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

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MMF1928H / STA 2503F –

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.

You might be also interested in a Short Course on Commodity Models

Location :

Tutorials: Mon 4pm - 6pm in WI 1016 ( 40 Willcocks St)

Lectures: Wed 2pm - 5pm in SS 2127 ( 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

  Description Video Notes
1 Binomial Model, No Arbitrage, Fundamental Theorem of Asset Pricing, Martingale Measure MMF1928-1A stream

MMF1928-1B stream

MMF1928-1C stream

MMF1928-1A download

MMF1928-1B download

MMF1928-1C download

2 Quick view of Incomplete markets, default equity model, European option valuation, American options MMF1928-2A stream

MMF1928-2B stream

MMF1928-2C stream

MMF1928-2A download

MMF1928-2B download

MMF1928-2C download

3 Measure changes, Iinterest rate trees, Vasicek model

MMF1928-3a stream

MMF1928-3b stream

MMF1928-3c stream

MMF1928-3d stream

MMF1928-3a download

MMF1928-3b download

MMF1928-3c download

MMF1928-3d download




4 Hull-White / Extended Vasicek model, Interest Rate Swaps, CCIRS MMF1928-4a stream

MMF1928-4b stream

MMF1928-4a download

MMF1928-4b download

6 Dynamic hedging in continuous time, Pricing PDE, Time and Move based hedging MMF1928-6a stream

MMF1928-6b stream

MMF1928-6c stream

7 Delta-Gamma Hedging, Feynman-Kac MMF1928-7a stream

MMF1928-7b stream

MMF1928-7c stream

8 Feynman-Kac, Measure Changes, Futures Hedging MMF1928-8 stream MMF1928-8.pdf
9 Options on Futures, Measure Changes continued MMF1928-9 stream MMF1928-9.pdf
10 Heston model, implied volatility, variance swaps and options MMF1928-10 stream MMF1928-10.pdf
11 Stochastic Interest rate models, extended Vasicek model, bond options MMF1928-11 stream MMF1928-11.pdf
12 Caps and swaptions MMF1928-12 stream MMF1928-12.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






~ every 2-3 weeks


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. 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. This will be conducted in teams of 3-4 people. These are normally distributed every two-three weeks, but you will be informed ahead of time when a challenge is to be conducted.


Your TA is Ryan Donnelly, one of my Ph.D. students (Dept. Mathematics) and an MMF grad.

Office Hours:

Tuesdays 10am - noon in SS 6005