Mathematical Finance, FIN 539, Spring 2024 Mini A

Philip H. Dybvig
Washington University in Saint Louis

Final Exam Results I was happy overall with the results of the final exam. Scores ranged from 6 to 98 out of 100, with 40% scoring 80 or above. These statistics do not include the students who are taking oral final exams or have a pending academic integrity case.

histogram of grades

final exam answers

Final Exam The final exam has been scheduled on Sunday, March 3, 4:00PM-7:00PM. Both sections will have the exam at the same time. The in-person exams will be held in Simon Hall 110, 112, and 113. The TAs will assign you seats for the exam, to avoid the appearance of people choosing seats next to friends to share exam answers.

Here is a practice exam, which was the final exam in Spring, 2022:

practice exam answers

The final will have the same format as the practice exam, but of course the questions and topics covered from the course will be somewhat different. Here is a document that gives more detail about what will and will not be covered on the final: howtofinal24.pdf.

Here are some additional exams from 2021. The course coverage was a little different from this time.

practice exam 21B answers

practice exam 21A answers

Important: Exam Rules

This is a closed-book exam with absolutely no electronics allowed. For the exam, you are not permitted to have access to notes or any electronics, including cell phones, computers, mp3 players, iPads etc. All of these devices are computers that can be used to store information that can give an unfair advantage and most allow communications which also could be used for cheating. I want to make sure there is not even an appearance of cheating. Please take care to follow these rules. I don't like reporting infractions, but it is my duty and you will not be happy if I have to report you. As in compliance in the finance industry, a lot of violations are by people who did not intend to cheat but were not careful to follow the rules.
(oral make-up) For anyone who cannot take the exam at the scheduled time, I will give an oral exam. In the oral exam, I will ask you questions on Zoom, starting with your choice of topic in the course. This way, I will not have to write a separate exam, and most students probably prefer a written exam and have an incentive to take the exam as scheduled unless there is a good reason to do otherwise. The oral exam is very fair, and if anything I can get a more accurate reading of what you know in an oral exam.

Welcome to Mathematical Finance! We will cover some interesting mathematical tools that are very useful in practice, with a focus on applications to investments.

Slides I will use the whiteboard in the classroom. This is a good format for technical material. However, I have also developed a set of slides for your use as supplemental material.

Lecture 0: Course overview

Lecture 1: Decision theory and static choice problems

Lecture 2: Dynamic programming

Lecture 3: Multiple assets, hedging state variables, and pricing models

Lecture 4: FTAP, valuation, and the one-shot approach

Homeworks Here are homeworks you can work to help to learn the material. Although they will not be graded, I urge you to work the homeworks before the TA session when they will be discussed.

Extra Readings I suggest the following book chapter for background readings on single-period models:

Download Dybvig, Philip H. and Stephen A. Ross (2003), Arbitrage, State Prices, and Portfolio Theory, in George Constantinides and René Stulz, ed., Handbook of the Economics of Finance, volume 1b, North-Holland.

There is no textbook for the class, and the class is designed to be self-contained. If you want a textbook for an alternative exposition and coverage of more topics, I recommend the following book:

Back, Kerry, 2017, Asset Pricing and Portfolio Choice Theory, second edition, Oxford University Press.

Kerry is a serious scholar and my co-author. He was formerly at Washington University, but he has moved to Rice University.