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: Prerequisites include elementary calculus, probability, and some linear algebra. For calculus, students are expected to have experience with derivatives and partial derivatives, finding maxima or minima of differentiable functions of one or more variables, the Taylor formula, and integrals. Topics in probability include random variables and probability distributions, in particular, the binomial and normal distributions, expectation, variance and covariance, conditional probability, and independence. Familiarity with the Central Limit Theorem would be a bonus. In linear algebra, the student should be able to solve systems of linear equations, add, multiply, transpose and invert matrices, and compute determinants. For a reference in probability theory, see Probability Through Problems by Marek Capinski and Tomasz Jerzy Zastawniak.

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

		Weights	Notes
1	Exam 1	25%	The exam will be conducted using open-ended questions and will be held in class during the midterm. Further instructions will be distributed.
2	Exam 2	25%	The exam will be conducted using open-ended questions and will be held in class towards the end of the term. Further instructions will be distributed.
3	Class Project	20%	Students are expected to work as a team and propose aproject idea by the midterm. The projects must build on the tools/ideas that are covered in the class, especially stochastic modeling. Additionally, the teams are expected to work with real data. Detailed instructions will be distributed. Presentation: upon submission, teams are expected to present their work and highlight individual contribution and synergy. Presentations will be graded on both the team and individual levels.
4	Homeworks	20%	There will be two major assignments over the course of the semester.
5	Participation	10%	Discussions are highly encouraged, including class attendance and general participation. Additionally, attendance will be taken over the course of the semester.