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Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)

Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)

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Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)

Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)

4.85 34,712 ratings · 62,960 reviews
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Overview: The world of quantitative finance (QF) is one of the fastestgrowing areas of research and its practical applications toderivatives pricing problem. Since the discovery of the famousBlack-Scholes equation in the 1970's we have seen a surge in thenumber of models for a wide range of products such as plain andexotic options, interest rate derivatives, real options and manyothers. Gone are the days when it was possible to price thesederivatives analytically. For most problems we must resort to somekind of approximate method. In this book we employ partial differential equations (PDE) todescribe a range of one-factor and multi-factor derivativesproducts such as plain European and American options, multi-assetoptions, Asian options, interest rate options and real options. PDEtechniques allow us to create a framework for modeling complex andinteresting derivatives products. Having defined the PDE problem wethen approximate it using the Finite Difference Method (FDM). Thismethod has been used for many application areas such as fluiddynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques topricing real-life derivative products. We use both traditional (orwell-known) methods as well as a number of advanced schemes thatare making their way into the QF literature:Crank-Nicolson, exponentially fitted and higher-order schemesfor one-factor and multi-factor optionsEarly exercise features and approximation using front-fixing, penalty and variational methodsModelling stochastic volatility models using SplittingmethodsCritique of ADI and Crank-Nicolson schemes; when they work andwhen they don't workModelling jumps using Partial Integro Differential Equations(PIDE)Free and moving boundary value problems in QFIncluded with the book is a CD containing information on how toset up FDM algorithms, how to map these algorithms to C++ as wellas several working programs for one-factor and two-factor models.We also provide source code so that you can customize theapplications to suit your own needs.

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Published March 30, 2006
ISBN 2047978
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Daniel J. Duffy
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Daniel J. Duffy
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Daniel J. Duffy is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Daniel J. Duffy can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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David Adams
David Adams October 06, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Laura Lee
Laura Lee July 07, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Rebecca Rodriguez
Rebecca Rodriguez February 02, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
John Green
John Green July 03, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Michael Robinson
Michael Robinson July 03, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Ryan Martinez
Ryan Martinez March 16, 2024
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Susan Baker
Susan Baker March 07, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Carol Smith
Carol Smith December 06, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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Eric Green June 12, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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Christopher Mitchell January 06, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Andrew Wilson May 05, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Edward Rivera June 16, 2024
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Sandra Collins December 04, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Nancy Taylor January 15, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Ryan Moore
Ryan Moore May 21, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Deborah Taylor
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I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Jennifer Baker March 11, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Carol Thompson
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Richard Thomas
Richard Thomas October 25, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Kimberly Hill July 10, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Mary Gonzalez October 03, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Michael Martin
Michael Martin July 16, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
Thomas Harris
Thomas Harris September 13, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Deborah Taylor
Deborah Taylor November 29, 2025
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Donald Thomas
Donald Thomas June 20, 2025
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Edward Cruz July 09, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Charles Lee
Charles Lee August 13, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Edward Rivera
Edward Rivera December 12, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Carol Hernandez
Carol Hernandez June 02, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Donald Lee
Donald Lee July 04, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Brian Adams December 21, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Kevin Taylor
Kevin Taylor January 20, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Sharon Scott July 11, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Christopher Thompson
Christopher Thompson January 20, 2024
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Nancy Diaz
Nancy Diaz October 18, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Eric White
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Joshua Nelson
Joshua Nelson September 12, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Joshua Martinez
Joshua Martinez October 16, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Deborah Jackson
Deborah Jackson March 15, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Joshua Flores
Joshua Flores June 29, 2024
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
Nicholas Walker
Nicholas Walker October 04, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Kenneth Allen
Kenneth Allen November 01, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Melissa Allen
Melissa Allen December 17, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Sandra Scott
Sandra Scott May 19, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Barbara Harris
Barbara Harris October 02, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Lisa Clark
Lisa Clark October 21, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Deborah Anderson
Deborah Anderson October 11, 2025
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Richard Hall
Richard Hall September 18, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Sarah Walker
Sarah Walker February 22, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Brian Robinson
Brian Robinson March 12, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
David Hernandez
David Hernandez August 25, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Robert Flores
Robert Flores October 12, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Karen Lopez
Karen Lopez July 03, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Robert Hernandez
Robert Hernandez February 17, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Gary Martin
Gary Martin March 23, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Brian Roberts
Brian Roberts January 18, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Donna Scott
Donna Scott September 09, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Carol Nguyen
Carol Nguyen June 20, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
George  Parker
George Parker December 30, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
George Evans
George Evans July 18, 2024
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Stephanie Ramirez
Stephanie Ramirez February 16, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
George Diaz
George Diaz May 03, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Edward Campbell
Edward Campbell May 02, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Joshua Flores
Joshua Flores March 21, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Paul Jackson
Paul Jackson January 02, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Thomas Harris
Thomas Harris June 27, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Andrew Lopez
Andrew Lopez May 28, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Lisa Scott
Lisa Scott April 18, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Donna Young
Donna Young October 24, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Joshua  Parker
Joshua Parker February 25, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Michelle Martin
Michelle Martin May 23, 2024
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Betty Mitchell
Betty Mitchell November 25, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Richard Hall
Richard Hall June 29, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Nancy Rodriguez
Nancy Rodriguez October 27, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Amanda White
Amanda White April 24, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Nancy  Parker
Nancy Parker March 09, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Deborah Gomez
Deborah Gomez January 16, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Barbara Torres
Barbara Torres February 23, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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