# Math 537 Course Info

• Course Meets: M, W, F 12:20-1:10 LGRT 177 (Section 1) and 11:15-12:05 LGRT 204 (Section 2)

• Instructor
Michael Sullivan, LGRT 1323G, 545-1909
Office Hours: Mon 10-11, Tues 11-12, Weds 930-1030 and by appointment. If you want help by email instead of in person, a yes/no question is much more likely to receive an answer.

Trang Minh Le, LGRT 1435F, trangle at math dot umass dot edu

• Prerequisites: Single-variable calculus (Math 131, 132), Probability with calculus (Stats 515), and multi-variable calculus (Math 233).

• Credit: 3 credit hours

• Required: A calculator should have a cummulative distribution function for the standard normal variable (also known as the ``Erf" function or ``normalcdf"). The inverse normalcdf feature is also necessary. The TI-83 or higher, for example, will work.
Typed Class Notes (freely available first day of class).

• Recommended, but not required:
Derivative Markets by Robert L. McDonald, 3rd edition.
The 2nd and 3rd editions are on reserve at the library.
The Big Short by Michael Lewis, 2010, W. Norton & Company
Weapons of Math Destruction by Cathy O'Neal, 2016, Crown Books

• Overview: This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing financial instruments, or "derivatives." The central topic will be options, culminating in the Black-Scholes formula. The goal is to understand how the models derive from basic principles of economics, and to provide the necessary mathematical tools for their analysis. Basic stochastic calculus will be introduced.

• Math 441, Math 437, Math 497FM and the actuarial exams: This class was previously called Math 441. Math 441/537 was updated in spring 2013 to reduce the amount of overlap with the relatively new course Math 437 (previously Math 497FM), ``Actuarial Financial Math." In Spring 2017, Math 537 was further updated to reflect the changing syllabus of the Actuarial Exam MFE effective Summer 2017. (People wishing to gain certain professional actuarial certifications are required to take certain nation-wide off-campus exams. Exams FM/2 and MFE/3F are two of these.) Because of this new change, there is about 2-3 weeks of overlap in material (forward constracts and basics on options) between Math 437 offered Fall 2016 or earlier, and Math 537 offered Spring 2017 and later. As of Fall 2017, Math 437 focuses solely on annuities and bonds. Math 437 requires no probability and almost no calculus, and is a preparatory class for the Actuarial Exam FM/2. Math 537 is MUCH MORE mathematical, combining proabability and calculus. It does NOT require Math 437 as a prerequisite. Math 537 ideally covers about 80% of the Actuarial Exam MFE/3F; however, unlike Math 437, it is not a preparatory class. Actuarial-oriented students are recommended to buy the 3rd edition of the McDonald book, which is the official book of Exam MFE/3F.

• Contents: (tentative)(all chapters are from the free class notes)
1 week: Interest rates and time-value of money (Chapter 1.1-1.7), basic overview on markets (Chapter 2).
1.25 weeks: Forward contracts (Chapter 5)
2.5 weeks: Introduction to options (Chapter 6)
1.25 weeks: Review of discrete probability (Chapter 7). Catch-up. Possible review for midterm. Exam 1.
2 weeks: Pricing options with binomial trees (Chapter 8).
1.25 week: Review of continuous probability, up to Central Limit Theorem (Chapter 9).
1.75 weeks: Modeling the stock price and its volatility. Pricing options with expectations, aka, the Black-Scholes formula (chapter 10).
1 week: Greeks (Chapter 11).
2 weeks: Stochastic calculus and the Black-Scholes equation (Chapters 12, 13)

• A note about coverage: The lectures and the book cover essentially the same material, but not exactly. You are responsible for all of the material in the chapters 5, 6, 7, 8, 9, 10, 11, 12, 13 parts of Chapter 1 and 2, as well as all material covered in lecture. Any of this material can be the basis for homework and exam problems. So if you miss a class, please ask me or another student at the next lecture about what you missed.

• A note about difficulty: Students tend to find that the material ramps up in difficulty as the semester progresses. For example, Chapter 5 on forwards requires basic high school math, while Chap 10 on option pricing requires probability with calculus and the Central Limit Theorem and Chap 12-13 is based on Brownian motion. So if you are struggling in the first half of the semester, be sure to talk to me before the withdrawal deadline.

• Exams: Midterm will be closed-book October 23 7:00PM-9:00PM. Both sections will meet in GOES 20. Final will be closed-book on December 19 1:00PM-3:00PM for Section 1 and December 13 10:30AM-12:30PM for Section 2. Final is determined by Spire and may change, so check Spire for any updates, including room location. Note especially the snow date (see UMass site) for the final exam which may run close to your desired winter travel. If you have a conflict, you must notify me at least 2 weeks in advance. You will need to fill out the following sheet signed by the Registrar's office. Make sure to not book any travel during exams. Travel is not an excuse to miss the exam. If a last-minute emergency occurs after the two-week deadline, you will need to present to me a note either from your medical provider for medical emergencies or from the Office of the Dean of Students for non-medical emergencies. A calculator as described above is essential for both exams. For both exams you may bring in an (8.5 by 11)-inch sheet of paper, double-sided, with whatever formulas and/or notes you want. I will not provide you with a formula sheet.

• Grading: The grade for the course has three components: Midterm (30%), Final (35%) and time-completion of HWs (35%).
If attendance starts to drop, there MAY be several short in-class quizzes that will supplement the homework grade component. These quizzes will be relatively easy. Some may be individual and some group efforts.
Note: UMass does not have the resources to pay for grading entire HWs, so only select problems will be graded.

• Overriding into the course: If there is no room on Spire for this class, you can, up until one/two weeks before class, sign onto the dept waitlist to request an override.The link to the override can be found on the spire page. I will go through the waitlist one/two weeks before class begins.