MMF1928H / STA 2503F –
Pricing Theory I / Applied Probability for Mathematical Finance
Important:
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 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.
FYI: STA2502
is open.
You might be also interested in a Short
Course on Commodity Models
Location :
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
# 
Description 
Video 
Notes 
1 



2 
Review Fundamental Theorem
of Finance, CRR model limiting distribution, riskneutral
distribution, call option price, using asset as numeraire,
American option and default model 

STA25032.pdf 
3 
Changing between two numeraires; shortrate model calibration
to bond prices 
STA25033a
STA25033b
STA25033c

STA25033.pdf 
4 
IR model calibration,
Vasicek model, IRS and CCIRS 
STA25034a
STA25034b
STA25034c
STA25034d
STA25034e

STA25304.pdf
(the 1/kappa factor is now corrected)

5 
Continuous time dynamic hedging; The pricing PDE;
BlackScholes case; FeynmanKac Theorem intro; Girsanov's
Theorem intro; The Greeks; Movebased hedging 
STA25035a
STA25035b
STA25035c
STA25035d
STA25035e

STA25035.pdf 
6 
Dividend paying assets,
Forward and Futures, Delta, Gamma, Girsanov's Theorem
cont'd 
STA2503a
STA2503b
STA2503c
STA2503d
STA2503e

STA25036.pdf 
7 
Dynamic hedging with multiple uncertainties; multivariate
Ito's lemma; Intro to Heston Model 

STA25037.pdf 
8 
Currency Options 
STA25038a
STA25038b
STA25038c

STA25038.pdf 
9 
default modeling, reduced form models, defaultable bonds,
CDS, stochastic intensity 

STA25039.pdf 
10 
Caps, caplets, swaptions 

STA250310.pdf 
11 



12 



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
Multiperiod 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
BlackScholes pricing
formula
Martingales and
measure change

Equity derivatives
Puts, Calls, and other
European options in BlackScholes
American contingent
claims
Barriers, LookBack
and Asian options

The Greeks and Hedging
Delta, Gamma, Vega,
Theta, and Rho
Delta and Gamma
neutral hedging
Timebased and
movebased hedging

Interest rate derivatives
Short rate and forward
rate models
Bond options, caps,
floors, swap options

Foreign Exchange and Commodity models

Stochastic Volatility and Jump Modeling

Numerical Methods
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.
 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:
Item

Frequency

Grade

Exam

End of Term

50%

Quizzes

weekly

25%

Challenges

~ every 23 weeks

25%

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 writeup a short report. This will be
conducted in teams of 34 people. These are normally distributed every
twothree weeks, but you will be informed ahead of time when a
challenge is to be conducted.
Tutorials:
Your TA is Xuancheng (Bill) Huang, Ph.D. candidate,
Dept. Statistical Sciences
Office Hours:
TBA
Academic Code of Conduct
http://www.utoronto.ca/academicintegrity/index.html
