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 SS 1085 ( 100 St. George Street )
Lectures: Wed 2pm - 5pm in SS 1085 ( 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
| # | Description | Video | Notes |
|---|---|---|---|
| 1 | |||
| 2 | Review Fundamental Theorem of Finance, CRR model limiting distribution, risk-neutral distribution, call option price, using asset as numeraire, American option and default model | STA2503-2.pdf | |
| 3 | Changing between two numeraires; short-rate model calibration to bond prices | STA2503-3a | STA2503-3.pdf |
| 4 | IR model calibration, Vasicek model, IRS and CCIRS | STA2503-4a | STA2530-4.pdf
(the 1/kappa factor is now corrected) |
| 5 | Continuous time dynamic hedging; The pricing PDE; Black-Scholes case; Feynman-Kac Theorem intro; Girsanov's Theorem intro; The Greeks; Move-based hedging | STA2503-5a | STA2503-5.pdf |
| 6 | Dividend paying assets, Forward and Futures, Delta, Gamma, Girsanov's Theorem cont'd | STA2503-a | STA2503-6.pdf |
| 7 | Dynamic hedging with multiple uncertainties; multi-variate Ito's lemma; Intro to Heston Model | STA2503-7.pdf | |
| 8 | Currency Options | STA2503-8a | STA2503-8.pdf |
| 9 | default modeling, reduced form models, defaultable bonds, CDS, stochastic intensity | STA2503-9.pdf | |
| 10 | Caps, caplets, swaptions | STA2503-10.pdf | |
| 11 | |||
| 12 |
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 Xuancheng (Bill) Huang, Ph.D. candidate, Dept. Statistical Sciences
Office Hours:
TBA