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STAC70 Statistics & Finance II (Winter 2022)

Syllabus

Instructor: Leonard Wong (email: [email protected])

Lectures: Monday 9am–10am (HW 215), Wednesday 12pm–2pm (BV 260).
The initial lectures (at least until January 31) will be conducted on Zoom at:

https://utoronto.zoom.us/j/7522990199

Announcements and course materials will be posted on Quercus.

Office hours: Monday 4–6pm or by appointment

Teaching assistant: Madhu Gunasingam (email: [email protected])

Online forum: You are encouraged to use Piazza to (anonymously) ask questions about the
course and discuss among yourselves. You can join using the following link:

piazza.com/utoronto.ca/winter2022/stac70h3

1 Outline

This course is an introduction to the basics of option pricing theory. Options, futures and other
derivatives are financial contracts that can be traded in the market for hedging and speculation,
and they play important roles in modern financial markets. Option pricing theory is about how
to value these contracts and how to manage their risks.

The main financial results in this course include:

� The Black-Scholes formula based on the ideas of no arbitrage and dynamic replication.
We will also see that the Black-Scholes(-Merton) model can be viewed as the limit of the
binomial model as the number of time periods tends to infinity.

� The martingale approach which puts option pricing on a rigorous probabilistic basis.

Along the way we will develop some theories of stochastic processes including martingale, Brow-
nian motion and stochastic integration. We try to offer a balanced treatment featuring financial
ideas, mathematical intuition and concrete examples. The R programming language will be used
to illustrate some of the concepts.

Upon completing the course, the student will have a good understanding of the basic ideas
of option pricing and some vocabularies of modern quantitative finance. The student will have
a solid background to tackle more advanced treatments on theory and implementation.

UTSC course website: https://utsc.calendar.utoronto.ca/course/STAD70H3

Textbook: We will use our own lecture notes.

Here are some books (from senior undergraduate to Master level) that may be consulted for
alternative treatments:

1

� Mathematical Finance: A Very Short Introduction by Mark Davis (2019).

� Mathematics of Finance: An Intuitive Introduction by Donald G. Saari (2019).

� Investment Science by David G. Luenberger (2013).

� Options, Futures, and Other Derivatives by John Hull (2017).

� The Concepts and Practice of Mathematical Finance by Mark S. Joshi (2008).

� Stochastic Calculus for Finance (two volumes) by Steve Shreve (2004).

� Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula by
Seán Dineen (2013).

� Stochastic Calculus and Financial Applications by J. Michael Steele (2010).

2 Grading scheme

� 25%: Assignments

� 30%: Midterm (2 hours) (around week 7, date to be confirmed)

� 45%: Final exam (3 hours)

Assignments (20%)

There will be 5 assignments. The assignments are to be submitted online through Quercus.
Your work may be handwritten (professionally scanned) or typed (preferably using LATEX).
Some assignment problems require R programming.

Late submission policy:

� 1 minute to 23 hours and 59 minutes: 20% penalty

� 24 hours to 1 day 23 hours 59 minutes: 40% penalty, and so on.

Midterm (30%)

The date and time will be announced later. If you are not able to attend the midterm for a
valid reason (e.g. medical), you must let me know as soon as possible. Then you will need to
take a make-up test (which may be conducted as an oral exam).

Final exam (45%)

The date and time will be announced later. It will cover all materials covered in the course
(before and after the midterm).

3 Tentative schedule

2

Week Topic

1 Introduction
2 Single period models
3 Martingales on the binomial tree
4 Conditional expectation and martingale
5 The binomial model
6 Brownian motion
7 Properties of Brownian motion
8 Stochastic integration
9 Stochastic calculus
10 The Black-Scholes-Merton model
11 Change of measure
12 From theory to practice

4 Important information

Accessibility

Students with diverse learning styles and needs are welcome in this course. In particular,
if you have a disability/health consideration that may require accommodations, please feel
free to approach the instructor and/or the UTSC AccessAbility Service as soon as possible.
Enquiries are confidential. The UTSC AccessAbility Services staff are available by appoint-
ment to assess specific needs, provide referrals and arrange appropriate accommodations, at
[email protected]

Religious accommodations

The University has a commitment concerning accommodation for religious observances. I will
make every reasonable effort to avoid scheduling tests, examinations, or other compulsory activ-
ities on religious holy days not captured by statutory holidays. According to University Policy, if
you anticipate being absent from class or missing a major course activity (like a test, or in-class
assignment) due to a religious observance, please let me know as early in the course as possible,
and with sufficient notice (at least two to three weeks), so that we can work together to make
alternate arrangements.

Academic integrity

The University treats cases of cheating and plagiarism very seriously. The University of Toronto’s
Code of Behaviour on Academic Matters (https://governingcouncil.utoronto.ca/secretariat/
policies/code-behaviour-academic-matters-july-1-2019) outlines the behaviours that con-
stitute academic dishonesty and the processes for addressing academic offences. Potential of-
fences in papers and assignments include using someone else’s ideas or words without appropriate
acknowledgement, submitting your own work in more than one course without the permission
of the instructor, making up sources or facts, obtaining or providing unauthorized assistance
on any assignment. On tests and exams cheating includes using or possessing unauthorized
aids, looking at someone else’s answers during an exam or test, misrepresenting your identity, or
falsifying or altering any documentation required by the University, including (but not limited

3

to) doctor’s notes.

