Syllabus - FIN 538

Stochastic Foundations for Finance

Instructor

Times and Location

Section 1

  •   Monday/Wednesday
  •   8:30am to 9:50am
  •   Bauer 240

Section 2

  •   Monday/Wednesday
  •   10:00am to 11:20am
  •   Bauer 240

Section 3

  •   Monday/Wednesday
  •   1:00pm to 2:20pm
  •   Simon Hall 106

Section 4

  •   Monday/Wednesday
  •   2:30pm to 3:50pm
  •   Simon Hall 106

Section 5

  •   Monday/Wednesday
  •   4:00pm to 5:20pm
  •   Simon Hall 106
Important

Please use your WashU email in all communications with me.

Class Information

Course Description

This course provides the necessary foundations in probability theory and stochastic process to FIN 539, Mathematical Finance. The course will benefit students in the Masters in Finance program who aim to attain quantitative positions in investment banks, hedge funds, and consulting firms. While the class will provide financial examples, the primary focus will be on stochastic processes and stochastic calculus theory. Students interested in applying the theory should take follow-on courses. The topics covered in the class include general probability theory, Brownian motion and diffusion processes, martingales, stochastic calculus, Ito’s lemma, and potentially jump processes.

Class Materials

All class materials are available on Canvas. In preparing the class materials, I have used the following textbooks:

  • Back, K. (2010). Asset pricing and portfolio choice theory. Oxford University Press.
  • Hamilton, J. D. (2020). Time series analysis. Princeton University Press.
  • Steele, J. M. (2001). Stochastic calculus and financial applications. New York: Springer.

Olin’s Pillars of Excellence

We have four pillars of excellence that guide our academic experience and make Olin graduates better leaders. Our pillars are Values-Based, Data Driven™, global outlook, experiential, and entrepreneurial spirit.

Olin students will:

  1. Embody a values-based and data-driven ethos in their approach to all business situations.
  2. Understand the global opportunities and challenges facing businesses.
  3. Engage with business issues through the application of experiential knowledge, in addition to the rigorous technical skills acquired in the classroom.
  4. Pursue world-changing initiatives with an entrepreneurial and innovative mindset and skill set.

Course Schedule

You can find the tentative course schedule below. The topics covered on each proposed date may change as the course progresses, but the main content and the general order should remain the same.

Session Date Topic
1 10/23 Difference Equations
2 10/28 The Normal Distribution
3 10/30 Modeling Equity Prices in Discrete Time
4 11/4 Calculus Primer
5 11/6 Modeling Stock Prices in Continuous Time (1)
6 11/11 Modeling Stock Prices in Continuous Time (2)
7 11/13 Option Pricing
8 11/18 Multivariate Ito’s Lemma
9 11/20 Asset Pricing in Continuous Time
10 11/25 Interest Rate Models and Bond Pricing (1)
– 11/27 Thanksgiving Break (No Classes)
11 12/2 Interest Rate Models and Bond Pricing (2)
12 12/4 Review for Final Exam
13 12/13 Final Exam (6:15 pm to 8:15 pm CST)

Grading

Following is the summary of weights on the various components that I will use to evaluate your performance in this course:

Assignment Weight
Problem Sets 30
Group Projects 20
Final Exam 40
Class Attendance 10

Grades are non-negotiable. If you feel I need to regrade one of the course assignments, please immediately bring it to my attention. Grade appeals (e.g., because your points do not add up correctly) must be submitted within a week after the grades are released. I certainly want all of you to receive the grades you have earned.

Attendance and Participation Policy

Class participation, classroom interaction, and collaboration are a signature of the Olin culture and Code of Conduct. Class time is critical to learning, and I expect prompt attendance during our class times.

The class starts on time and ends on time. Being late to class is not professional. If you are late for class, I ask you to say “Hello” to me when you enter the class.

I will take attendance by either roll calling your name. Students over 20 minutes late will only get half of the attendance points.

Important

You must attend the section you are enrolled in to receive attendance points.

Important

You can use your personal computer to take notes and view the slides. Using a computer for anything else is forbidden. I will ask you to stop using your computer if I notice loud clicks because you are writing a lengthy document. In addition,

  • You cannot use a computer if you sit in the last row.
  • Using an external mouse is strictly forbidden.
  • Using an additional platform to raise your computer is also not allowed.
  • Using headphones in class is not allowed.

I will take points out of your attendance grade if you violate these rules.

Important

All students must attend in person. A class recording will be posted on Canvas using Kaltura. If you miss a class, please watch the corresponding recording and ask me questions if you need help.

