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Technically sophisticated undergraduates and graduates should be able to read it on their own. Mathematical materials are added where they are needed. In many instances, they provide the coupling between earlier chapters and upcoming themes. Applications to nance are generally added to set the stage. Numerical techniques are presented algorithmically and clearly; programming them should therefore be straightforward. The underlying nancial theory is adequately covered, as understanding the theory underlying the calculations is critical to nancial innovations.

The large number of exercises is an integral part of the text. Exercises are placed right after the relevant materials. Hints are provided for the more challenging ones.

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There are also numerous programming assignments. Those readers who aspire to become software developers can learn a lot by implementing the programming assignments. Thoroughly test your programs. The famous adage of Hamming , The purpose of computing is insight, not numbers, does not apply to erroneous codes. Answers to all nontrivial exercises and some programming assignments can be found near the end of the book.

Most of the graphics were produced with Mathematica []. It is a remarkable fact that most if not all of the programming works could have been done with spreadsheet software [, ]. Some computing platforms admit the integration of the spreadsheets familiar graphical user interface and programs written in more efcient high-level programming languages [].

Although such a level of integration requires certain sophistication, it is a common industry practice. Freehand graphics were created with Canvas and Visio. I thank Knuth and Lamport for their gifts to technical writers. Software Many algorithms in the book have been programmed.

Financial Engineering And Computation: Principles, Mathematics, And Algorithms

However, instead of being bundled with the book in disk, my software is Web-centric and platform-independent []. Any machine running a World Wide Web browser can serve as a host for those programs on The Capitals page at www. This new way of software development and distribution, made possible by the Web, has turned software into an Internet service. Organization Here is a grand tour of the book: Chapter 1 sets the stage and surveys the evolution of computer technology.

Chapter 2 introduces algorithm analysis and measures of complexity. My convention for expressing algorithms is outlined here. Chapter 3 contains a relatively complete treatment of standard nancial mathematics, starting from the time value of money. Chapter 4 covers the important concepts of duration and convexity.

Chapter 5 goes over the static term structure of interest rates. The coverage of classic, static nance theory ends here.


Chapter 6 marks the transition to stochastic models with coverage of statistical inference. Chapters are about options and derivatives. Chapter 7 presents options and basic strategies with options. Chapter 8 introduces the arbitrage argument and derives general pricing relations. Chapter 9 is a key chapter. It covers option pricing under the discrete-time binomial option pricing model.

The celebrated BlackScholes formulas are derived here, and algorithms for pricing basic options are presented. Chapter 10 presents sensitivity measures for options. Chapter 11 covers the diverse applications and kinds of options. Additional derivative securities such as forwards and futures are treated in Chap. Chapters introduce the essential ideas in continuous-time nancial mathematics.

Chapter 13 covers martingale pricing and Brownian motion, and Chap.

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Together they give a fairly complete treatment of the subjects at an accessible level. From time to time, we go back to discrete-time models and establish the linkage.

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Chapter 15 focuses on the partial differential equations that derivative securities obey. Chapter 16 covers hedging by use of derivatives. Chapters probe deeper into various technical issues. Chapter 17 investigates binomial and trinomial trees. One of the motives here is to demonstrate the use of combinatorics in designing highly efcient algorithms.

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Chapter 18 covers numerical methods for partial differential equations, Monte Carlo simulation, and quasi Monte Carlo methods. Chapter 19 treats computational linear algebra, least-squares problems, and splines. Factor models are presented as an application. Chapter 20 introduces nancial time series analysis as well as popular time-series models. Chapters are related to interest-rate-sensitive securities.

Chapter 21 surveys the wide varieties of interest rate derivatives. Chapter 22 discusses yield curve tting. Chapter 23 introduces interest rate modeling and derivative pricing with the elementary, yet important, binomial interest rate tree. Chapter 24 lays the mathematical foundations for interest rate models, and Chaps. Finally, Chap. Chapters are concerned with mortgage-backed securities.

Chapter 28 introduces the basic ideas, institutions, and challenging issues. Chapter 29 investigates the difcult problem of prepayment and pricing. Chapter 30 surveys collateralized mortgage obligations. Chapter 31 discusses the theory and practice of portfolio management. Chapter 32 documents the Web software developed for this book. Chapter 33 contains answers or pointers to all nontrivial exercises.

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This book ends with an extensive index. There are two guiding principles behind its structure. First, related concepts should be grouped together. Second, the index should facilitate search. An entry containing parentheses indicates that the term within should be consulted instead, rst at the current level and, if not found, at the outermost level.

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In particular, Andy Liao and Andy Sparks taught me a lot about the markets and quantitative skills. This book beneted greatly from the comments of several anonymous reviewers. As the rst readers of the book, their critical eyes made a lasting impact on its evolution. As with my rst book with Cambridge University Press, the editors at the Press were invaluable.