STA 2503 – Math Finance

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:

  1. Email me your CV and transcript, with a short description about yourself, and why you wish to take the course.
  2. 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).
  3. 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:


Discrete Time Models

  • Arbitrage Strategies and replicating portfolios

  • Multi-period model ( Cox, Ross, Rubenstein )

  • European, Barrier and American options

  • Change of Measure and Numeraire assets

Continuous Time Limit

  • Random walks and Brownian motion

  • Geometric Brownian motion

  • Black-Scholes pricing formula

  • Martingales and measure change

Equity derivatives

  • Puts, Calls, and other European options in Black-Scholes

  • American contingent claims

  • Barriers, Look-Back and Asian options

The Greeks and Hedging

  • Delta, Gamma, Vega, Theta, and Rho

  • Delta and Gamma neutral hedging

  • Time-based and move-based hedging

Interest Rate Derivatives

  • Short rate modesl : Vasicek, Hull-White, Cox-Ingersoll-Ross

  • Forward rate models : HJM and LIBOR market models

  • Bond options, caps, floors, and swap options

Foreign Exchange

  • Cross currency options

  • Quantos

  • Spot and forward price models

  • commodity-FX derivatives

Stochastic Volatility and Jump Modeling

  • Heston model

  • Compound Poisson and Levy models

  • Volatility Options

Numerical Methods

  • Monte Carlo and Least Square Monte Carlo

  • Finite Difference Schemes

  • 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

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 20162015, 2014, 2013 (with 12 videos), 2012 (with 11 videos), 2010 (with 20 videos), 

2017
 # Description Notes
1 Discrete time models: no-arbitrage; numeraire measures; CRR model

matlab code: Generate CRR grid, and simulate it’s path (matlab 2016b)

STA2503-01

Code: CRRSim

2  Multi-period models; self-financing conditions; no-arbitrage; FTAP; valuing Call options

matlab code: value European options using CRR tree

STA2503-02

Code: EuropeanOptionsCRR

3  Continuous time; self-financing; arbitrage; dynamic hedging; solving heat equation

matlab: simulation of functions of Ito processes, explicit PDE scheme for heat equation

STA2503-03

Code: Lec03-matlab

4 Feynman-Kac; PDE and Simulation; Delta-Hedging STA2503-04
5 Delta-Gamma Hedging; Girsanov’s Theorem STA2503-05

Code: Hedging

6 Numeraire Change;self-financing strategies;Intro to Heston model STA2503-06
7 Numeraire Change & Girsanov;Milstein Discretization; More on Heston model STA2503-07

Code: HestonModel

8 Review; Variance Swaps STA2503-08
9 Variance Swap replication; VIX; Forwards and Futures; Intro to Stochastic Interest Rates STA2503-09

CBOE-notes

CBOE-notes-VIX

10 Review; Coupon Bonds; Bermudan & American Options STA2503-10

Code: AmericanPut

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 write-up 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 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.

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:

http://www.utoronto.ca/academicintegrity/index.html