Financial Mathematics

Financial Mathematics: A Comprehensive Treatment

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ISBN 9781439892428
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Features

  • Provides material for a complete undergraduate program in financial mathematics as well as some master’s level courses
  • Uses a mathematically rigorous yet simple, student-friendly style that bridges basic concepts and techniques with more advanced ones
  • Presents balanced coverage of financial theory and mathematical/computational methods
  • Gives an in-depth treatment of both discrete- and continuous-time theory and methodology
  • Includes numerous fully worked out examples and exercises in every chapter

Solutions manual available upon qualifying course adoption

Summary

Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels

Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones.

Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems.

With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.

Table of Contents

INTRODUCTION TO PRICING AND MANAGEMENT OF FINANCIAL SECURITIES
Mathematics of Compounding
Primer on Pricing Risky Securities
Portfolio Management
Primer on Derivative Securities

DISCRETE-TIME MODELING
Single-Period Arrow-Debreu Models
Introduction to Discrete-Time Stochastic Calculus
Replication and Pricing in the Binomial Tree Model
General Multi-Asset Multi-Period Model

CONTINUOUS-TIME MODELING
Essentials of General Probability Theory
One-Dimensional Brownian Motion and Related Processes
Introduction to Continuous-Time Stochastic Calculus
Risk-Neutral Pricing in the (B, S) Economy: One Underlying Stock
Risk-Neutral Pricing in a Multi-Asset Economy
American Options
Alternative Models of Asset Price Dynamics
Interest-Rate Modeling and Derivative Pricing

COMPUTATIONAL TECHNIQUES
Introduction to Monte Carlo and Simulation Methods
Numerical Applications to Derivative Pricing

Appendix: Some Useful Integral Identities and Symmetry Properties of Normal Random Variables

Glossary of Symbols and Abbreviations

References

Index

Editorial Reviews

"As the owner of literally thousands of books on the mathematics of arbitrage, I’m sorely tempted to sell my collection and buy this book as a replacement. Or better yet, one for the office and one for the home office. I commend the authors for their authoritative and comprehensive treatment."
—Peter Carr, PhD, Managing Director, Morgan Stanley, and Executive Director, NYU Courant Master of Science Program in Mathematics in Finance

"This is a monumental effort to bring together topics from quantitative finance into one book; one no longer needs to go to different references to get the full scope of contents in the book. The authors treat the subjects rigorously but with plenty of examples, paying close attention to an audience that may encounter the subject matter for the first time, but aware that others will have seen it in different form earlier and may be looking for a different angle. This is a book that will find its way into classrooms worldwide."
—Luis Seco, Professor, Department of Mathematics, University of Toronto