MMF1928H / STA 2503F –
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.
You might be also interested in a Short Course on Commodity Models
Location :
Tutorials: Mon 4pm - 6pm in WI 1016 ( 40 Willcocks St)
Lectures: Wed 2pm - 5pm in SS 2127 ( 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
| Description | Video | Notes | |
|---|---|---|---|
| 1 | Binomial Model, No Arbitrage, Fundamental Theorem of Asset Pricing, Martingale Measure | MMF1928-1A stream | MMF1928-1.pdf |
| 2 | Quick view of Incomplete markets, default equity model, European option valuation, American options | MMF1928-2A stream | MMF1928-2.pdf |
| 3 | Measure changes, Iinterest rate trees, Vasicek model | MMF1928-3.pdf | |
| 4 | Hull-White / Extended Vasicek model, Interest Rate Swaps, CCIRS | MMF1928-4a stream | MMF1928-4.pdf |
| 6 | Dynamic hedging in continuous time, Pricing PDE, Time and Move based hedging | MMF1928-6a stream | MMF1928-6.pdf |
| 7 | Delta-Gamma Hedging, Feynman-Kac | MMF1928-7a stream | MMF1928-7.pdf |
| 8 | Feynman-Kac, Measure Changes, Futures Hedging | MMF1928-8 stream | MMF1928-8.pdf |
| 9 | Options on Futures, Measure Changes continued | MMF1928-9 stream | MMF1928-9.pdf |
| 10 | Heston model, implied volatility, variance swaps and options | MMF1928-10 stream | MMF1928-10.pdf |
| 11 | Stochastic Interest rate models, extended Vasicek model, bond options | MMF1928-11 stream | MMF1928-11.pdf |
| 12 | Caps and swaptions | MMF1928-12 stream | MMF1928-12.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 |
25% |
Challenges |
~ every 2-3 weeks |
25% |
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. 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. This will be conducted in teams of 3-4 people. These are normally distributed every two-three weeks, but you will be informed ahead of time when a challenge is to be conducted.
Tutorials:
Your TA is Ryan Donnelly, one of my Ph.D. students (Dept. Mathematics) and an MMF grad.
Office Hours:
Tuesdays 10am - noon in SS 6005