An introduction to exotic option pricing
By: Peter Buchen
Series: Chapman & hall/CRC financial mathematics series
Publisher: Chapman and Hall/CRC
Published: 2012
Place of publication: Boca Raton
Language: eng
Number of pages: 302
ISBN-13: 9781420091007
Subjects: Options (Finance); Prices; MATHEMATICS / Probability & Statistics / General; MATHEMATICS / General; BUSINESS & ECONOMICS / Finance
Description: "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 The author incorporates much of his own unpublished work, including ideas and techniques new to the general quantitative finance community.The first part of the text presents the necessary financial,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"--

"Preface This book is a collection of a large amount of material developed from my teaching, research, and supervision of student projects and PhD theses. It also contains a significant quantity of original unpublished work. One of my main interests in Financial Mathematics was to seek elegant methods for pricing derivative securities. Although the literature on derivatives is vast, virtually none outside the academic journals, concentrates solely on pricing methods. Where it is considered, details are often glossed over, with comments like: "ʺ ʺ ʺ and after a length integration, we arrive at the result", or "ʺ ʺ ʺ this partial differential equation can be solved to yield the answer". In my experience, many students, even the mathematically gifted ones, found the subject of pricing any but the simplest derivatives, somewhat unsatisfactory and often quite daunting. One aim of this book is to correct the impression that exotic option pricing is a subject only for the technophiles. My plan is to present it in a mathematically elegant and easily understood fashion. To this end: I show in this book how to price, in a Black-Scholes economy, the standard exotic options, and a host of non-standard ones as well, without generally performing a single integration, or formally solving a partial differential equation. How is this to be achieved? In a nutshell, the book devotes a lot of space to developing specialized methods based on no-arbitrage concepts, the Black- Scholes model and the Fundamental Theorem of Asset Pricing. These include the Principal of Static Replication, the Gaussian Shift Theorem and the Method of Images. The last of these, which has been borrowed from Theoretical Physics, is ideally suited to pricing barrier and lookback options"--
Notes: Includes bibliographical references and index.