MMF1952Y / STA 2503F – Pricing Theory / Applied Probability for Mathematical Finance
Important:
This course is restricted and enrollment is limited.
FYI: STA2502 is open.
You might be also interested in a Short Course on Commodity Models
Class Notes / Lectures :
Class notes and videos will be made available as the course progresses.
If you would like to obtain access please contact me.
| Lecture | Topic | Class Video | Class Notes |
| 1 | Binomial Model; No Arbitrage; Numeraires; Replication | MMF1952-1.wmv | MMF1952-1.pdf |
| 2 | Multi-period binomial model; CRR trees; simple default model | MMF1952-2.wmv | MMF1952-2.pdf |
| 3 | Measure change and sample paths; Price Sensitivity; Intro to Interest Rates | MMF1952-3.wmv | MMF1952-3.pdf |
| Portfolios.xls | |||
| 4 | Interest Rate Models; Vasicek; Interest Rate Swaps, Counterparty Credit IRS | MMF1952-4.wmv | MMF1952-4.pdf |
| 5 | IR Calibration; Arrow-Debreu; Discrete Forward Fokker-Planck Equations | MMF1952-5.wmv | MMF1952-5.pdf |
| Example calibration to yields and option prices | ADCalib.xls | ||
| 6 | Equity Numeraire; Stochastic Calculus review | MMF1952-6.wmv | MMF1952-6.pdf |
| last year's notes | MMF1952-6-08.pdf | ||
| stochastic calculus main results | StochCalc.pdf | ||
| 7 | Continuous Time Dynamic Hedging | MMF1952-7.wmv | MMF1952-7.pdf |
| 8 | More Dynamic Hedging; Mismatch Hedging; Solutions of the Black-Scholes PDE | MMF1952-8.wmv | MMF1952-8.pdf |
| Nov 2 | Tutorial session | MMF1952-tut-Nov2.pdf | |
| PS2 solutions | MMF1952-PS2-Sol.pdf | ||
| Delta Hedge simulation | DeltaHedge.m | ||
| 9 | Feynman-Kac, Interest Rate Models, Delta-Gamma-Vega hedging | MMF1952-9.wmv | MMF1952-9.pdf |
| Nov 9 | Tutorial Session: check ACT460 site for problem sets. | MMF1951-tut-Nov9.pdf | |
| 10 | Measure Changes and Numeraires | MMF1952-10.wmv | MMF1952-10.pdf |
| Nov 16 | Tutorial Session | MMF1952-tut-NOV16.pdf | |
| 11 | Accrual Swaps; Commodity model | MMF1952-11.wmv | MMF1952-11.pdf |
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; commodity models.
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
Commodity Models
- Schwartz spot price model
- Real Options
- jumps and regime switchin
Commodity 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
Deliverables:
Problem sets, Quizzes and Challenges will be handed out throughout the term.
Problem sets are invovled questions that will require you to go beyond basics. You are responsible to cover basic exercises on your own. Typically handed out every other week.
Quizzes test basic knowledge of the material and are conducted in the tutorials every other week.
Challenges are problems that require an implementation, interpretation and a write-up and are completed in teams of 4. You will be informed ahead of time when a challenge is to be conducted.
Grading Scheme:
The following is the grading scheme used in this course:
|
Date |
Mark |
Exam 1 |
TBA |
25% |
Exam 2 |
TBA |
25% |
Problem Sets |
bi-weekly |
20% |
Quizzes |
bi-weekly |
10% |
Challegnes |
bi-weekly |
15% |
| Participation | weekly | 5% |
Exams are open book -- anything goes. They are designed to probe your understanding of the material.
Participation is not simply a matter of showing up in class. You must be actively involved in the discussions to acheive a 5/5.
Tutorials:
Your TA is TBA
There will be weekly tutorials – the 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.