Math/Stats 458 Financial Mathematics for Actuaries II

Welcome!

Welcome to Math 458 - Financial Mathematics for Actuaries II at Michigan State University. This site has all the class information that you need to be successful. Here you will find the class schedule, its policies, homework and exams details, as well as various opportunities for help & support. In addition, student accomodation information can be found here.

Who, What, When, Where?

Instructor Information	Professor Darren E. Mason, Ph.D; Wells Hall C346; masond@msu.edu.
Course Description	Utilize modern computational methods to price contracts in insurance and mathematical finance. Rational valuation of derivative securities using put-call parity and calculation of European and American options. Introduce hybrid contracts and features, such as equity-indexed annuities.
Prerequisites	Math 361 - Financial Mathematics for Actuaries I and STT 441 - Probability and Statistics I: Probability.
Class Time & Location	TR: 2:40PM - 4:00PM in Wells Hall A330.
Student Hours	MWF: 9:00AM - 10:00AM; TR: 1:00PM - 2:00PM; Wells Hall C346. See Student Hours for more information.
Text	A Discussion of Financial Economics in Actuarial Models - A Preparation for the Actuarial Exam MFE/3 by Marcel B. Finan; Arkansas Tech University; September 13, 2016. Mathematical Finance: Theory, Review, and Exercises by Emaunuela Rosazza Gianin and Carlo Sgarra; Springer, Second Edition, ISBN: 978-3-031-28377-2, April 18, 2023.
Asking Questions	If you have question during class or student hours, I will answer them at that time. If you have questions at other times, you can email them to me. I promise to respond within 24 hours, either by email or in person. DO NOT expect a response after 5pm on any given day as I may be busy with my family. However, I will do my best to be as fast as possible.

Course Policies

• Device Etiquette: Using devices during class time for non-class activities (i.e., YouTube, Twitch, Tik-Tok, gaming, etc.) is prohibited. Professional and courteous behavior is demonstrated by turning off distractions and focusing on class. We owe this to each other.


• Email/Writing Expectations: All correspondences to me should be courteous and professional, following standard rules of grammar. One way to guarantee that you don't get a response from me is to send an email that opens with "Hey how do i do problem X". You will get a helpful response if you write "Hi Professor Mason, I am working on problem X and I am stuck. I don't understand how to organize my decision variables. Thank you, Student Name". Regardless of your career path, professional correspondence is a necessity. If not already present, it is a good habit to aquire at this stage of your life.


• Intellectual Property: As members of a learning community, students are expected to respect the intellectual property of course instructors.  All course materials presented to students are the copyrighted property of the course instructor and/or the associated text.


• Social Media Guideline: Unless explicitly given permission by the instructor, students may not record any classroom activities. This includes posting anything from class to Tik-Tok, Snapchat, YouTube, Kik, Facebook, Instagram, etc. Doing so is a violation of the privacy expectation of your fellow students and the instructor. Any student violating this policy may face academic disciplinary sanctions.


• Attendance and Participation:
  
  
  • Daily attendance and participation in class is strongly encouraged - but NOT required. Substantial educational research exists that demonstrate a strong correlation between student attendance and student grades. This is particulary true in technical classes where so much of the problem is focused on problem solving. My advice? Don't blow off class :)
  • Attendance for quizzes and examinations is required. Legitimate reasons to miss an examination include a  family emergencies (i.e., a death, hardship, car accident, etc.), student illness with a written excuse from a medical professional / appropriate college official, or a college sanctioned event (e.g. class field trip or athletic events).    Students who do miss an exam due to an excused absence must make arrangements as soon as possible to make up the missed work.  If you know in advance that you will be gone, you need to make arrangements with Dr. Mason before the date of the examination in question.
  • Participation requires coming to class ready to learn.   This includes reading the material being covered in class before coming to class. If you must miss class, then get a copy of a fellow student's notes as soon as possible. Read those notes as you are responsible for all content in the class, even if you are absent.
  • The MSU policy on attendance is here.


