ARCHIVE [ 2006-2007]
MMF1952Y / STA 2503F – Pricing Theory / Applied Probability for Mathematical Finance
Class Photo:
Important:
This course is restricted and enrollment is limited. FYI: STA2502 is open.
If you would like to obtain a DVD of the course lectures, notes, problem sets and excel files, (together with those from STA 2502) please contact me.
Class Notes / Lectures :
| Date | Topic | Class Video | Class Notes |
| 14-09-06 | Discrete Time Modeling: Arbitrage; Contingent Claim Valuation; Introduction to Numeraire and Measure Changes. | Lecture1.mpg [56MB] |
Lecture1.pdf |
| 21-09-06 | Numeraire changes, Continuous time limit of Binomial model | Lecture2.mpg [53MB] |
Lecture2.pdf |
| 28-09-06 | Barrier and American Options | Lecture3.mpg |
|
| 02-10-06 | Review of the CRR infinite time limit | Lecture3-R.mpg |
Lecture3-R.pdf |
| 05-10-06 | Black-Scholes Pricing for European Options; Simple Numeraire Change; Joint Probabilities; Monte Carlo Simulation |
Lecture4.mpg [69MB] |
Lecture4.pdf |
| 12-10-06 | Brownian motion; Stochastic Integrals; Ito's Lemma | Lecture5.mpg | Lecture5.pdf |
| 19-10-06 | Multidimensional Brownian motions; Multidimensional Ito's Lemma | Lecture6.mpg | Lecture6.pdf |
| 20-10-06 | Tutorial on Multidimensional Ito's Lemma; Solving SDEs | Tutorial.mpg | Tutorial.pdf |
| 26-10-06 | The Black-Scholes PDE, Feynman-Kac formulae | Lecture7.mpg | Lecture7.pdf |
| 02-11-06 | Martingale perspectives on the Black-Scholes PDE | Lecture8.mpg | Lecture8.pdf |
| 09-11-06 | Implementing Dynamic Hedging; Multi-Dimensional Black-Scholes | Lecture9.mpg | Lecture9.pdf |
| 16-11-06 | Measure changes induced by numeraire assets | Lecture10.mpg | Lecture10.pdf |
| 23-11-06 | Stochastic Interest Rate modeling | Did not record properly | Lecture11.pdf |
| 30-11-06 | Stochastic Interest Rate modeling | Lecture12.mpg | Lecture12.pdf |
| 04-12-06 | Review Session | ReviewDec04.mpg | ReviewDec04.pdf |
| 07-12-06 | Options in a Stochastic Interest Rate environment | Lecture13.mpg | Lecture13.pdf |
| 08-12-06 | Review | Dec8Review.mpg | Dec8Review.pdf |
| 26-04-07 | Credit Derivatives Overview; Defaultable Bonds and Stock Intro | Lecture14.mpg | |
| 03-05-07 | Credit Default Swaps; Calibrating Hazard Rates | Lecture15.mpg | Lecture15.pdf |
| 10-05-07 | Doubly Stochastic Poisson Processes; Stochastic Interest Rate and Hazard Rates; CDS revisted | Lecture16.mpg | Lecture16.pdf |
| 17-05-07 | Review; Copulas and CDOs | Lecture17.pdf CDOannotated.pdf |
|
| 24-05-07 | Guest Lecture on Electricity Modeling | ||
| 31-05-07 | Black Model for Caps/Floos and Swaptions; HJM and BGM models intro; LFM and LSM | Lecture19.mpg | Lecture19.pdf |
| 7-06-07 | Simulating LFM to value swaptions | Lecture20.mpg | Lecture20.pdf |
| 14-06-07 | Beyond Black-Scholes; Volatility Surfaces; and Jump-Diffusion Models | Lecture21.mpg | Lecture21.pdf |
| 21-06-07 | Heston Model; Mixing Method; Review | Lecture22.pdf |
Arbitrage Theory in Discrete Time
Credit Default Swaps and Collaterized Debt Obligations
*Here is the setup file for the Excel sheets for the binomial model, the trinomial model and a portfolio of basic options. This setup will create a new folder in your start menu called Tyrico, run the register.cmd file before opening any Excel sheet. You must have macros enabled (at a minimum set to medium security under Tools -> Macros -> Security). Also, you must have the .NET framework version 1.1 installed - a free download from Microsoft.
To view these note you may need to download the free Adobe Acrobat Reader from this link 
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
- The Concepts and Practice of Mathematical Finance, Mark Joshi, Cambridge 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). Participation means actively providing comments, and answering questions intelligently throughout the year.
|
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.