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.
Extra office hours: Friday, Monday and Tuesday 10  noon.
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Exam "Hints"
1. Describe two pricing theory concepts
2. true / false ( ranging over concepts in the entire course )
3. sketching some typical plots you’ve seen in the course
4. “BlackScholes” pricing
5. Related to the Vasicek model and IRS
6. Related to FX options
7. Something “new"
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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.

Description 
Video 
Notes 
1. 
Binomial Model, Three Assets, Numeraires, Default Model 
MMF192820121 stream
download 
MMF192820121.pdf 
2. 
Measure Change, BlackScholes Formula, Minimum Variance Hedge, Interest Rate Trees 
MMF192820122 stream
download 
MMF192820122.pdf 
3. 
ArrowDebreu Securities, FokkerPlanck Equation, Vasicek Model, CCIRS 
MMF192820123 stream
download 
MMF192820123.pdf 
4. 
Continuous Time Finance; Pricing PDE and No Arbitrage; FeynmanKac; RiskNeutral Measure 
MMF192820124 stream
download 
MMF192820124.pdf 
5. 
BlackScholes PDE solutions, Time and Movebased hedging, Delta and Gamma 
sorry sound did not record 
MMF192820125.pdf 
6. 
Measure Changes, Girsanov's Theorem, Numeraires 


7. 
Implied Volatility, Local Volatility & Heston Model, Var Swaps 
MMF192820127 stream
download 
MMF192820127.pdf 
8. 
More on Heston, Volatility Index (VIX) and Var Swaps, Tutorial 
MMF192820128 stream
download

MMF192820128.pdf 
9. 
Interest Rate Derivatives, Vasicek Model, Bond Options, ForwardNeutral measure 
MMF192820129 stream
download 
MMF192820129.pdf 
10. 
Interest Rate Caps and Swaptions 
MMF1928201210 stream
download 
MMF1928201210.pdf 
11. 
Foreign Exchange (FX) Options 
MMF1928201211 stream
download 
MMF1928201211.pdf 
12 
Options on Dividend Paying Assets & Futures 
MMF1928201212 stream
download 
MMF1928201212.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

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 Ryan Donnelly, one of my Ph.D. students (Dept. Mathematics) and an MMF grad.
Office Hours:
I will hold office hours on Tuesday's from 10:00am to 12:00 noon in my office SS6005.