Note

Students who have symptoms of COVID-19 must call the COVID-19 Call Center or Habif Health and Wellness Center for testing and should not attend any in-person class. Missing in-person class sessions for this reason will be considered an excused absence. Students must provide appropriate documentation from Habif to obtain this exception.

Problem Sets

Weekly problem sets will be due at 11:59 pm CST on the dates indicated below. All problem sets are individual. You must submit your work via Canvas.

Assignment Due Date
PS #1 10/30
PS #2 11/6
PS #3 11/13
PS #4 11/27
PS #5 12/9

There is a 5% grade deduction per day for late submissions.

Group Projects

Two graded group projects will allow you to work with actual data and see how the theory works in practice. Groups can have at most three students. You will work on both projects using Python, and the deliverable is a well-formatted Jupyter Notebook saved as an HTML file. The format and presentation of your assignment will count for 40% of the assignment grade.

Assignment Due Date
Project #1 11/22
Project #2 12/13

There is a 5% grade deduction per day for late submissions.

Final Exam

There will be a final exam that covers all the material covered in the class. The exam will be online and is scheduled on Friday, Dec 13 at 6:15 pm. I will update you later on the exact duration of the exam.

The exam is an individual assignment and is closed-notes and closed-book. You must have your camera on and use Respondus Lockdown Browser to do it. The exam will test your understanding of the main issues we discussed in class, and questions will be similar to the ones on the problem sets and concepts we covered.

The exam time is non-negotiable. If you have a conflict, you must inform me by the end of the first week of the course. Hence, please check your schedule early (e.g., ensure the exam dates do not conflict with a religious holiday). If you think you will miss the final exam, please (1) immediately email me before the exam and (2) send me a justifiable and reliable proof of absence. Without clear and hard evidence, you will get no credit.

Honor Code and Code of Conduct

This course will follow the standards specified in the Code of Conduct and Code of Academic Integrity, which apply to the Olin Business School faculty and students. Students must be familiar with the codes. Section 5.8 includes some relevant parts of the Code.

Other Important Matters

COVID-19 Health and Safety Protocols

Students experiencing symptoms consistent with COVID-19 or concerned about possible exposure should contact Habif Health and Wellness Center (314 935-6666) to arrange for testing as indicated. If instructed by Habif to quarantine or isolate, students should notify their instructor as soon as possible by forwarding the email they received from Habif. The student and instructor should discuss any accommodation needs for COVID-related absences not covered in an instructor’s standard course policies.

While on campus, students must follow all public health guidelines established to reduce the risk of COVID-19 transmission within our community. The full set of University protocols can be found at here, and includes:

  • Masking is strongly recommended in indoor spaces. Masking remains a valuable tool in mitigating COVID-19, particularly in light of new and emerging variants. Students and instructors are encouraged to treat requests to mask with care and consideration, considering that some individuals may be at a higher risk, caring for others at a higher risk, or feeling less comfortable in a mask-optional environment. A mask requirement may be implemented as needed based on monitoring regional and campus conditions. For current masking policies, see the WashU Together website.

Students with disabilities for whom masked instructors or classmates create a communication barrier are encouraged to contact Disability Resources or talk to their instructor for assistance in determining reasonable adjustments. Adjustments may involve amplification devices, captioning, or transparent masks but will not allow for disregarding mask policies should a requirement be in place.

  • Maintaining physical distancing as needed. While distancing requirements no longer apply for vaccinated students, those who are not fully vaccinated are strongly encouraged, for their health, to maintain a distance of 6 ft from others in the classroom. If you cannot be vaccinated or have conditions that may put you at increased risk of failed immunity and classroom activities would bring you in frequent proximity to other students, contact your instructor to discuss alternatives.

  • Practicing healthy personal hygiene, including frequent hand washing with soap and warm water for at least 20 seconds and using hand sanitizer with at least 60% alcohol.

Reporting Sexual Assault and Harassment

If a student discusses or discloses an instance of sexual assault, sex discrimination, sexual harassment, dating violence, domestic violence, or stalking, or if a faculty member otherwise observes or becomes aware of such an allegation, the faculty member will keep the information as private as possible. Still, as a faculty member of Washington University, they are required to immediately report it to the Department Chair or Dean or directly to Ms. Cynthia Copeland, the University’s Associate Title IX Coordinator, at (314) 935-3411, cmcopeland@wustl.edu. Additionally, you can report incidents or complaints to the Office of Student Conduct and Community Standards or by contacting WUPD at (314) 935-5555 or your local law enforcement agency. See: Title IX.

Disability Resources (DR)

WashU supports the right of all enrolled students to an equitable educational opportunity and strives to create an inclusive learning environment. If the physical or online environment results in barriers to the inclusion of a student due to a disability, they should notify the instructor as soon as possible.

