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.
This book has evolved from several mathematics courses that the authors have taught mainly within the bachelor’s and master’s programs in ﬁnancial mathematics at Wilfrid Laurier University. The contents of this book are a culmination of course material that spans over a decade of the authors’ teaching experiences, as well as course and curriculum development, in ﬁnancial mathematics programs at both undergraduate and master’s graduate levels. The material has been tested and reﬁned through years of classroom teaching experience. As the title suggests, this book is a comprehensive, self-contained, and uniﬁed treatment of the main theory and application of mathematical methods behind modern day ﬁnancial mathematics.
In writing this book, the authors have really strived to create a single volume that can be used as a complete standard university textbook for several interrelated courses in ﬁnancial mathematics at the undergraduate as well as graduate levels. As such, the authors have aimed to introduce both the ﬁnancial theory and the relevant mathematical methods in a mathematically rigorous, yet student-friendly and engaging style, that includes an abundance of examples, problem exercises, and fully worked out solutions. In contrast to most published single volumes on the subject of ﬁnancial mathematics, this book presents multiple problem solving approaches and hence bridges together related comprehensive techniques for pricing diﬀerent types of ﬁnancial derivatives. The book contains a rather complete and in-depth comprehensive coverage of both discrete-time and continuous-time ﬁnancial models that form the cornerstones of ﬁnancial derivative pricing theory.
This book also provides a self-contained introduction to stochastic calculus and martingale theory, which are important cornerstones in quantitative ﬁnance. The material in many of the chapters is presented at a level that is mainly accessible to undergraduate students of mathematics, ﬁnance, actuarial science, economics, and other related quantitative ﬁelds. The textbook covers a breadth of material, from beginner to more advanced levels, that is required, i.e., absolutely essential, in the core curriculum courses on ﬁnancial mathematics currently taught at the second, third, and senior year undergraduate levels at many universities across the globe. As well, a signiﬁcant portion of the more advanced material in the textbook is meant to be used in courses at the master’s graduate level. These courses include formal derivative pricing theory, stochastic calculus, and courses in simulation (Monte Carlo) and other numerical methods. The combination of analytical and numerical methods for solving various derivative pricing problems can also be a useful reference for researchers and practitioners in quantitative ﬁnance.
The book has the following key features:
- Comprehensive treatment covering a complete undergraduate program in ﬁnancial mathematics as well as some master’s level courses in ﬁnancial mathematics;
- Student-friendly presentation with numerous fully worked out examples and exercise problems in every chapter;
- In-depth coverage of both discrete-time and continuous-time theory and methodology;
- Mathematically rigorous and consistent, yet simple, style that bridges various basic and more advanced concepts and techniques;
- Judicious balance of ﬁnancial theory, mathematical, and computational methods.
- Mathematics of Compounding
- Primer on Pricing Risky Securities
- Portfolio Management
- Primer on Derivative Securities
- 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
- 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
- Interest-Rate Modelling and Derivative Pricing
- Alternative Models of Asset Price Dynamics
- Introduction to Monte Carlo and Simulation Methods
- Numerical Applications to Derivative Pricing