Mathematics of Financial Options
Financial Mathematics 3613
Winter 2020 - Course Outline
Instructor Information
Instructor: Hristo Sendov
Office: WSC 205
E-mail: hssendov@stats.uwo.ca
Phone: 519-661-2111 ext 86985
Office Hours: Mondays 11:30am-12:30pm & Wednesdays 1:30-2:30pm.
Lecture Hours: Mondays, Wendesdays and Fridays 2:30-3:30pm in PAB-148
Course Information
Course Description
An introduction to modern financial mathematics using a differential equations approach. Stochastic
differential equations and their related partial differential equations. The Fokker-Planck and Kolmogorov
PDEs. No-arbitrage pricing, the Black-Scholes equation and its solutions. American options. Exotic options.
Prerequisites Applied Mathematics 2402A or the former Differential Equations 2402A;
or Statistical Sciences 2503A/B.
Course Objectives
This course is about modern financial mathematics -- the study of making financial decisions under
uncertainty. Such decisions are shaped by three main drivers – the balance between future and present,
quantified by the interest rate; the role of uncertainty, often quantified in terms of the volatility, and
investors attitudes toward risk. Several products are available to trade and manage risk: stocks and bonds
at a basic level; forwards, futures, and options at a more advanced level. We will develop theories for pricing
and hedging both individual securities and portfolios of them. By the end of the course we will understand
two Nobel-prize winning economic theories – the Capital Asset Pricing Model of Markowitz, Sharpe, and
Miller (Nobel Prize 1990) and the Black-Scholes-Merton theory of options pricing (Nobel Prize 1997).
We will learn how to price and hedge a variety of stock options and briefly discuss the challenges involved
in extending this pricing technology to options on other underlying assets. Along the way we will use
mathematics ranging from basic stochastic calculus and linear differential equations to the asymptotic
expansion of integrals.
The topics covered are:
1) Intuition about uncertainty and risk
2) The classical approach to decision making under uncertainty
3) Repaying loans over time
4) Bond pricing with default: using difference equations
5) Tranching and collateralized debt obligations
6) Modeling stock prices
7) Mean-variance portfolio optimization
8) A qualitative introduction to options
9) Pricing options using binomial trees
10) Random walks
11) Black Scholes PDE for pricing options in continuous time
12) Solving the Black Scholes PDE
13) Some approximate values of the Black Scholes call formula
Assessment
Assignments and/or Quizzes
I will be assigning questions as we go for your practice at home. The midterms and the final exam will use
some of these questions and material from the textbook and lecture notes.
Midterms or Tests
Midterm test 1 (Thursday, February 13, 8:30-10:30PM, in SSC 3026)
Midterm test 2 (Thursday, March 19, 8:30-10:30PM, in SSC 3026)
Final Exam
The final exam will be on TBA. It will cover all of the course material.
Evaluation
Midterm 1 - 25%
Midterm 2 - 25%
Essay - 10%
Final Exam - 40%
Computing and/or Calculator Requirement
A non-programmable calculator may be used on the exams.
Missed Exams
If a student is unable to meet a course requirement due to illness or other serious circumstances, the
student must provide valid medical or other supporting documentation to the Dean's office as soon as
possible and contact his or her instructor immediately. It is the student's responsibility to make alternative
arrangements with his or her instructor once the accommodation has been approved and the instructor
has been informed. In the event of a missed final exam, a “Recommendation of Special Examination”
form must be obtained from the Dean's Office immediately. For further information please see:
http://www.uwo.ca/univsec/handbook/appeals/medical.pdf
Accommodation and Accessibility
If you are unable to meet a course requirement due to illness or other serious circumstances, you must
seek approval for the absence as soon as possible. Approval can be granted either through a
self-reporting of absence or via the Dean’s Office/Academic Counselling unit of your Home Faculty. If you
are a Science student, the Academic Counselling Office of the Faculty of Science is located in NCB 280,
and can be contacted at scibmsac@uwo.ca.
For further information, please consult the university’s policy on academic consideration for student
absences:
https://www.uwo.ca/univsec/pdf/academic_policies/appeals/Academic_Consideration_for_absences.pdf.
If you miss the Final Exam, please contact your faculty’s Academic Counselling Office as soon as you
are able to do so. They will assess your eligibility to write the Special Exam (the name given by the
university to a makeup Final Exam).
You may also be eligible to write the Special Exam if you are in a “Multiple Exam Situation”
(see http://www.registrar.uwo.ca/examinations/exam_schedule.html).
Academic Policies
The website for Registrarial Services is http://www.registrar.uwo.ca.
In accordance with policy, http://www.uwo.ca/its/identity/activatenonstudent.html,
the centrally administered e-mail account provided to students will be considered the individual’s official
university e-mail address. It is the responsibility of the account holder to ensure that e-mail received from
the University at his/her official university address is attended to in a timely manner.
You will be permitted to use non-programmable calculators on the Quizzes and Final Exam. You may
not use any other electronic device in place of a calculator.
Scholastic offences are taken seriously and students are directed to read the appropriate policy,
specifically, the definition of what constitutes a Scholastic Offence, at this website:
http:// www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_undergrad.pdf.
Support Cervices
Please contact the course instructor if you require lecture or printed material in an alternate format or if
any other arrangements can make this course more accessible to you. You may also wish to contact
Student Accessibility Services (SAS) at 661-2147 if you have any questions regarding accommodations.
The policy on Accommodation for Students with Disabilities can be found here:
www.uwo.ca/univsec/pdf/academic_policies/appeals/accommodation_disabilities.pdf
The policy on Accommodation for Religious Holidays can be found here:
http://www.uwo.ca/univsec/pdf/academic_policies/appeals/accommodation_religious.pdf
Learning-skills counsellors at the Student Development Centre (http://www.sdc.uwo.ca) are ready to help
you improve your learning skills. They offer presentations on strategies for improving time management,
multiple-choice exam preparation/writing, textbook reading, and more. Individual support is offered
throughout the Fall/Winter terms in the drop-in Learning Help Centre, and year-round through individual
counselling.
Students who are in emotional/mental distress should refer to Mental Health@Western
(http://www.health.uwo.ca/mental_health) for a complete list of options about how to obtain help.
Additional student-run support services are offered by the USC, http://westernusc.ca/services.
Announcements (1)
Textbook
Matt Davison, Quantitative Finance: A Simulation--Based Introduction Using Excel, CRC Press, (2014)
