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 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 :
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
|
MMF1928-1.pdf |
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
|
MMF1928-2.pdf |
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
|
MMF1928-3.pdf
MeasureChanges.xlsx
MeasureChanges.pdf
|
4 |
Hull-White / Extended
Vasicek model, Interest Rate Swaps, CCIRS |
MMF1928-4a
stream
MMF1928-4b
stream
MMF1928-4a
download
MMF1928-4b
download
|
MMF1928-4.pdf |
6 |
Dynamic hedging in continuous time, Pricing PDE, Time and
Move based hedging |
MMF1928-6a
stream
MMF1928-6b
stream
MMF1928-6c
stream
|
MMF1928-6.pdf |
7 |
Delta-Gamma Hedging, Feynman-Kac |
MMF1928-7a
stream
MMF1928-7b
stream
MMF1928-7c
stream
|
MMF1928-7.pdf |
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 |
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 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
Time-Stepping
|
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 2-3 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 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.
Tutorials:
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
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