CS 476/676: Numeric Computation for Financial Modelling Assignment
Introduction to Options
Random Walks on a Lattice
No Arbitrage Pricing
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Lattice Construction
Option pricing on Lattice
Ito’s Lemma, Black-Scholes Model
Risk Neutral Valuation
MC Method I
Hedging, Delta, Gamma and Greeks
VaR and CVaR Risk Measures
Implied Volatility, Volatility Smile
Feb 19-27 Reading week
MC Method II: Correlated Assets
PDE for European and American Option Pricing
Finite Difference Method
Explicit Finite Difference Method Assignment 3 : Due Mar 17 Implicit Finite Difference Method, Stability, Convergence
Penalty Method
Option Model Calibration.
CVaR Portfolio Optimization
Nonlinear Optimization, Optimality Assignment 4 : Due April 5
Winter 2022
Office: DC3623 DC 3594 (SciCom) DC 2303 (CGL) MW 4-5:20pm. Tues 3-4pm
Calendar Description: http://www.ucalendar.uwaterloo.ca/1112/COURSE/course-CS.html#CS476 Schedule of Classes: http://www.adm.uwaterloo.ca/infocour/CIR/SA/under.html
Course Description
The interaction of financial models, numerical methods, and computing environments. Basic computational aspects of option pricing and hedging. Numerical methods for stochastic differential equations, strong and weak convergence. Generating correlated random numbers. Time-stepping methods. Finite difference methods for the Black-Scholes equation. Discretization, stability, convergence. Computational optimization, portfolio optimization and model calibration, data driven optimization.
Course Objectives
To provide students with an overview of modern numerical algorithms for use in financial applications.
• COVID Contigent Plan Following UW guideline, lectures are planned to be delivered online until Jan 27. We plan to return to in-person as soon as the public health situation allows on or after
Assignment 1 : Due Jan 31
Assignment 2 : Due Feb 22
January 24, 2022. A student is responsible for all materials covered in all lectures, delivered online and in-person.
In the event of cancellation of in-person final examination, the course grade will come from the assign- ment component entirely.
• Reference Material Course notes can be downloaded in LEARN. The notes also have a list of reference books.
• Background Assumed You should have taken
– An introductory course in numerical computation, similar to CS370. – An introductory course in statistics.
– Basic calculus and linear algebra.
– Ability to program in Matlab
The course assumes some mathematics as well as computing maturity from students. No finance background is assumed.
• Course Accounts You will need to register in the course to obtain a computing account on the CS student computing environment. You should register in CS476/676. If you use a research machine, you may not have a license for matlab (depending on your supervisor).
• Assignments Assignments will be posted in LEARN. Make sure that you check for announcements in LEARN frequently. Assignments must be submitted on the due date to Crowdmark. A link with be sent to you for submission. Please check Crowdmark website for information, If you need further assistance, please contact TA.
• Assignment Marking. The assignments will consist of programming problems and analytic work. IMPORTANT: most of the marks for the programming problems will be given for your description of your algorithms (i.e. pseudo-code) and explanation of the results. Simply handing in “raw code” will get very few marks.
Assignment figures and graphs should be carefully thought out to present the data and your conclusions in an effective and clear manner. Poor presentation of your work will result in a poor mark.
In all cases, I expect you to explain your algorithms, and describe what you see in detail. You should also submit hard copies of your code, along with some documentation. Matlab has good plotting facilities. Create figures with Matlab to include in your assignments.
Assignment solutions will be discussed in online recording. Assignment solutions will not be posted.
• Late Policy On the due date of an assignment, the work done to date should be submitted via Crowdmark; further material may be submitted for one-half credit 24 hours after the due date.
• Grade The course is planned to have four marked assignments and a final examination. The course grade will be made at the discretion of the instructor; the guidelines for this are as follows. For undergraduate students, the assignments count 60% and the final exam, 40%. For graduate students, the assignments count 70% and the final exam, 30%. There will be extra assignment questions for the graduate students. The final exam will be open book (all course notes and your notes and assignments may be used). You must pass the final examination (i.e. 20/40) in order to pass the course. If you fail the final examination, the final examination mark will be the mark awarded.
The weights of the 4 assignments in the assignment component (e.g.,., 60% assignment component for the undergrad) of the course grade calculation are as follows:
– Assignment 1: 20%
– Assignment 2: 20% – Assignment 3: 30% – Assignment 4: 30%
• Graduate Students To obtain credit for CS676, graduate students will have to complete extra questions.
• Programming Languages There are many sources of Matlab information on the Web. There are also many reference books available. You are responsible for getting up to speed on Matlab.
• Final Examination: Students are advised not to make any travel arrangements before the final examination times are posted. Note that in the event that the final examination is postponed, the final examination will be rescheduled for the day following the end of the regular examination schedule. Under no circumstances will alternate examinations be scheduled for students who have made travel arrangements which conflict with the final examination.
Students must inform the registrar’s office if they have a conflict in the final examination schedule, by the date posted on the registrar’s web site. Note that there is a precise definition of conflict as defined by the registrar. The course instructors will then be contacted by the registrar’s office to make alternate arrangements. Under no circumstances will the instructor’s make alternate arrangements for a final examination unless given instructions by the registrar’s office.
• Assignment Retention Unclaimed assignments will be retained for one month after term grades become official in quest. After that time, they will be destroyed in compliance with UW’s confidential shredding procedures:
http://www.adm.uwaterloo.ca/infostor/Confidential Shredding procedures 2008.htm
• Collaboration We encourage you to discuss general concepts and problems with classmates, TAs, and instructors. However, the solution that you submit must be worked through by yourself and written in your own words. It is not acceptable to work on an assignment with somebody else and write it up individually. When discussing course matters, do not take notes, and do not look at another person’s partial solutions, or show them yours.
Note that current Math faculty policy is that a mark of -100% can be recorded for the assignment in question in the case of cheating/copying.
• Academic Integrity: In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility.
[Check www.uwaterloo.ca/academicintegrity/ for more information.]
• Grievance: A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances, Section 4, www.adm.uwaterloo.ca/infosec/Policies/policy70.htm. When in doubt please be certain to contact the department’s administrative assistant who will provide further assistance.
• Discipline: A student is expected to know what constitutes academic integrity to avoid committing an academic offence, and to take responsibility for his/her actions.
[check www.uwaterloo.ca/academicintegrity/]
A student who is unsure whether an action constitutes an offence, or who needs help in learning how to avoid offences (e.g., plagiarism, cheating) or about ’rules’ for group work/collaboration should seek guidance from the course instructor, academic advisor, or the undergraduate Associate Dean. For infor- mation on categories of offences and types of penalties, students should refer to Policy 71, Student Dis- cipline, www.adm.uwaterloo.ca/infosec/Policies/policy71.htm. For typical penalties check Guidelines for the Assessment of Penalties, www.adm.uwaterloo.ca/infosec/guidelines/penaltyguidelines.htm.
• Appeals: A decision made or penalty imposed under Policy 70 (Student Petitions and Grievances) (other than a petition) or Policy 71 (Student Discipline) may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72 (Student Appeals) www.adm.uwaterloo.ca/infosec/Policies/policy72.htm.
Note for Students with Disabilities: Note for Students with Disabilities: AccessAbility Services, lo- cated in Needles Hall, Room 1401, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with AccessAbility Services at the beginning of each academic term.
• Intellectual Property:
Students should be aware that this course contains the intellectual property of their instructor, TA,
and/or the University of Waterloo. Intellectual property includes items such as:
– Lecture content, spoken and written (and any audio/video recording thereof);
– Lecture handouts, presentations, and other materials prepared for the course (e.g., PowerPoint slides);
– Questions or solution sets from various types of assessments (e.g., assignments, quizzes, tests, final exams); and
– Work protected by copyright (e.g., any work authored by the instructor or TA or used by the instructor or TA with permission of the copyright owner).
Course materials and the intellectual property contained therein, are used to enhance a student’s educational experience. However, sharing this intellectual property without the intellectual property owner’s permission is a violation of intellectual property rights. For this reason, it is necessary to ask the instructor, TA and/or the University of Waterloo for permission before uploading and sharing the intellectual property of others online (e.g., to an online repository). Permission from an instructor, TA or the University is also necessary before sharing the intellectual property of others from completed courses with students taking the same/similar courses in subsequent terms/years. In many cases, instructors might be happy to allow distribution of certain materials. However, doing so without expressed permission is considered a violation of intellectual property rights.
• Mental Health Support
The Faculty of Math encourages students to seek out mental health support if needed. On-campus Resources:
– Campus Wellness? https://uwaterloo.ca/campus-wellness/
– Counselling ext 32655?
– MATES: one-to-one peer support program offered by Waterloo Undergraduate Student Associa- tion (WUSA) and Counselling Services:
– Health Services: located across the creek from the Student Life Centre,?519-888-4096. Off-campus Resources:
– Good2Talk (24/7): Free confidential help line for post-secondary students. Phone: 1-866-925-5454 (Ontario and Nova Scotia only)
– Here 24/7: Mental Health and Crisis Service Team. Phone: 1-844-437-3247 (Waterloo Region only)
– OK2BME: set of support services for lesbian, gay, bisexual, transgender or questioning teens. Phone: 519-884-0000 extension 213 (Waterloo Region only)
– EMPOWER ME 1-833-628-5589 for Cdn./USA other countries see: http://studentcare.ca/ rte/en/IHaveAPlan_WUSA_EmpowerMe_EmpowerMe
– EMPOWER ME in China: China North 108007142831 China South ?108001402851
• Diversity
It is our intent that students from all diverse backgrounds and perspectives be well served by this course, and that students? learning needs be addressed both in and out of class. We recognize the immense value of the diversity in identities, perspectives, and contributions that students bring, and the benefit it has on our educational environment. Your suggestions are encouraged and appreciated. Please let us know ways to improve the effectiveness of the course for you personally or for other students or student groups. In particular:
– We will gladly honour your request to address you by an alternate/preferred name or gender pronoun. Please advise us of this preference early in the term so we may make appropriate changes to our records.
– We will honour your religious holidays and celebrations. Please inform of us these at the start of the course.
– We will follow AccessAbility Services guidelines and protocols on how to best support students with different learning needs.