MMF1952Y / STA 2503F – Pricing Theory / Applied Probability for Mathematical Finance
Important:
This course is restricted and enrollment is limited. FYI: STA2502 is open.
Class Notes / Lectures :
Class notes and videos will be made available as the course progresses.
If you would like to obtain a copy of last year's material, please contact me. You can view the topics at this link.
| Date | Topic | Class Video | Class Notes |
| Sept 5, 07 | One-period binomial model | MMF1952-1.mpg | MMF1952-1.pdf |
| Sept 12, 07 | Multi-period model, Continuous Time Limit, Defaultable Stock | MMF1952-2a.wmv | MMF1952-2.pdf |
| Explicit Two Period Model Example | MMF1952-2b.wmv | MMF1952-2b.pdf | |
| Put on defaultable stock simple Excel imp | DefPut.xls | ||
| Sept 19, 07 | Interest Rate Modeling; Forward Trees for Arrow-Debreu Prices; Black-Derman-Toy Model and Calibration | MMF1952-3.wmv | MMF1952-3.pdf |
| Sept 26, 07 | Swaps and Swaptions; Monte Carlo Basics | MMF1952-4.wmv | MMF1952-4.pdf |
| Simple Monte Carlo Excel file | MonteCarlo.xls | ||
| Portfolios Excel file | Portfolios.xls | ||
| Oct 3, 07 | Stochastic Calculus Tools I | MMF1952-5.wmv | MMF1952-5.pdf |
| Oct 5, 07 | Stochastic Calculus Tutorial | Tutorial-5.mvw | Tutorial-5A.pdf |
| Simulating some SDEs | StochIntSim.xls | ||
| PPT Notes | StochCalc.pdf | ||
| Oct 12, 07 | Ito's lemma for Ito processes; Black-Scholes dynamic hedging; Feynman-Kac | MMF1952-6.wmv | MMF1952-6.pdf |
| Oct 31, 07 | Dynamic Hedging II | MMF1952-7.wmv | MMF1952.pdf |
| discrete time hedging simulation | HedgeSim.xls | ||
| Nov 2, 07 | Delta-Gamma Hedging; Martingale representation and dynamic hedging | MMF1952-8.wmv | MMF1952-8.pdf |
| discrete time hedging simulation II | HedgeSim2.xls | ||
| Nov 9, 07 | Incomplete Markets; Intro Continuous Time Interest Rate Modesl | MMF1952-9.wmv | MMF1952-9.pdf |
| Nov 14, 07 | Incomplete Markets II; Martingale representations; Stochastic Volatility Model | MMF1952-10.wmv | MMF1952-10.pdf |
| Nov 21, 07 | Interest Rate Models II; Numeraire Changes | MMF1952-11.wmv | MMF1952-11.pdf |
| Nov 27, 07 | Numeraire Changes; Convertible Bonds; Hull-White model outline | MMF1952-12.wmv | MMF1952-12.pdf |
| Apr 25, 08 | Credit Derivatives Overview, Poisson Process, CDS basics | MMF1952-13.wmv | MMF1952-13.pdf |
| May 1, 08 | CDS; piecewise constant rates; doubly stochastic Poisson processes; PDEs | MMF1952-14.wmv | MMF1951-14.pdf |
| May 8, 08 | Codependent defaults: doubly stochastic Poisson; Copulas; Factor Models | MMF1952-15.wmv |
To view these note you may need to download the free Adobe Acrobat Reader from this link 
Problem Sets:
Biweekly problem sets will be handed out in class, and solutions posted on the due dates.
Outline:
This course features studies in derivative pricing theory. The course is broken into two half courses.
The first half focuses on building basic financial theory and their applications 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: fixed income products; forwards and futures; binomial pricing model; the Black-Scholes model; the Greeks and hedging; European, American, Asian, barrier and other path-dependent options; short rate models and interest rate derivatives; convertible bonds.
The second half uses the knowledge base built in the fall term and adds more advanced theory and applications. The topics include, but are not limited to: LFM and LSM market models; foreign exchange options; defaultable bonds; credit default swaps, equity default swaps and collateralized debt obligations; intensity and structural based models; jump processes and stochastic volatility.
Here is a list of topics covered in both halves:
Fixed Income Instruments
- Term structure of interest rates
- Coupon bearing bonds
- Bootstrapping
- Interest rate swaps
Forwards and Futures
- Equity, Commodity, Fixed-income and Foreign currency forwards
- Relationship between forwards and futures
Binomial Model
- Arbitrage Strategies
- Replicating Portfolios
- Multi-period model ( Cox, Ross, Rubenstein )
- European, Barrier and American options
- Change of Measure
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
Interest rate derivatives
- Short rate and forward rate models
- Bond options, caps, floors, swap options
- Heath-Jarrow-Morton framework
- Brace-Gatarek-Musiela Jamshidian models
- Log-normal Forward and Swap rate models
Defaultable Securities
- Intensity Based Approach
- Structural Approach
- Correlation Modeling: correlated intensities and copulas
Credit Derivatives
- Credit Default Swaps:
- Collateralized Debt Obligations
- Equity Default Swaps
- Credit Linked Notes
Implied Volatility Matching
- Local and Implied Volatility modeling
- Stochastic volatility models
- Jump models
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:
The final grade for this course will be based on two exams (27.5% each), problem sets (25%), quizzes (15%) and in-class participation (5% total).
|
Date |
Mark |
Exam 1 |
TBA |
27.5% |
Exam 2 |
TBA |
27.5% |
Problem Sets |
bi-weekly |
25% |
Quizzes |
bi-weekly |
15% |
Participation |
weekly |
5% |
Tutorials:
Your TA is Samuel Hikspoors, a Ph.D. student in the Department of Statistics. Samuel is working on research problems in Mathematical Finance, specifically on commodity modeling and energy derivatives There will be weekly tutorials – the location and times are still to be announced.
Office Hours:
I will not have regularly scheduled office hours. Instead, contact me and arrange an appointment. I will of course linger after and before class for questions.