• Time Commitment OUTSIDE of class: Anywhere from 0 hours to 4+ hours per day of classroom instruction.  Typical time commitments that correlate with success in this course is 1-3 hours/day, at least five days per week.  Precisely how much time you will need to spend studying outside of class is based on, at least, how well you are prepared mathematically and the grade you want to earn in the class. Preparation for exams will add to the time you need outside of class.   Your mileage may vary.  

• Homework: Homework problems are assigned in the schedule portion of this website. Homework is worth 15% of your grade. See the homework section for more detail.

• Projects: There will be five group coding projects during the semestesr that involve using the programming language R. In total, projects account for 15% of your final grade so each project is worth 3%. More information is available in the project section of the website.

• Quizzes: There will be five quizzes during the semester and only the top four quiz scores will count. Therefore, each quiz is worth 5% of your final grade for the course so that quizzes account for 20% of your final grade. If you miss a quiz for illness or any other reason, that will have to be the quiz that doesn't count (so don't waste a quiz by skipping class). All quizzes are closed book and closed notes. An authorized calculator is allowed. More information is available in the quiz section of the website.
  

• Examinations: There will be two exams during the semester on Thursdays. Your lowest scoring exam is worth 10% of your final grade and the highest scoring exam is worth 20%. Therefore, both exams are worth 30% of your final grade for the course. Each examination is closed book and closed notes. However, you can use an authorized calculator. More information is available in the exam section of the website.

• Final Exam: The final examination for this class will be at 10:00AM - 12:00PM on Wednesday, December 13, 2023. The test is cumulative and accounts for 20% of your final grade.

• Grading: The following table provides the basic partition of points for this class:
  
  

  Evaluation	Homework	Projects	Quizzes	Exams	Final Exam
  Weight	15%	15%	20%	30%	20%

  
  

  • Using the above table as a guide, here are step-by-step instructions on how to compute a "ball-park" estimate of your grade.  First, let your average percentage score be H for your homework, P for your projects, Q your weighted quiz score, S your weighted exam score, and F the score on your final project, with each corresponding to a number between 0 and 1.  Your total raw score R in the class is then determined by the equation R = 0.15H + 0.15P + 0.20Q + 0.30S + 0.20F. The maximum possible value for R is 1.0; the minimum possible value for R is 0.0.  Then, your grade in the class will be calculated according to the following rubric.

    
    

    If R ≥	0.90	0.85	0.80	0.75	0.70	0.65	0.60
    Your grade is ≥	4.0	3.5	3.0	2.5	2.0	1.5	1.0

    
    



• Important Dates:
  
  

  Event	Date
  Last Day For Open Add	Friday, September 01
  Last Day to Drop With Refund	Thursday, September 21
  Last Day Drop With No Grade Reported	Monday, October 16



• Ethics: The Spartan Code of Honor Academic Pledge embodies the principles of academic integrity through a personal commitment to ethical behavior in a student’s studies and research. All undergraduate students are expected to uphold the academic pledge throughout their enrollment at MSU. Student conduct that is inconsistent with the academic pledge is addressed through existing policies, regulations, and ordinances governing academic honesty and integrity.
  
  
  • For detailed information on the expectations of academic honesty by MSU, please look here.
  • Violation of this policy will be prosecuted to the fullest extent allowed by the University.
  • Documented cases in this class will, at a minimum, result in a ZERO on the corresponding assignment as well as a 10% reduction in your final grade. So be sure to NOT violate the copying policy discussed above.

• Accomodations Statement: Students at MSU with a disability that substantially limits a major life activity can register with the Resource Center for Persons with Disabilities (RCPD). If you have a disability, not registering with RCPD may delay or compromise the availability of accommodations. As many reasonable accommodations require significant pre-planning, registration with the RCPD prior to situations requiring accommodations is essential.

• Discrimination Statement: The MSU Anti-Discrimination Policy prohibits acts of discrimination and harassment against any university community member(s) by inappropriately limiting employment opportunities, access to university residential facilities, or participating in educational, athletic, social, cultural, or other university activities on the basis of age, color, gender, gender identity, disability, height, marital status, national origin, political persuasion, race, religion, sexual orientation, veteran status or weight. Complaints under this policy may be submitted to the MSU Office of Institutional Equity for investigation. The policy prohibits discrimination and harassment against individuals based on characteristics protected under federal and state law, but also includes political persuasion, veteran status, sexual orientation, and gender identity as protected categories.

