreas Kyprianou
Publisher: John Wiley & Sons
Total Pages: 344
Release: 2006-06-14
Genre: Business & Economics
ISBN: 0470017201

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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

Exotic Options and Hybrids

Exotic Options and Hybrids
Author: Mohamed Bouzoubaa
Publisher:
Total Pages: 372
Release: 2010
Genre: Exotic options (Finance)
ISBN: 9781119206965

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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. iExotic Options and Hybrids/i 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.

An Introduction to Exotic Option Pricing

An Introduction to Exotic Option Pricing
Author: Peter Buchen
Publisher: CRC Press
Total Pages: 298
Release: 2012-02-03
Genre: Mathematics
ISBN: 142009100X

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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.

Advanced Option Pricing Models

Advanced Option Pricing Models
Author: Jeffrey Owen Katz
Publisher: McGraw Hill Professional
Total Pages: 449
Release: 2005-03-21
Genre: Business & Economics
ISBN: 0071454705

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Advanced Option Pricing Models details specific conditions under which current option pricing models fail to provide accurate price estimates and then shows option traders how to construct improved models for better pricing in a wider range of market conditions. Model-building steps cover options pricing under conditional or marginal distributions, using polynomial approximations and “curve fitting,” and compensating for mean reversion. The authors also develop effective prototype models that can be put to immediate use, with real-time examples of the models in action.

American and Exotic Option Pricing with Jump Diffusions and Other Lévy Processes

American and Exotic Option Pricing with Jump Diffusions and Other Lévy Processes
Author: Justin Kirkby
Publisher:
Total Pages: 33
Release: 2017
Genre:
ISBN:

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In general, no analytical formulas exist for pricing discretely monitored exotic options, even when a geometric Brownian motion governs the risk-neutral underlying. While specialized numerical algorithms exist for pricing particular contracts, few can be applied universally with consistent success and with general Lévy dynamics. This paper develops a general methodology for pricing early exercise and exotic financial options by extending the recently developed PROJ method. We are able to efficiently obtain accurate values for complex products including Bermudan/American options, Bermudan barrier options, survival probabilities and credit default swaps by value recursion, European barrier and lookback/hindsight options by density recursion, and arithmetic Asian options by characteristic function recursion. This paper presents a unified approach to tackling these and related problems. Algorithms are provided for each option type, along with a demonstration of convergence. We also provide a large set of reference prices for exotic, American and European options under Black-Scholes-Merton, Normal Inverse Gaussian, Kou's double exponential jump diffusion, Variance Gamma, KoBoL/CGMY and Merton's jump diffusion models.

Exotic Options

Exotic Options
Author: Peter G. Zhang
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 692
Release: 1998
Genre: Business & Economics
ISBN: 9789810234829

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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, beginning 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.