Disabled students requiring adjustments to equitably complete expectations in this course equitably should contact WashU’s Disability Resources (DR) and engage in a process for determining and communicating reasonable accommodations. Because accommodations are not applied retroactively, DR recommends initiating requests before or at the beginning of the academic term to avoid delays in accessing accommodations once classes begin. Once established, Disability Resources, faculty, and the student share responsibility for disability-related accommodations and access. You can contact Disability Resources at (314) 935-5970 or disabilityresources@wustl.edu.

Military Service Leave

Washington University recognizes that students serving in the U.S. Armed Forces and their family members may encounter situations where military service forces them to withdraw from a course of study, sometimes with little notice. Students may contact the Office of Military and Veteran Services at (314) 935-2609 or veterans@wustl.edu and their academic dean for guidance and assistance. See: Veterans.

Preferred Name and Gender-Inclusive Pronouns

Washington University in St. Louis recognizes that many students prefer to use names other than their legal ones to identify themselves. In addition, to affirm each person’s gender identity and lived experiences, we must ask and check in with others about pronouns. This simple effort can profoundly affect a person’s understanding of safety, respect, and support. See: Pronouns Information, Preferred Name.

Emergency Preparedness

Before an emergency, familiarize yourself with the building(s) that you frequent. Know the layout, including exit locations, stairwells, and the Emergency Assembly Point (EAP). Review the “Quick Guide for Emergencies” posted near the door in many classrooms and main lobby areas for specific emergency information and instructions. For additional information and EAP maps, visit emergency.wustl.edu. To ensure you receive emergency notifications, ensure your information and cell phone number are up-to-date in SIS, and download the WashU Safe app and enable notifications.

To report an emergency:

  • Danforth Campus: (314) 935-5555
  • School of Medicine Campus: (314) 362-4357
  • North/West/South and Off Campus: 911 then (314) 935-5555

Academic Integrity

Effective learning, teaching, and research all depend upon the ability of members of the academic community to trust one another and to trust the integrity of work that is submitted for academic credit or conducted in the broader arena of scholarly research. Such an atmosphere of mutual trust fosters the free exchange of ideas and enables all community members to achieve their highest potential.

In all academic work, you must appropriately acknowledge the ideas and contributions of others, and work that is presented as original must be, in fact, original. Faculty, students, and administrative staff are responsible for ensuring the honesty and fairness of the intellectual environment at Washington University in St. Louis.

Code of Conduct

Olin’s Code of Conduct aims to clarify expectations about academic and professional behavior. The Code’s purpose is to encourage and clarify appropriate academic, classroom, interpersonal, and extra-curricular etiquette expected of each individual by their peers, the faculty, and the institution. The Code also helps describe the overall environment of excellence and professionalism that members of the Olin community seek to establish and enhance continually. It is the responsibility of each member of the Olin community to uphold the spirit, as well as the principles, of the Code.

Please refer to the publication Integrity Matters for specific responsibilities, guidelines, and procedures regarding academic integrity.

Olin’s Code of Conduct As It Relates to Academic Matters

The following is a summary of the Code as it applies to Academic matters.

It is dishonest and a violation of student academic integrity if you:

  • Plagiarize — You commit plagiarism by taking someone else’s ideas, words, or other product types and presenting them as your own. You can avoid plagiarism by using proper documentation and acknowledgment.
  • Cheat on an examination — You must not receive or provide any unauthorized assistance on an examination. During an examination, you may only use material authorized by the faculty.
  • Copy or collaborate on assignments without permission — Collaborating with others when completing graded assignments or tests, performing laboratory experiments, writing and documenting computer programs, writing papers or reports, and completing problem sets (unless expressly discussed in class) is dishonest.
  • Fabricate or falsify data or records — It is dishonest to fabricate or falsify data in laboratory experiments, research papers, reports, or other circumstances; fabricate source material in a bibliography or “works cited” list; or provide false information on a resume or other document in connection with academic efforts. It is also dishonest to take data developed by someone else and present it as your own.
  • Engage in other forms of deceit or dishonesty that violate the spirit of the Code.

If you have any questions regarding the definition of allowable behavior, you must ask for clarification before engaging in the collaboration.