Class Schedule

This is a tentative schedule of what we will be covering in Math 458 this semester. In the case of unforeseen delays or modifications to our daily life, its subject to change.

Week	Sections Covered	Homework	Date Due
08/28 - 09/01	Introduction; Course Overview; Review of Derivatives	NA	NA
09/05 - 09/08	Review of Derivatives (continued)	1.4, 1.9, 1.15, 2.6, 2.12, 2.14, 3.2, 3.9, 3.17, 4.4, 4.10, 5.1, 5.5, 5.8, 7.2, 7.5	09/14
09/11 - 09/15	Early Exercise of American Options; Monotonicity, and Convexity	9.4, 9.6, 10.2, 10.9, 11.4, 11.8, 12.3, 12.7, 13.3, 13.4, 13.9	09/20
09/14	Quiz #1 (Sections 1 - 5; 7)	NA	NA
09/18 - 09/22	Discrete Time Pricing Models	14.1, 14.3, 14.8, 15.1, 15.3, 15.8, 16.1, 16.5, 16.9, 16.10, 17.2, 17.4, 17.9, 18.1, 18.3, 18.7, 19.1, 19.6, 19.9, 20.2, 20.5, 20.9	09/27
09/25 - 09/29	Discrete Time Pricing Models (concluded)	21.1, 21.5, 23.1, 23.5, 24.2, 24.3, 24.6, 24.8, 25.3, 25.7, 26.1, 26.8	10/04
09/28	Quiz #2 (Sections 9 - 20)	NA	NA
10/02 - 10/06	The Black-Scholes-Merton Model & The Greeks	27.2, 27.6, 28.2, 28.4, 28.6, 28.11, 28.15, 29.2, 29.4, 29.8, 29.11	10/11
10/09 - 10/13	The Black-Scholes-Merton Model & The Greeks	30.1, 30.4, 30.10, 31.3, 31.8, 31.10	10/18
10/12	Exam #1	NA	NA
10/16 - 10/20	The Greeks - Applications	32.2, 32.5, 32.10, 32.15 (use ΔB = 3.4), 33.3, 33.5, 34.3 (w/o dividends), 34.6	10/25
10/23 - 10/24	Fall Break	NA	NA
10/25 - 10/27	Option Hedging	35.1, 35.6 (use r = 8% in 35.5), 35.8, 36.3, 36.8, 36.12, 37.2, 37.4, 37.7, 38.2, 38.8, 38.1	11/01
10/30 - 11/03	Lognormal Asset Pricing	46.4, 46.11, 46.17, 47.2, 47.4; Derive the median, mode, and sth-moment E[Ys] of a lognormal variable Y; 47.13, 48.3, 48.11, 49.4, 49.6, 49.1	11/08
11/02	Quiz #3 (Sections 29 - 39)	NA	NA
11/06 - 11/10	Monte Carlo Simulations; Stochastic Calculus & Applications	58.1, 58.4, 58.7, 59.2, 59.5, 59.10, 60.2, 60.5, 60.7, 61.2, 61.4, 61.7	11/21
11/13 - 11/17	Stochastic Calculus & Applications (concluded)	62.1, 62.4, 64.2, 64.6	11/28
11/16	Exam #2	NA	NA
11/20 - 11/22	The Black Scholes Partial Differential Equation	65.1, 66.1, 66.4, 67.2, 67.9	11/28
11/21	Quiz #4		NA
11/23 - 11/24	Thanksgiving Break	NA	NA
11/27 - 12/01	Binary Options; Interest Rate Models	TBA	NA
11/30	Quiz #5	NA	NA
12/04 - 12/08	Interest Rate Models (concluded)	TBA	NA
12/13	Final Examination; 10:00AM - 12:00PM	NA	NA

Homework

Homework problems from the book are assigned in the schedule portion of this website. Although not collected, you are expected to work out these problems in a dedicated problem book and ask questions as they arise. Numerical answers are in the back of the book. Successful completion of these problems will be of great benefit on required quizzes and examinations.

