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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Derivative Securities and Difference Methods (Paperback, Softcover reprint of the original 2nd ed. 2013)
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Derivative Securities and Difference Methods (Paperback, Softcover reprint of the original 2nd ed. 2013)
Series: Springer Finance
Expected to ship within 10 - 15 working days
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This book is mainly devoted to finite difference numerical methods
for solving partial differential equations (PDEs) 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
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 in
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
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