Exotic Options Pricing Under Stochastic Volatility
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Exotic Options Pricing Under Stochastic Volatility
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Author : Nabil Tahani
language : en
Publisher:
Release Date : 2012
Exotic Options Pricing Under Stochastic Volatility written by Nabil Tahani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
This paper proposes an analytical approximation to price exotic options within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, we derive an approximation for option prices using a Taylor expansion around two average defined volatilities. The moments of the average volatilities are computed analytically at any order using a Frobenius series solution to some ordinary differential equation. Pricing some exotics such as barrier and digital barrier options, the approximation is found to be very efficient and convergent even at low Taylor expansion order.
Exotic Options Pricing Under Stochastic Volatility Framework
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Author : 翟雲飛
language : en
Publisher:
Release Date : 2012
Exotic Options Pricing Under Stochastic Volatility Framework written by 翟雲飛 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Options (Finance) categories.
Exotic Option Pricing In Heston S Stochastic Volatility Model
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Author : Susanne A. Griebsch
language : en
Publisher:
Release Date : 2008
Exotic Option Pricing In Heston S Stochastic Volatility Model written by Susanne A. Griebsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Exotic Options And Hybrids
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Author : Mohamed Bouzoubaa
language : en
Publisher: John Wiley & Sons
Release Date : 2010-03-30
Exotic Options And Hybrids written by Mohamed Bouzoubaa and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-30 with Business & Economics categories.
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.
Exotic Option Pricing And Advanced L Vy Models
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Author : Andreas Kyprianou
language : en
Publisher: John Wiley & Sons
Release Date : 2006-06-14
Exotic Option Pricing And Advanced L Vy Models written by Andreas Kyprianou and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-14 with Business & Economics categories.
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
Pricing And Hedging Exotic Options In Stochastic Volatility Models
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Author : Zhanyu Chen
language : en
Publisher:
Release Date : 2013
Pricing And Hedging Exotic Options In Stochastic Volatility Models written by Zhanyu Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Emerging Financial Derivatives
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Author : Jerome Yen
language : en
Publisher: Routledge
Release Date : 2014-11-27
Emerging Financial Derivatives written by Jerome Yen and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Business & Economics categories.
Exotic options and structured products are two of the most popular financial products over the past ten years and will soon become very important to the emerging markets, especially China. This book first discusses the products' recent development in the world and provides comprehensive overview of the major products. The book also discusses the risks of issuing and buying such products as well as the techniques to price them and to assess the risks. Volatility is the most important factor in determining the return and risk. Therefore, significant part of the book's content discusses how we can measure the volatility by using local and stochastic volatility models — Heston Model and Dupire Model, the volatility surface, the term structure of volatility, variance swaps, and breakeven volatility. The book introduces a set of dimensions which can be used to describe structured products to help readers to classify them. It also describes the more commonly traded exotic options with details. The book discusses key features of each exotic option which can be used to develop structured products and covers their pricing models and when to issue such products that contain such exotic options. This book contains several case studies about how to use the models or techniques to price and hedge risks. These case analyses are illuminating.
Exotic Option Pricing In Stochastic Volatility Levy Models And With Fractional Brownian Motion
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Author : Ferdinand Graf
language : en
Publisher:
Release Date : 2007
Exotic Option Pricing In Stochastic Volatility Levy Models And With Fractional Brownian Motion written by Ferdinand Graf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
An Introduction To Exotic Option Pricing
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Author : Peter Buchen
language : en
Publisher: CRC Press
Release Date : 2012-02-03
An Introduction To Exotic Option Pricing written by Peter Buchen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-03 with Mathematics categories.
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.
The Hybrid Stochastic Local Volatility Model With Applications In Pricing Fx Options
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Author : Yu Tian
language : en
Publisher:
Release Date : 2013
The Hybrid Stochastic Local Volatility Model With Applications In Pricing Fx Options written by Yu Tian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. On the other hand, the local volatility model can reproduce the implied volatility surface, whereas it does not consider the stochastic behaviour of the volatility. To combine the advantages of stochastic volatility (SV) and local volatility (LV) models, a class of stochastic-local volatility (SLV) models has been developed. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In the thesis, we first review the fundamental theories of stochastic differential equations and the classic option pricing models, and study the behaviour of the volatility in the context of FX market. We then introduce the SLV model and illustrate our implementation of the calibration and pricing procedure. We apply the SLV model to exotic option pricing in the FX market and compare pricing results of the SLV model with pure local volatility and pure stochastic volatility models. Numerical results show that the SLV model can match the implied volatility surface very well as well as improve the pricing performance for barrier options. In addition, we further discuss some extensions of the SLV project, such as parallelization potential for accelerating option pricing and pricing techniques for window barrier options. Although the SLV model we use in the thesis is not entirely new, we contribute to the research in the following aspects: 1) we investigate the hybrid volatility modeling thoroughly from theoretical backgrounds to practical implementations; 2) we resolve some critical issues in implementing the SLV model such as developing a fast and stable numerical method to derive the leverage function; and 3) we build a robust calibration and pricing platform under the SLV model, which can be extended for practical uses.