• Homework is worth 15% of your grade. To receive credit for the recommended homework in a given week, you must send me a PDF of a photograph of your work by email to masond@msu.edu by midnight on due date so that I can review your assess your progress.
• The subject line of your email should clearly state "Homework from YOUR NAME for Sections XY - ZW".
• The name of your attached PDF file should be "FIRSTNAMELASTNAME_SectionXY-WZ.pdf".
• Your grade will be 0 if you do not show any work, 1 if you do but your work is more incomplete than not (e.g., less than 50% complete), and a 2 if your work is satisfactory (e.g. above 50% complete).

All homework must satisfy the following requirements:

• Submitted homework must be neat and clearly written. Homework that is unreadable will not be accepted or graded. If you are unsure what is meant by this standard, feel free to drop by and ask!
• Students may work together on homework so long as a) individual assignments that are submitted are NOT identical to another student's homework (i.e., solutions should be clearly written in your own words and style), b) all aspects of the submission is reflective of the student’s efforts, and c) all collaborations are acknowledged.

Advice: Homework assignments in this course vary from being doable in a few minutes to taking considerably longer. Consequently, you should start working on your homework problems as soon as they are assigned. This practice will afford you the time required to understand the material and to ask questions during class/office hours in regards to problems/concepts you may not understand.

Projects

There are four projects during the semester, listed in the below table along with project descriptions.

Project	Topic	Due Date
0	Introduction to R	09/11
1	The Efficient Frontier	10/02
2	Options & Lognormal Pricing	11/13
3	Monte Carlo Simulations	12/04

Rules of the Game...

• Due Dates: Projects will be assigned according to the above schedule. All projects - including raw R code/scripts that I can run and clearly presented and typed output must be emailed to Dr. Mason by midnight on the day it is due.

• Late Project Policy: For every day after the due date that a project is late, the assignment will penalized 25% of the total possible points for that assignment. For example, if the assignment is due on a Monday at 5pm, and instead it is turned in between 5:01 pm on that Monday and 5:00pm on Tuesday (the next day), the student will lose 25% of the total possible points for that assignment. If the assignment is turned in at 5:01pm on Tuesday, the student will lose 50% of the total possible points from the assignment.

• Clarity Requirements for Work: Submitted projects must be

  • Supported by written narratives that explain your groups problem solving process, observations, and answers to questions in each project. The narrative should be submitted as a single PDF file and the code as a single R script. Each files should have a filename consisting of the Last names of your group members. For example, if I am submitting project #3 with my partner with the last name Esteban, then the PDF should be named "EstebanMason_Project3.pdf" and the R script named "EstebanMason_Project3.R". Proper grammar, including complete sentences, paragraphs, and not just a list of answers is expected. I should be able to read your narrative without knowing the project questions.
  
  
  • CLEAR. Each project solution should inclulde clear and concicse algorithms so that it can be understood by someone other than members of your group.
  
  
  • COMMENTED. Proper commenting on, and explanation of, coding is an essential skill. Remember that over time you are likely to forget what code is "doing" without a reminder, AND if others are to maintain/modify your code, they should not be saddled with obscure operations and obligated to divine your intentions.
  
  Note: Projects that are unreadable will not be accepted or graded. Instead they will be returned to you untouched. If you are unsure what is meant by this standard, feel free to drop by and ask! Or show me and I will tell you in class. However, if your group is just not able to complete a part of a project, simply let me know and move on. Or, if you have partial code that won't run, include it and tell me about the problem.

• Collaboration: Project teams may NOT work with other teams on projects. If you need help, contact Dr. Mason or ask your partner.

Some advice...

• You should start working on assigned projects as soon as possible! Some are longer than others -- but you absolutely want to get started quickly. This practice will afford you the time required to understand the material and to ask questions during class or student hours on problems/concepts/syntax/coding bugs you may not understand. I love helping -- but I need your group to get in far enough to get stuck -- and not on the night it is due.