A Primer for the Mathematics of Financial Engineering

✍ Scribed by Dan Stefanica

• Publisher: FE Press
• Year: 2008
• Tongue: English
• Leaves: 305
• Edition: First Edition
• Category: Library

✦ Synopsis

This book is meant to build the solid mathematical foundation required to understand the quantitative models used financial engineering. The financial applications range from the Put-Call parity, bond duration and convexity, and the Black-Scholes model, to the numerical estimation of the Greeks, implied volatility, and bootstrapping for finding interest rate curves. On the mathematical side, useful but sometimes overlooked topics are presented in detail: differentiating integrals with respect to nonconstant integral limits, numerical approximation of definite integrals, convergence of Taylor series expansions, finite difference approximations, Stirling's formula, Lagrange multipliers, polar coordinates, Newton's method for higher dimensional problems. A Solutions Manual containing complete solutions to every exercise, as well as to over 50 supplemental exercises, is available on amazon.com. International shipping and the Errata are available at www.fepress.org

✦ Table of Contents

Front Cover......Page 1
Back Cover......Page 2
Copyright......Page 6
Contents......Page 9
List of Tables......Page 13
Preface......Page 15
Acknowledgments......Page 17
How to Use This Book......Page 19
0. Mathematical preliminaries......Page 21
1. Calculus review. Plain vanilla options.......Page 39
2. Improper integrals. Numerical integration. Interest Rates. Bonds.......Page 65
3. Probability concepts. Black-Scholes formula. Greeks and Hedging.......Page 101
4. Lognormal variables. Risk-neutral pricing.......Page 137
5. Taylor's formula and Taylor series. ATM approximation of Black-Scholes formulas.......Page 163
6. Finite Differences. Black-Scholes PDE.......Page 197
7. Multivariable calculus: chain rule, integration by substitution, and extremum points. Barrier options. Optimality of early exercise.......Page 223
8. Lagrange multipliers. N-dimensional Newton's method. Implied volatility. Bootstrapping.......Page 255
Bibliography......Page 299
Index......Page 302