Olin’s Code of Conduct As It Relates to Professional Behavior

Olin Business School expects students to conduct themselves professionally at all times. Professional behavior includes, but is not limited to, the following:

  • Attendance: Students should attend each class session. Students who must miss a session for any reason should try to notify the instructor before the class meeting. Students should never register for courses scheduled in conflict with one another.
  • Punctuality: Students are expected to arrive and be seated before the start of each class session. They should display their name cards in all classes at all times.
  • Behavior: Classroom interaction might be spirited, but always while displaying professional courtesy and personal respect.
  • Preparation: Students must complete the readings, case preparations, and other assignments prior to each class session and participate actively in class discussions.
  • Distractions:
    • Exiting and Entering: Students should remain in the classroom for the class session unless an urgent need arises or prior arrangements have been made with the professor.
    • Laptop, PDA, and Other Electronic Device Usage: Students are expected to not use laptops, PDAs, and other electronic devices in classrooms unless with the instructor’s consent and for activities directly related to the class session. Accessing email or the Internet during class is not permitted as they can be distracting for peers and faculty.
    • Cellular Phone and Pager Usage: Students are expected to keep their mobile phones and pagers turned off or set them on silent/vibrate during class. Answering phones or pagers while class is in session is not permitted.
    • Other distractions: Those identified by individual instructors, such as eating in the classroom.

Resources for Students

Confidential Resources for Instances of Sexual Assault, Sex Discrimination, Sexual Harassment, Dating Violence, Domestic Violence, or Stalking

The University is committed to offering reasonable academic accommodations (e.g., a no-contact order, course changes) to students who are victims of relationship or sexual violence, regardless of whether they seek criminal or disciplinary action. Suppose a student needs to explore medical care, protection, or reporting options or would like to receive individual counseling services. In that case, free, confidential support resources and professional counseling services are available through the Relationship and Sexual Violence Prevention (RSVP) Center. If you need to request such accommodations, please get in touch with RSVP to schedule an appointment with a confidential and licensed counselor. Although information shared with counselors is confidential, the appropriate University administrators and faculty will coordinate requests for accommodations. The RSVP Center is located in Seigle Hall, Suite 435, and can be reached at rsvpcenter@wustl.edu or (314) 935-3445. Call (314) 935-6666 or (314) 935-5555 and ask to speak with an RSVP Counselor on call for after-hours emergency response services. See: RSVP Center.

Bias Reporting

The University has a process through which students, faculty, staff, and community members who have experienced or witnessed incidents of bias, prejudice, or discrimination against a student can report their experiences to the University’s Bias Report and Support System (BRSS) team. See: BRSS.

Mental Health Services

Mental Health Services’ professional staff members work with students to resolve personal and interpersonal difficulties, many of which can affect a student’s academic experience. These include conflicts with or worry about friends or family, concerns about eating or drinking patterns, and feelings of anxiety, depression, and thoughts of suicide. See: Mental Health Services.

The Division of Student Affairs also offers a telehealth program to students called TimelyCare. While students are encouraged to visit the Habif Health and Wellness Center during business hours, this additional service also provides after-hours access to medical care and 24/7 access to mental telehealth care across the United States, with no cost at the time of your visit. Students who pay the Health and Wellness fee are eligible for this service.

See the mental health services offered through the RSVP Center listed above.

WashU Cares

WashU Cares, within the Health and Wellness Unit, provides resources to all students on the Danforth Campus who may be having a hard time. WashU Cares is committed to helping create a culture of caring. Through proactive, collaborative, and systemic approaches, WashU Cares works with students to identify interventions, resources, and supports that allow them success. If there is a concern about a student’s physical or mental well-being, please file a report on the WashU Cares website. See: WashU Cares.

The Writing Center

The Writing Center offers all Washington University undergraduate and graduate students free writing support. Staff members will work with students on any writing project, including essays, writing assignments, personal statements, theses, and dissertations. They can help at any process stage, including brainstorming, developing and clarifying an argument, organizing evidence, or improving style. Instead of simply editing or proofreading papers, the tutors will ask questions and talk with the writer about their ideas and reasoning, allowing for a higher-order revision of the work. They will also look at sentence-level patterns to teach students to edit their work. The Center is located in Mallinckrodt and is open Sunday through Thursday from 11:00 am to 9:00 pm and Friday from 11:00 am to 5:00 pm. Students are seen primarily by appointment, but walk-ins will be accepted as scheduled. Both in-person and online appointments are available. To make an appointment, go to writingcenter.wustl.edu. Email: writingcenter@wustl.edu.

The Learning Center

The Learning Center provides support programs, including course-specific mentoring and academic skills coaching (study and test-taking strategies, time management, etc.), that enhance undergraduate students’ academic progress. Contact them at learningcenter@wustl.edu or visit ctl.wustl.edu/learningcenter to find out what support they may offer for your classes.

Center for Diversity and Inclusion (CDI)

The Center for Diversity and Inclusion (CDI) supports and advocates for undergraduate, graduate, and professional school students from underrepresented and marginalized populations, collaborates with campus and community partners, and promotes dialogue and social change to cultivate and foster a supportive campus climate for students of all backgrounds, cultures, and identities. See: https://diversityinclusion.wustl.edu.