S. Jaimungal
Department of Statistics and Mathematical Finance Program, University of Toronto

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MMF1928H / STA 2503F – Sep - Dec, 2015

Pricing Theory I / Applied Probability for Mathematical Finance


This course is restricted and enrollment is limited, please contact me if you are interested in taking the couse.

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.

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Location :

Tutorials: Mon 4pm - 6pm in SS 1087 ( 100 St. George Street )

Lectures: Wed 2pm - 5pm in SS 1087 ( 100 St. George Street )

Class Notes / Lectures :

Class notes and videos will be updated as the course progresses.

Archived content from 2010 can be found here.

Archived content from 2012 can be found here

Archived content from 2013 can be found here

Archived content from 2014 can be found here

 # Description Notes
1 Binomial model, the notion of arbitrage, pricing measures, measure changes STA-2503-01.pdf
2 Incomplete markets; CRR model, limiting distributions, asset as a numeraire, Black-Scholes formula STA-2503-02.pdf
3 default model; American option pricing; Continuous time dynamic hedging STA-2503-03.pdf
4 Solving the pricing PDE; Feynman-Kac Theorem; Girsanov's Theorem STA-2503-04.pdf
5 The Fundamental Theorem of Finance, the Heston model STA-2503-05.pdf
6 Numeraires, Measure changes, Bond options STA-2503-06.pdf
7 more on bonds and bond options, interest rate swaps STA-2503-07.pdf


8 swaptions; caps; LMM, LFM and LSM STA-2503-08.pdf
9 Foreign Exchange markets and options STA-2503-09.pdf
10 FX options continued STA-2503-10.pdf



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 and forward rate models

  • Bond options, caps, floors, swap options

 Foreign Exchange and Commodity models

  • 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


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:





End of Term





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 TA is Ali Al-Aradi, a Ph.D. student in the Department of Statistical Sciences and a former MMF student.

Tutorials are held weekly on Mondays from 4 pm – 6 pm in SS 1087 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:


Academic Code of Conduct

Below is a link to the academic code of conduct at the University of Toronto: