Fall 2021  STAT 490 D100
Selected Topics in Probability and Statistics (3)
Class Number: 5146
Delivery Method: In Person
Overview

Course Times + Location:
Tu 12:30 PM – 2:20 PM
AQ 5015, BurnabyTh 12:30 PM – 1:20 PM
AQ 5015, Burnaby 
Exam Times + Location:
Dec 20, 2021
7:00 PM – 10:00 PM
AQ 5046, Burnaby

Instructor:
JeanFrancois Begin
jbegin@sfu.ca

Prerequisites:
Dependent on the topic covered.
Description
CALENDAR DESCRIPTION:
Topics in areas of probability and statistics not covered in the regular undergraduate curriculum of the department.
COURSE DETAILS:
Prerequisties: None. Students should have some knowledge of option pricing and undergraduate nonmeasure
theoretic probability.
Crosslisting: This course is crosslisted with ACMA 830.
Student Learning Objectives:
As a result of taking STAT 490, students should be able to:
Course Outline:
This course is divided into fifteen chapters.
Part 1: Stochastic Processes
 Chapter 1, Probabilistic Foundations: Sample space, Random variable, Probability measure, Distribution, Sigmaalgebra, Measurable space, Probability triple.
 Chapter 2, Stochastic Processes: Stochastic process, Filtration.
 Chapter 3, Expectations: Independence, Conditional probability, Expectation, Moments, Conditional expectation.
 Chapter 4, Martingales: Definition, Examples.
 Chapter 5, Brownian Motion: Scaled random walks, Construction of the Brownian motion.
 Chapter 6, Stochastic Integral: Riemann integration, Ito integration.
 Chapter 7, Stochastic Differential Equations and Ito’s Lemma: Ordinary differential equations, Ito’s lemma, Product rule, Multidimensional Ito’s lemma.
 Chapter 8, Jump Processes: Poisson process, Compound Poisson process, Jump processes and their integrals, Stochastic calculus for jump processes.
 Chapter 9, Asset Models: Stylized facts of returns, Continuoustime models (the BlackScholesMerton model, the Merton model, the Heston model, the Bates model, the Duffie, Pan, and Singleton framework), Discretization, Discretetime models (Regimeswitching models, Autoregressive conditional heteroskedasticity, generalized ARCH, the stochastic volatility model).
 Chapter 10, Parameter Estimation: Momentbased methods, Likelihoodism and likelihoodbased methods, Direct likelihood calculations, Presence of latent variables, Bayesianism and Bayesianbased methods, Markov chain Monte Carlo, Issues and challenges.
 Chapter 11, Economic Scenario Generators: Overview of ESGs, Need for ESGs, Roles of physical and riskneutral scenarios, Inflation models, Interest rate models, Corporate bond models, Equity index models, International considerations, Integrated models (e.g., Wilkie, AAA model).
 Chapter 12, DiscreteTime Market Models: Review of the binomial option pricing model, Price systems and martingale measures, Selffinancing strategy and arbitrage, Arbitrage and martingale measures, Attainable claims and price uniqueness, Admissible strategy and martingales, Relationship between replication and pricing, Riskneutral and martingale measures, Market completeness.
 Chapter 13, Girsanov’s Theorem and Fundamental Theorems of Asset Pricing: RadonNikodym theorem, Girsanov’s theorem, Multidimensional Girsanov’s theorem.
 Chapter 14, Replication Strategies and Martingale Representation Theorem: Selffinancing strategies, Martingale representation theorem, Asset replication.
 Chapter 15, Option Pricing in Practice: Common option pricing models (BlackScholesMerton, Merton, Heston, HestonNandi), The Dueffie, Pan and Singleton (2000) framework, Monte Carlo simulation, Fourier inversion.
 Students will learn inclass through: formal lectures, presentations and problem solving. Outofclass learning will consist of: readings, internet research, and problem solving.
 There will be four hours of lecture per week. Some lectures might be rescheduled if necessary.
 Course material, references, links and messages will be posted on the course website (Canvas). Students are expected to read the material and to attempt as many problems as possible before attending the lectures.
 Regular assignments will be given throughout the semester.
 Office hours may be used for further explanations and relevant discussions.
 You are encouraged to discuss problems in small groups. However, you must work alone when writing up the solutions to the problems.
 Every attempt will be made for the exam questions to verify the objectives given above. Therefore, it is recommended that students regularly consult these objectives when working on problems during the semester and when studying for the exams
COURSELEVEL EDUCATIONAL GOALS:
This course aims to develop a thorough understanding of stochastic calculus and the standard probabilistic tools used in the financial and the insurance practice.
Grading
 Assignments 20%
 Projects and Presentations 50%
 Final Exam 30%
NOTES:
The pass mark is 50%. The final grade will be allocated according to the student’s achievement in the course. Under no circumstances will late assignments be accepted.
Missing an exam will result in a mark of 0 unless the student was prevented from taking it due to medical reasons with convincing evidence. Students should use the “Health Care Provider Statement” form available at http://www.sfu.ca/content/dam/sfu/students/pdf/healthcarestatementgeneral.pdf. Should you miss an exam, you must let the instructor know as soon as possible. Under no circumstances will make up exams be given. A student present at the start of an exam will have his/her exam marked even if he/she leaves early for any reason.
Academic Dishonesty:
Students are expected to take responsibility for their learning. To assist students in understanding scholarly expectations, the following actions are examples of violations of the Student Academic Integrity Policy. Please note that this list is not exhaustive.
 Plagiarism
 Submitting shared work as individual work (i.e, collusion)
 Submitting an assignment or paper more than once (i.e, cheating)
 Cheating during an exam: Using any device/mobile phone to receive or share information during the exam
 Submitting a purchased assignment or essay (i.e, contract cheating)
 Falsifying documents (e.g., Doctor’s note) to gain an advantage Accessing exam information from an unauthorized source (i.e., pay to pass)
Materials
REQUIRED READING:
None
RECOMMENDED READING:
 Hull, J. C. (2006). Options, Futures, and Other Derivatives. Pearson.
 Lyaso, A. (2017). Stochastic Methods in Asset Pricing. The MIT Press.
 McDonald, R. L. (2006). Derivatives Markets. Pearson.
 Shreve, S. (2012). Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer Science & Business Media.
 Shreve, S. (2004). Stochastic Calculus for Finance II: ContinuousTime Models. Springer Science & Business Media.
Department Undergraduate Notes:
Students with Disabilities:
Students requiring accommodations as a result of disability must contact the Centre for Accessible Learning 7787823112 or csdo@sfu.ca
Tutor Requests:
Students looking for a tutor should visit hhttps://www.sfu.ca/statactsci/allstudents/otherresources/tutoring.html. We accept no responsibility for the consequences of any actions taken related to tutors.
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the University community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s1001.html
TEACHING AT SFU IN FALL 2021
Teaching at SFU in fall 2021 will involve primarily inperson instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place. Whether your course will be inperson or through remote methods will be clearly identified in the schedule of classes. You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).
Enrolling in a course acknowledges that you are able to attend in whatever format is required. You should not enroll in a course that is inperson if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for inperson classes.
Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 7787823112) as early as possible in order to prepare for the fall 2021 term.