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.
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:
Arbitrage Strategies and replicating portfolios
Multi-period model ( Cox, Ross, Rubenstein )
European, Barrier and American options
Change of Measure and Numeraire assets
Random walks and Brownian motion
Geometric Brownian motion
Black-Scholes pricing formula
Martingales and measure change
Puts, Calls, and other European options in Black-Scholes
American contingent claims
Barriers, Look-Back and Asian options
Delta, Gamma, Vega, Theta, and Rho
Delta and Gamma neutral hedging
Time-based and move-based hedging
Short rate modesl : Vasicek, Hull-White, Cox-Ingersoll-Ross
Forward rate models : HJM and LIBOR market models
Bond options, caps, floors, and swap options
Cross currency options
Spot and forward price models
Compound Poisson and Levy models
Monte Carlo and Least Square Monte Carlo
Finite Difference Schemes
Fourier Space Time-Stepping
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
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.
|1||Discrete time models: no-arbitrage; numeraire measures; CRR model
matlab code: Generate CRR grid, and simulate it’s path (matlab 2016b)
|2|| Multi-period models; self-financing conditions; no-arbitrage; FTAP; valuing Call options
matlab code: value European options using CRR tree
|3|| Continuous time; self-financing; arbitrage; dynamic hedging; solving heat equation
matlab: simulation of functions of Ito processes, explicit PDE scheme for heat equation
|4||Feynman-Kac; PDE and Simulation; Delta-Hedging||STA2503-04|
|5||Delta-Gamma Hedging; Girsanov’s Theorem||STA2503-05
|6||Numeraire Change;self-financing strategies;Intro to Heston model||STA2503-06|
|7||Numeraire Change & Girsanov;Milstein Discretization; More on Heston model||STA2503-07
|8||Review; Variance Swaps||STA2503-08|
|9||Variance Swap replication; VIX; Forwards and Futures; Intro to Stochastic Interest Rates||STA2503-09|
|10||Review; Coupon Bonds; Bermudan & American Options||STA2503-10
|Exam||End of Term||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.
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 1085 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.
Friday’s 13:00 to 14:00 in Stewart 410 E
Academic Code of Conduct
Below is a link to the academic code of conduct at the University of Toronto: