ACT 460 / STA 2502 – Stochastic Methods for Actuarial Science
Outline:
This course is an introduction to the stochastic models used in Finance and Actuarial Science. 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 the pricing of derivative instruments will be investigated. Some exotic equity derivative products will be explored together with stochastic models for interest rates.
[ Prequisites: ACT 370 and STA 347 ]
Tentative Topics List:
- Review of Arbitrage in Discrete Time and Tree models
- Interest rate trees
- Defaultable Securities
- Continuous time limit of binomial model
- Monte-Carlo option valuation
- Control Variates
- Options on Correlated Assets
- Brownian Motions
- Stochastic Differential Equations
- Ito's Lemma
- Simulating SDEs
- Black-Scholes dynamic hedging and PDEs
- Continuous time short rate models
Time & Location
Time: Tuesday's 2pm - 5pm
Location: SS2135
Office Hours: Tuesday's 10:00am to 12:00 noon in my office SS6005
Important:
Here are some old term tests:
STA2502-TermTest-2008.pdf ; STA2502-TermTest-2008-sol.pdf
STA2502-TermTest-2009.pdf ; STA2502-TermTest-2009-sol.pdf
Here are some additional problems & partial solutions:
Class Notes / Lectures :
Class notes and videos will be uploaded regularly on completion of lectures.
| Lecture | Topic | Class Videos | Class Notes |
| 1 | Binomial models; arbitrage portfolio; replication | ACT460-2012-1.pdf | |
| 2 | Multiple steps, CRR Model, Limiting log-normal distribution, European & American Options | ACT460-2012-2.pdf | |
| 3 | Alternate Discret Models, Measures and Drifts, Forward-Starting Options, Monte Carlo Simulation |
|
ACT460-2012-3.pdf |
| 4 | Barrier Options, Interest Rate Trees, Ho-Lee Model, Calibration to Bond Prices |
|
ACT460-2012-4.pdf |
| 5 | Continuous limit of Ho-Lee Model, Vasicek Model, Interest Rate Swaps | sorry video did not record | ACT460-2012-5.pdf |
| 6 | Midterm | ||
| 7 | Random Walk, Brownian Motion, Total Variation & Quadratic Variation | ACT460-2012-7.pdf | |
| 8 | Sotchastic Integrals and Ito's Lemma | ACT460-2012-8 stream download |
ACT460-2012-8.pdf |
| 9 | Ito's Lemma continued, SDEs, Vasicek Model | ACT460-2012-9 stream download |
ACT460-2012-9.pdf |
| 10 | Ito's Isometry; Dynamic Hedging & Black-Scholes PDE; Discrete Delta Hedging | ACT460-2012-10 stream download |
ACT460-2012-10.pdf |
| 11 | Delta-Gamma Hedging, Options on Dividen Paying Assets and Futures | ACT460-2012-11 stream download |
ACT460-2012-11.pdf |
| 12 | Feynman-Kac; sketching Delta-Gamma | ACT460-2012-12 stream download |
ACT460-2012-12.pdf |
Textbook:
The recomended (but not required) textbooks for this course are:
- Options, Futures and other Derivatives, J. Hull, 6th edition, Prentice Hall
- Introductory Stochastic Analysis for Finance and Insurance, X.S. Lin, Wiley Series in Probaility and Statistics
Grading Scheme:
The final grade for undergraduate students (ACT 460) will be based on an exam, a term test and quizzes
|
Date |
Mark |
Exam |
Dec |
50% |
Term Test |
Oct 16 |
35% |
Quizzes |
Weekly |
15% |
IF YOU MISS THE TERM TEST, YOU MUST INFORM ME WITHIN 1 WEEK - OTHERWISE YOU WILL RECEIVE A ZERO. The make-up will consist of a 40 minute verbal test with the TA and Prof. Jaimungal.
The final grade for graduate students (STA 2502) will be based on an exa, a term test, quizzes and a final project:
|
Date |
Mark |
Exam |
TBA |
30% |
Term Test |
Oct 16 |
30% |
Quizzes |
Weekly |
10% |
Project |
early Jan, 13 |
30% |
The project involves two components a written component and a verbal component. The written component consists of an approximately 20 page report on a topic related to the course and involving some computer implementations. The verbal component will be based on the written report and involves the student presenting their report and answering related questions.
Tutorials:
Your TAs are Jason Ricci and Zhen Qin Ph.D. students in the Deparment of Statistics.
Office Hours:
I will hold office hours on Tuesday's from 10:00am to 12:00 noon in my office SS6005.