Course materials, including lecture notes

Course materials are provided for the exclusive use of enrolled students. Do not share them with
others. I do not want to discover that a student has put any of my materials into the public
domain, has sold my materials, or has given my materials to a person or company that is using
them to earn money. The University will support me in asserting and pursuing my rights, and
my copyrights, in such matters.

4

STAD70 Statistics & Finance II (Winter 2022)

Syllabus

Instructor: Leonard Wong (email: [email protected])

Lectures: Monday 2pm–4pm (HL B106), Wednesday 4pm–5pm (IC 326).
The initial lectures (at least until January 31) will be conducted on Zoom at:

https://utoronto.zoom.us/j/7522990199

Announcements and course materials will be posted on Quercus.

Office hours: Wednesday 3–4pm and 5–6pm or by appointment

Grader: Peng Liu (email: [email protected])

Online forum: You are encouraged to use Piazza to (anonymously) ask questions about the
course and discuss among yourselves. You can join using the following link:

piazza.com/utoronto.ca/winter2022/stad70

1 Outline

This course is an introduction to some applications of statistical and computational tools in
quantitative finance. Specifically, we focus on two important and closely related topics:

(i) Financial econometrics, i.e., statistical modeling of financial data and tests of finan-
cial/economic hypotheses.

(ii) Quantitative investment, i.e., the construction, backtesting, and implementation of invest-
ment strategies using quantitative methods.

UTSC course website: https://utsc.calendar.utoronto.ca/course/STAD70H3

Textbook: We will use our own lecture notes whose materials are mainly taken from the
following textbooks:

� Statistics and Data Analysis for Financial Engineering (2nd edition) by Ruppert and
Matteson (2019).

� Analysis of Financial Time Series (3rd edition) by Tsay (2010).

� Financial Econometrics: Models and Methods by Linton (2019).

1

2 Grading scheme

� 30%: Assignments

� 30%: Midterm (2 hours) (around week 7, date to be confirmed)

� 40%: Final exam (3 hours)

Assignments (30%)

There will be 4 assignments. The assignments are to be submitted online through Quercus.
Your work may be handwritten (professionally scanned) or typed (preferably using LATEX).
Some assignment problems require R programming.

Late submission policy:

� 1 minute to 23 hours and 59 minutes: 20% penalty

� 24 hours to 1 day 23 hours 59 minutes: 40% penalty, and so on.

Midterm (30%)

The date and time will be announced later. If you are not able to attend the midterm for a
valid reason (e.g. medical), you must let me know as soon as possible. Then you will need to
take a make-up test (which may be conducted as an oral exam).

Final exam (40%)

The date and time will be announced later. It will cover all materials covered in the course
(before and after the midterm).

3 Tentative schedule

Week Topic

1 Introduction
2 Asset returns
3 Stylized facts of asset returns
4 Tools from time series analysis
5 Efficient market hypothesis
6 Volatility modelling
7 Risk management
8 Mean-variance portfolio selection
9 Capital asset pricing model
10 Factor models
11 Statistical arbitrage
12 Growth optimal portfolio

2

4 Important information

Accessibility

Students with diverse learning styles and needs are welcome in this course. In particular,
if you have a disability/health consideration that may require accommodations, please feel
free to approach the instructor and/or the UTSC AccessAbility Service as soon as possible.
Enquiries are confidential. The UTSC AccessAbility Services staff are available by appoint-
ment to assess specific needs, provide referrals and arrange appropriate accommodations, at
[email protected]

Religious accommodations

The University has a commitment concerning accommodation for religious observances. I will
make every reasonable effort to avoid scheduling tests, examinations, or other compulsory activ-
ities on religious holy days not captured by statutory holidays. According to University Policy, if
you anticipate being absent from class or missing a major course activity (like a test, or in-class
assignment) due to a religious observance, please let me know as early in the course as possible,
and with sufficient notice (at least two to three weeks), so that we can work together to make
alternate arrangements.

Academic integrity

The University treats cases of cheating and plagiarism very seriously. The University of Toronto’s
Code of Behaviour on Academic Matters (https://governingcouncil.utoronto.ca/secretariat/
policies/code-behaviour-academic-matters-july-1-2019) outlines the behaviours that con-
stitute academic dishonesty and the processes for addressing academic offences. Potential of-
fences in papers and assignments include using someone else’s ideas or words without appropriate
acknowledgement, submitting your own work in more than one course without the permission
of the instructor, making up sources or facts, obtaining or providing unauthorized assistance
on any assignment. On tests and exams cheating includes using or possessing unauthorized
aids, looking at someone else’s answers during an exam or test, misrepresenting your identity, or
falsifying or altering any documentation required by the University, including (but not limited
to) doctor’s notes.

Course materials, including lecture notes

Course materials are provided for the exclusive use of enrolled students. Do not share them with
others. I do not want to discover that a student has put any of my materials into the public
domain, has sold my materials, or has given my materials to a person or company that is using
them to earn money. The University will support me in asserting and pursuing my rights, and
my copyrights, in such matters.

3