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.
Extra office hours: Friday, Monday and Tuesday 10 - noon.
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Exam "Hints"
1. Describe two pricing theory concepts
2. true / false ( ranging over concepts in the entire course )
3. sketching some typical plots you’ve seen in the course
4. “Black-Scholes” pricing
5. Related to the Vasicek model and IRS
6. Related to FX options
7. Something “new"
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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: Wed 1pm - 3pm in WB 342 ( 200 College Street )
Lectures: Wed 3pm - 6pm in GB 119 ( 35 St. George Street )
Office Hours: Tuesday's 10:00am to 12:00 noon in my office SS 6005.
Class Notes / Lectures :
Class notes and videos will be updated as the course progresses.
Archived content from 2010 can be found here.
| Description | Video | Notes | |
|---|---|---|---|
| 1. | Binomial Model, Three Assets, Numeraires, Default Model | MMF1928-2012-1.pdf | |
| 2. | Measure Change, Black-Scholes Formula, Minimum Variance Hedge, Interest Rate Trees | MMF1928-2012-2.pdf | |
| 3. | Arrow-Debreu Securities, Fokker-Planck Equation, Vasicek Model, CCIRS | MMF1928-2012-3.pdf | |
| 4. | Continuous Time Finance; Pricing PDE and No Arbitrage; Feynman-Kac; Risk-Neutral Measure | MMF1928-2012-4.pdf | |
| 5. | Black-Scholes PDE solutions, Time and Move-based hedging, Delta and Gamma | sorry sound did not record | MMF1928-2012-5.pdf |
| 6. | Measure Changes, Girsanov's Theorem, Numeraires | ||
| 7. | Implied Volatility, Local Volatility & Heston Model, Var Swaps | MMF1928-2012-7 stream download |
MMF1928-2012-7.pdf |
| 8. | More on Heston, Volatility Index (VIX) and Var Swaps, Tutorial | MMF1928-2012-8.pdf | |
| 9. | Interest Rate Derivatives, Vasicek Model, Bond Options, Forward-Neutral measure | MMF1928-2012-9 stream download |
MMF1928-2012-9.pdf |
| 10. | Interest Rate Caps and Swaptions | MMF1928-2012-10 stream download |
MMF1928-2012-10.pdf |
| 11. | Foreign Exchange (FX) Options | MMF1928-2012-11 stream download |
MMF1928-2012-11.pdf |
| 12 | Options on Dividend Paying Assets & Futures | MMF1928-2012-12 stream download |
MMF1928-2012-12.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:
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Discrete Time Models
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Continuous Time Limit
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Equity derivatives
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The Greeks and Hedging
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Interest rate derivatives
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Foreign Exchange and Commodity models
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Stochastic Volatility and Jump Modeling
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Numerical Methods
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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:
I will hold office hours on Tuesday's from 10:00am to 12:00 noon in my office SS6005.