ACT 460 / STA 2502 – Stochastic Methods for Actuarial Science
Class Photo :
Important:
- Congratulations to all who completed the course! I very much enjoyed teaching it, and although it was the first time it was offered, I believe it went relatively smoothly. I am sure it has been challenging at times; however, I hope that you all had an overall positive experience and have gained a deeper appreciation of stochastic modeling and how it can be practically applied. HAPPY HOLIDAYS AND HAVE A GREAT NEW YEAR!
- I will have the exams graded by the end of the first week of January.
- I am looking for someone to do some RA work with me next term. The work requires *strong* knowledge of the material in this course, as well as very good programming skills in Excel VBA and C / C++ and very good communication skills. It will involve systematically creating Excel spread sheets and C++ engines for pricing, hedging and risk management of various derivatives. If you are interested, please send me your CV/resume, a photocopy of your academic transcript, and a statement of interest regarding working in the financial sector.
Location and TiMe:
Where: Lash Miller 162
When: Tuesdays 2 - 5pm
The first class will be held on Tuesday Sept 12, 2006.
Outline:
This course is an introduction to the stochastic models used in Actuarial Science at the interface of Finance. Students will be exposed to the basics of stochastic calculus, particularly focusing on Brownian motions and simple stochastic differential equations. The role that martingales play in pricing of derivative instruments will be investigated. Some exotic equity derivative products will be explored together with stochastic models for interest rate derivatives.
The course will cover most of chapters 18-25 of Mc Donald. Additional topics will be included based on class interest and time.
Class Notes / Lectures :
Please not that all Excel projects are for illustrative and educational purposes only!
| Date | Topic | Chap. | Class Videos | Class Notes |
| 12-09-06 | Review of Arbitrage in Discrete Time | 10; 11 | Lecture1.mpg [28MB] |
|
| 14-09-06 | Review of Arbitrage in Discrete Time cont'd | 10; 11 | Lecture2.mpg [15MB] |
ExcelSheets.zip |
| 19-09-06 | American and Barrier Options in Discrete Time; |
11; 18 | see below | |
| I have re-recorded lecture 3 to ellaborate on the topics covered; Also, I have deferred the discussions based on the Excel Sheets for a later date. |
Lecture3b.mpg |
Lecture3b.pdf | ||
| 26-09-06 | Black-Scholes pricing using lognormal assumptions; |
18; 19 | Lecture4.mpg [56MB] |
|
| 03-10-06 | Black-Scholes Pricing; Sketching value of options; Monte-Carlo review; Introduction to Jump models |
19 | Lecture5.mpg [45MB] |
|
| 10-10-06 | Control Variates; Options on Correlated Assets; Simulating correlated Asset prices; Introduction to Brownian motion | 19, 20 | Lecture6.mpg |
Lecture6.pdf |
| 12-10-06 | Tutorial Session | - | Tutorial.mpg | Tutorial4.pdf |
| 17-10-06 | Term Test | - | - |
- |
| 19-10-06 | Reviewed solutions for the term test on Black-Board | - | - |
- |
| 24-10-06 | Brownian Motion; Intro to Stochastic Differential Equations; Ito processes; Ito's Lemma | 20 | Lecture7.mpg | Lecture7.pdf |
| 26-10-06 | More on SDEs and Ito's Lemma | 20 | Lecture8.mpg | Lecture8.pdf |
| 31-10-06 | Simulating SDEs; Ito's lemma applied to Ito processes; Intro to Martingales; Solving GBM and mean-reverting SDEs; | 20 | Lecture9.mpg |
Lecture9.pdf |
| 07-11-06 | The Black-Scholes PDE; The Delta of an Option | 21 | Lecture10.mpg | |
| 14-11-06 | The two-dimensional Black-Scholes PDE; Options on two assets; Hedging in discrete time | 21 | Lecture11.mpg | Lecture11.pdf |
| 21-11-06 | Foreign Exchange Options | 22 | Lecture12.mpg | Lecture12.pdf |
| 28-11-06 | Foreign Stock Options; Interest rate Trees | 22, 24 | Lecture13.mpg | Lecture13.pdf |
| 05-12-06 | Review | Lecture14.pdf | ||
| 14-12-06 | Review / Tutorial | TutorialDec14.mpg | TutorialDec14.pdf | |
| 18-12-06 | Review / Tutorial | TutorialDec18.mpg | TutorialDec18.pdf |
*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.
Problem Sets :
Problem sets will be handed out on a biweekly basis; however, only one or two questions will be graded. You are strongly encouraged to carry out the exercises in Mc Donald as preparation for the problem sets which will be more involved than those in the course text.
You can find student resources for the course text (solutions and more sample problems) from the publisher's student resource or the book resource.
Problem Set 1 - Problem Set 1 Solutions - PS1Q2.xls
Problem Set 2 - Problem Set 2 Solutions - PS2Q3.xls
Term Test Solutions - Term Test Grade Histogram
Problem Set 3 - Problem Set 3 Solutions
Problem Set 4 - Problem Set 4 Solutions
Textbook:
The required textbook for this course is
- Derivatives Markets, R. L. Mc Donald, 2nd edition, Pearson / Addison-Wesley
You can find student resources for the course text (solutions and more sample problems) from the publisher's student resource or the book resource.
Grading Scheme:
The final grade for undergraduate students will be based on an exam ( 50% ), a term test ( 30% ), and problem sets ( 20% ):
|
Date |
Mark |
TBA |
50% |
|
Term Test |
Oct 17 |
30% |
Problem Sets |
bi-weekly |
20% |
The final grade for graduate students will be based on an exam ( 30% ), a term test ( 30% ), problem sets ( 20% ) and a final project ( 20% ):
|
Date |
Mark |
TBA |
30% |
|
Term Test |
Oct 17 |
30% |
Problem Sets |
bi-weekly |
20% |
| Project | TBA | 20% |
Tutorials:
Your TA is Georg Sigloch, a Ph.D. student in the Department of Mathematics. Georg is working on research problems in Mathematical Finance, specifically on indifference valuation for defaultable claims.
Office Hours:
The office hours are yet to be determined.