Introduction

Building on mathematical models of bond and stock prices, the course leverage the two theories in different directions: Black-Scholes arbitrage pricing of options and other derivative securities on the one hand, and Markowitz portfolio optimization and the Capital Asset Pricing Model on the other hand. Models based on the principle of no-arbitrage can also be developed to study interest rates and their term structure. These are three major areas of mathematical finance, all having an enormous impact on the way modern financial markets operate. The course presents the topics at an introductory level aimed at senior undergraduate students, not only of mathematics, but also business management, finance, or economics.
Prerequisite: Having taken an undergraduate course in business information systems or by permission of the instructor.

Course Outcomes

After successful completion of this course, students will be able to

• Understand basic financial concepts in FE, e.g., time value of money and no-arb pricing
• Build discrete-time models, e.g., binomial trees
• Develop continuous-time models, e.g., Brownian motion
• Value different asset classes and derivatives
• Perform statistical and numerical analysis

Textbook

Mathematics for Finance: An Introduction to Financial Engineering 2nd ed. 2011 Edition by Marek Capiński and Tomasz Zastawniak (CZ)

Additional References

1. Paul Wilmott Introduces Quantitative Finance (second edition)
2. Risk Management and Financial Institutions (Wiley Finance) 4th Edition by John C. Hull
3. Practical Methods of Financial Engineering and Risk Management: Tools for Modern Financial Professionals by Rupak Chatterjee

Grading Policies