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 14 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:

Arbitrage Strategies and replicating portfolios

Multiperiod model ( Cox, Ross, Rubenstein )

European, Barrier and American options

Change of Measure and Numeraire assets

Random walks and Brownian motion

Geometric Brownian motion

BlackScholes pricing formula

Martingales and measure change

Puts, Calls, and other European options in BlackScholes

American contingent claims

Barriers, LookBack and Asian options

Delta, Gamma, Vega, Theta, and Rho

Delta and Gamma neutral hedging

Timebased and movebased hedging

Short rate modesl : Vasicek, HullWhite, CoxIngersollRoss

Forward rate models : HJM and LIBOR market models

Bond options, caps, floors, and swap options

Cross currency options

Quantos

Spot and forward price models

commodityFX derivatives

Heston model

Compound Poisson and Levy models

Volatility Options

Monte Carlo and Least Square Monte Carlo

Finite Difference Schemes

Fourier Space TimeStepping
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
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 2016, 2015, 2014, 2013 (with 12 videos), 2012 (with 11 videos), 2010 (with 20 videos),
2017  

#  Description  Notes 
1  Discrete time models: noarbitrage; numeraire measures; CRR model
matlab code: Generate CRR grid, and simulate it’s path (matlab 2016b) 
STA250301
Code: CRRSim 
2  Multiperiod models; selffinancing conditions; noarbitrage; FTAP; valuing Call options
matlab code: value European options using CRR tree 
STA250302
Code: EuropeanOptionsCRR 
3  Continuous time; selffinancing; arbitrage; dynamic hedging; solving heat equation
matlab: simulation of functions of Ito processes, explicit PDE scheme for heat equation 
STA250303
Code: Lec03matlab 
4  FeynmanKac; PDE and Simulation; DeltaHedging  STA250304 
5  DeltaGamma Hedging; Girsanov’s Theorem  STA250305
Code: Hedging 
6  Numeraire Change;selffinancing strategies;Intro to Heston model  STA250306 
7  Numeraire Change & Girsanov;Milstein Discretization; More on Heston model  STA250307
Code: HestonModel 
8  Review; Variance Swaps  STA250308 
9  Variance Swap replication; VIX; Forwards and Futures; Intro to Stochastic Interest Rates  STA250309 
10  Review; Coupon Bonds; Bermudan & American Options  STA250310
Code: AmericanPut 
11  Bond options, Swaps and Swap options  STA250311
Code: Bonds and Swaptions 
Grading Scheme:
Item  Frequency  Grade 
Exam  End of Term  50% 
Quizzes  weekly  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 writeup a short report. These challenges are not to be handed in, but you are strongly encouraged to work through them in teams.
Tutorials:
Your TAs are AliAl 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 makeup quiz consisting of a short verbal exam will replace it.
Office Hours:
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: