# Financial Engineering and Computation: Principles, Mathematics, Algorithms

Cambridge University Press, 2002 - Business & Economics - 627 pages
Nowadays students and professionals intending to work in any area of finance must master not only advanced concepts and mathematical models but also learn how to implement these models computationally. This comprehensive text combines the theory and mathematics behind financial engineering with an emphasis on computation, in keeping with the way financial engineering is practiced in today's capital markets. Unlike most books on investments, financial engineering, or derivative securities, the book starts from very basic ideas in finance and gradually builds up the theory. It offers a thorough grounding in the subject for MBAs in finance, students of engineering and sciences who are pursuing a career in finance, researchers in computational finance, system analysts, and financial engineers. Along with the theory, the author presents numerous algorithms for pricing, risk management, and portfolio management. The emphasis is on pricing financial and derivative securities: bonds, options, futures, forwards, interest rate derivatives, mortgage-backed securities, bonds with embedded options, and more. Each instrument is treated in a short, self-contained chapter for ready reference use. Many of these algorithms are coded in Java as programs for the Web, available from the book's home page (www.csie.ntu.edu/~lyuu/Capitals/capitals.htm)

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### Contents

 Analysis of Algorithms 7 Bond Price Volatility 32 Term Structure of Interest Rates 45 Option Basics 75 Arbitrage in Option Pricing 84 Option Pricing Models 92 Sensitivity Analysis of Options 123 Extensions of Options Theory 131
 Time Series Analysis 284 Interest Rate Derivative Securities 295 Term Structure Fitting 321 Introduction to Term Structure Modeling 328 Foundations of Term Structure Modeling 345 Equilibrium Term Structure Models 361 NoArbitrage Term Structure Models 375 FixedIncome Securities 399

 Forwards Futures Futures Options Swaps 155 Stochastic Processes and Brownian Motion 177 ContinuousTime Financial Mathematics 190 ContinuousTime Derivatives Pricing 206 Hedging 224 Trees 234 Numerical Methods 249 Matrix Computation 268
 Introduction to MortgageBacked Securities 415 Analysis of MortgageBacked Securities 427 Collateralized Mortgage Obligations 451 Modern Portfolio Theory 458 Software 480 Bibliography 553 Glossary of Useful Notations 585 Copyright