This textbook contains the fundamentals for an undergraduate course in mathematical finance aimed primarily at students of mathematics. Assuming only a basic knowledge of probability and calculus, the material is presented in a mathematically rigorous and complete way. The book covers the time value of money, including the time structure of interest rates, bonds and stock valuation; derivative securities (futures, options), modelling in discrete time, pricing and hedging, and many other core topics. With numerous examples, problems and exercises, this book is ideally suited for independent study.

Introduction: A Simple Market Model.- Risk-Free Assets.- Risky Assets.- Discrete Time Market Models.- Portfolio Management.- Forward and Futures Contracts.- Options: General Properties.- Option Pricing.- Financial Engineering.- Variable Interest Rates.- Stochastic Interest Rates.