Financial mathematics: a comprehensive treatment in discrete time (Second edition.)

The book has been tested and refined through years of classroom teaching experience. 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.

This textbook provides complete coverage of discrete-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives.

Key features:

• In-depth coverage of discrete-time theory and methodology.
• Numerous, fully worked out examples and exercises in every chapter.
• Mathematically rigorous and consistent yet bridging various basic and more advanced concepts.
• Judicious balance of financial theory, mathematical, and computational methods.
• Guide to Material.

This revision contains:

• Almost 200 pages worth of new material in all chapters.
• A new chapter on elementary probability theory.
• An expanded the set of solved problems and additional exercises.
• Answers to all exercises.

This book is a comprehensive, self-contained, and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics.

List of Figures and Tables

Preface

I Introduction to Pricing and Management of Financial Securities

1 Mathematics of Compounding
2 Primer on Pricing Risky Securities

3 Portfolio Management

4 Primer on Derivative Securities

II Discrete-Time Modelling

5 Single-Period Arrow-Debreu Models

6 Introduction to Discrete-Time Stochastic Calculus

7 Replication and Pricing in the Binomial Tree Model

8 General Multi-Asset Multi-Period Model

Appendices

A Elementary Probability Theory

B Glossary of Symbols and Abbreviations

C Answers and Hints to Exercises

References

Index