Course: ORF335
Instructor: Sircar, Ronnie
S 2018

### Description of Course Goals and Curriculum

ORF 335 (Introduction to Financial Mathematics) primarily focuses on mathematical techniques for option pricing, with some content about other types of financial derivatives. The course assumes prior knowledge of probability (ORF 309) and directly applies these concepts to option pricing. The course starts out by introducing simple models to build an intuitive understanding of how no-arbitrage option pricing works for different types of options using discrete time intervals and involves coding these models using MATLAB. As the course progresses, you will learn about pricing options in continuous time and the Black-Scholes model is introduced, which is the main option-pricing model emphasized in this course. Other types of derivatives, such as futures and credit derivatives, are also discussed. In addition to computational implementation of the models, the course also introduces students to the factors that affect option prices (such as volatility) and how theoretical models can differ from what happens in practice. The course also touches on the role of various financial instruments in causing the financial crisis. Overall, the course uses progressively more complex mathematical models, so it is important for students to ensure that they understand the math involved, so they can understand its application to financial derivative pricing as they go through the course.

### Learning From Classroom Instruction

The course consists of traditional lectures and precepts. The lectures focus on deriving equations and explaining broad concepts regarding options and derivatives, while the precepts apply these equations and concepts to solve related problems. The precepts occasionally consist of computational work. The precepts follow the lectures closely and are good preparation for the assignments. Organized lecture notes are posted on blackboard, and a good way to reinforce the material is to closely reread the lecture notes and see if you can come up with the formulas on your own. It is important to ask clarifying questions to fill any gaps in your understanding of the lecture material because the assignment problems build on this material, but are more challenging than the types of problems you will see during lecture and precept. The second half of the course is fast-paced, so it is crucial to have a solid understanding of the first half and to constantly keep up with the material and ask questions when necessary during the second half.

### Learning For and From Assignments

The assignments are in the form of problem sets, and there are 6 assignments during the semester. The assignments are more difficult than the precept problems, but they focus on the same material. There is usually more than a week given per assignment, since some of them can be long, but it is important to start early, as the assignments can be challenging. Students are allowed to collaborate with each other on most assignments, as long as students submit their own work, so it is good to form a study group to work on the assignments. Office hours are also a great resource for getting help with the assignments. Some of the problems in the assignments involve coding on MATLAB, so it is important to get help with the syntax of MATLAB early on, so that you can work on the assignment.

The course has a midterm and a final exam. Exams problems are very similar to assignment problems, so the best way to study for exams is by reviewing problem sets again. The exams allow 1-page cheat sheets, so this is a good opportunity to review equations. The practice exams are also great preparation for the exams because the style of the problems is similar. There isn’t a programming aspect for the exams, but it is important to know the algorithms discussed in the course, so it can be helpful to look back at past assignments and experiment with MATLAB code to develop an intuitive understanding of the algorithms.

### External Resources

There is an optional textbook for the course, but lecture notes cover all the material you’ll need, so it isn’t necessary to use the book unless you need the material presented differently. There are online resources that can supplement the material for the course as well. Furthermore, if you have not used MATLAB before and need assistance with that aspect, there are many tutorials available online that are straightforward to follow.