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＜電子ブック＞
Derivative Securities and Difference Methods / by You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
(Springer Finance. ISSN:21950687)

版	2nd ed. 2013.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	XXII, 647 p : online resource
著者標目	*Zhu, You-lan author Wu, Xiaonan author Chern, I-Liang author Sun, Zhi-zhong author SpringerLink (Online service)
件　名	LCSH:Social sciences -- Mathematics  全ての件名で検索 LCSH:Differential equations LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Numerical analysis LCSH:Finance FREE:Mathematics in Business, Economics and Finance FREE:Differential Equations FREE:Computational Mathematics and Numerical Analysis FREE:Numerical Analysis FREE:Financial Economics
一般注記	Introduction -- European Style Derivatives -- American Style Derivatives -- Exotic Options -- Interest Rate Derivative Securities -- Basic Numerical Methods -- Finite Difference Methods -- Initial-Boundary Value and LC Problems -- Free-Boundary Problems -- Interest Rate Modeling This book is mainly devoted to finite difference numerical methods for solving partial differential equation (PDE) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts. In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE initial/initial-boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems. In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods of financial derivatives. For this new edition, the book has been updated throughout with many new problems added. More details about numerical methods for some options, for example, Asian options with discrete sampling, are provided and the proof of solution-uniqueness of derivative security problems and the complete stability analysis of numerical methods for two-dimensional problems are added. Review of first edition: “…the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS, 2005 HTTP:URL=https://doi.org/10.1007/978-1-4614-7306-0

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