MMF1928H / STA 2503F – Sep - Dec, 2015
Pricing Theory I / Applied Probability for Mathematical Finance
Important:
This course is restricted and enrollment is limited, please contact me if you are interested in taking the couse.
If you are interested in taking this course, please read through chapters 1-4 of Shreve's book on Stochastic Calculus for finance volume 2. Spend more time on chapters 3 and 4, with a light reading of chapters 1 and 2.
FYI: STA2502 is open.
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Location :
Tutorials: Mon 4pm - 6pm in SS 1087 ( 100 St. George Street )
Lectures: Wed 2pm - 5pm in SS 1087 ( 100 St. George Street )
Class Notes / Lectures :
Class notes and videos will be updated as the course progresses.
Archived content from 2010 can be found here.
Archived content from 2012 can be found here
Archived content from 2013 can be found here
Archived content from 2014 can be found here
| # | Description | Notes | |
|---|---|---|---|
| 1 | Binomial model, the notion of arbitrage, pricing measures, measure changes | STA-2503-01.pdf | |
| 2 | Incomplete markets; CRR model, limiting distributions, asset as a numeraire, Black-Scholes formula | STA-2503-02.pdf | |
| 3 | default model; American option pricing; Continuous time dynamic hedging | STA-2503-03.pdf | |
| 4 | Solving the pricing PDE; Feynman-Kac Theorem; Girsanov's Theorem | STA-2503-04.pdf | |
| 5 | The Fundamental Theorem of Finance, the Heston model | STA-2503-05.pdf | |
| 6 | Numeraires, Measure changes, Bond options | STA-2503-06.pdf | |
| 7 | more on bonds and bond options, interest rate swaps | STA-2503-07.pdf | |
| 8 | swaptions; caps; LMM, LFM and LSM | STA-2503-08.pdf | |
| 9 | Foreign Exchange markets and options | STA-2503-09.pdf | |
| 10 | FX options continued | STA-2503-10.pdf | |
Outline:
This course focuses on financial theory and its application to various derivative products. A working knowledge of basic probability theory, stochastic calculus, knowledge of ordinary and partial differential equations and familiarity with the basic financial instruments is assumed. The topics covered in this course include, but are not limited to:
Discrete Time Models
|
Continuous Time Limit
|
Equity derivatives
|
The Greeks and Hedging
|
Interest rate derivatives
|
Foreign Exchange and Commodity models
|
Stochastic Volatility and Jump Modeling
|
Numerical Methods
|
Textbook:
The following are recommended (but not required) text books for this course.
- Options, Futures and Other Derivatives , John Hull, Princeton Hall
- Arbitrage Theory in Continuous Time, Tomas Bjork, Oxford University Press
- Stochastic Calculus for Finance II : Continuos Time Models, Steven Shreve, Springer
- Financial Calculus: An Introduction to Derivative Pricing, Martin Baxter and Andrew Rennie
Grading Scheme:
Item |
Frequency |
Grade |
Exam |
End of Term |
50% |
Quizzes |
weekly |
50% |
The exam focuses on theory and will be closed book, but I will provide a single sheet with pertinent formulae.
Quizzes test basic knowledge of the material and are conducted in the tutorials every week.
Challenges are real world inspired problems that are based on the theory. To solve them you will be required to understand the theory, formulate an approach to the problem, implement the numerics in matlab or R, interpret the results and write-up a short report. These challenges are not to be handed in, but you are strongly encouraged to work through them in teams.
Tutorials:
Your TA is Ali Al-Aradi, a Ph.D. student in the Department of Statistical Sciences and a former MMF student.
Tutorials are held weekly on Mondays from 4 pm – 6 pm in SS 1087 and quizzes are conducted at the start of tutorials. If you must miss a quiz for an interview or for health reasons, you must inform me with proof and a make-up quiz consisting of a short verbal exam will replace it.
Office Hours:
TBA
Academic Code of Conduct
Below is a link to the academic code of conduct at the University of Toronto: