Important
This course has restricted enrollment, please contact me if you are interested in taking the course.
If you are interested in taking this course:
- Email me your CV and transcript, with a short description about yourself, and why you wish to take the course.
- If I give you permission, please fill out the SGS add/drop form, have your graduate chair sign it, print the email with permission, and bring it to the Statistical Sciences main office (SS6018).
- 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. The video lectures 7, 8 and 9 from STA 2502 may also be helpful.
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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Arbitrage Strategies and replicating portfolios
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Multi-period model ( Cox, Ross, Rubenstein )
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European, Barrier and American options
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Change of Measure and Numeraire assets
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Random walks and Brownian motion
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Geometric Brownian motion
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Black-Scholes pricing formula
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Martingales and measure change
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Puts, Calls, and other European options in Black-Scholes
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American contingent claims
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Barriers, Look-Back and Asian options
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Delta, Gamma, Vega, Theta, and Rho
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Delta and Gamma neutral hedging
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Time-based and move-based hedging
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Short rate modesl : Vasicek, Hull-White, Cox-Ingersoll-Ross
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Forward rate models : HJM and LIBOR market models
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Bond options, caps, floors, and swap options
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Cross currency options
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Quantos
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Spot and forward price models
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commodity-FX derivatives
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Heston model
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Compound Poisson and Levy models
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Volatility Options
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Monte Carlo and Least Square Monte Carlo
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Finite Difference Schemes
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Fourier Space Time-Stepping
Textbook:
The following are recommended (but not required) text books for this course:
- Stochastic Calculus for Finance II : Continuous Time Models, Steven Shreve, Springer
- Options, Futures and Other Derivatives , John Hull, Princeton Hall
Two additional books that you may find useful are:
- Arbitrage Theory in Continuous Time, Tomas Bjork, Oxford University Press
- Financial Calculus: An Introduction to Derivative Pricing, Martin Baxter and Andrew Rennie
Location(2018)
Tutorials: Mon 4pm – 6pm in SS 2110 ( 100 St. George Street )
Lectures: Wed 2pm – 5pm in UC 161 ( King’s College Circle )
Class Notes / Lectures
Class notes and videos will be updated as the course progresses.
Archived content from 2017, 2016, 2015, 2014, 2013 (with 12 videos), 2012 (with 11 videos), 2010 (with 20 videos),
Notes for 2018 are posted on Quercus
Grading Scheme:
| Item | Frequency | Grade |
| Exam | End of Term | 50% |
| Mini-Projects | 4 / Term | 50% |
The exam focuses on theory and will be closed book, but I will provide a single sheet with pertinent formulae.
Mini-Projects 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 python, matlab or R, interpret the results and write-up a short report.
Tutorials:
Your TAs are Ali-Al Aradi and Philippe Casgrain, both Ph.D. students in the Department of Statistical Sciences focusing on research in Financial Mathematics.
Tutorials are held weekly on Mondays from 4 pm – 6 pm in SS 2110.
Office Hours:
TBA in Stewart 410 E
Academic Code of Conduct
Below is a link to the academic code of conduct at the University of Toronto: