ACT 460 / STA 2502 – Stochastic Methods for Actuarial Science
NEW
For Sept 2012, the course will be held on Tuesday's from 2-5pm in SS2135
This page will be updated shortly
Important:
You might be also interested in a Short Course on Commodity Models or Applied Probability for Mathematical Finance
Exam Office hours:
I will have extra office hours on Thursday & Friday from 10:30am to 12:30pm.
The TA will hold office hours on Dec 8 4pm -5pm and Dec 10 2pm-3pm in SS6027A .
Here are some old final exams:
STA2502-Exam-2008.pdf ; STA2502-Exam-2008-Sol.pdf
Here are some old problems (NOT BE TO HANDED IN):
STA2502-PS1.pdf ; STA2502-PS1-PartialSol.pdf
STA2502-PS2.pdf ; STA2502-PS2-PartialSol.pdf
STA2502-PS3.pdf ; STA2502-PS3-PartialSol.pdf
Here are some old term tests:
STA2502-TermTest-2008.pdf ; STA2502-TermTest-2008-sol.pdf
STA2502-TermTest-2009.pdf ; STA2502-TermTest-2009-sol.pdf
Term Test Office Hours:
Friday Oct 15, 2:30pm - 4:00pm - TA available in the Stats Lounge SS 6028A
Moday Oct 18, 10am - 2pm - My Office SS 6005
Time & Location
Time: Tuesday's 2pm - 5pm
Location: RW110
Class Notes / Lectures :
Class notes and videos will be uploaded regularly on completion of lectures. Entries in italics are last years notes, these will be updated to bold when this years material is uploaded.
| Lecture | Topic | Class Videos | Class Notes |
| 1 | Binomial models; arbitrage portfolio; replication | ACT460-1.wmv | ACT460-1.pdf |
| 2 | Incomplete markets; Asset Calibration; Continuous time limit; | ||
| matlab code for simulating CRR sample paths | SimCRR.m | ||
| SimCRRdriver.m | |||
| 3 | Price Sensitivity of Options, American Options | ACT460-3.pdf | |
| Excel sheet for investigating sensitivity on model paramters | Portfolios.xls | ||
| matlab code for American options | American.m | ||
| 4 | Trinomial Trees, Exotic Options: Barriers and forward starting options | ACT460-4.wmv | ACT460-4.pdf |
| matlab code for American option valuation using a trinomial tree | TriTree.m | ||
| Barrier Option valuation on a Tree | BarrierTree.xls | ||
| 5 | More on Barrier Options, Interest Rate Trees, Calibration of IR models, Options on Bonds | ACT460-5.wmv | ACT460-5.pdf |
| Barrier Option Simulation | BarrierSim.xls | ||
Interest Rate Tree Calibration & Option example |
IRTrees.xls | ||
| 6 | Term Test | STA2502-TermTest-2010-sol.pdf | |
| 7 | Brownian Motion; Total Variation; Quadratic Variation | ACT460-7.wmv | ACT460-7.pdf |
| 8 | Computations with Brownian motions, The Ito Integral, Ito's Lemma - part I | ACT460-8.wmv | ACT460-8.pdf |
| 9 | Ito's isometry and Ito's Lemma | ACT460-9.wmv | ACT460-9.pdf |
| 10 | Dynamics Hedging, Black-Scholes PDE, Time-based / Move-based hedging | ACT460-10.wmv | ACT460-10.pdf |
| Delta Hedge time/move based | DHedge.m | ||
| Delta-Gamma Hedge time/move based | DGHedge.m | ||
| GBM sample path -- needed for DHedge and DGHedge | SimPath.m | ||
| 11 | Feynman-Kac; incomplete markets; insurance products | ACT460-11.wmv | ACT460-11.pdf |
| 12 | 2-d Ito's Lemma, past exam questions | sorry video did not record properly | ACT460-12.pdf |
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
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 19 |
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 |
40% |
Term Test |
Oct 19 |
30% |
Quizzes |
Weekly |
10% |
Project |
early Jan, 11 |
20% |
The project involves two components a written component and a verbal component. The written component consists of a 20 page report on a topic related to the course and invovling some computer implementations. The verbal component will be based on the written report and involves the student answering questions related to their report topic.
Tutorials:
Your TA is Jason Ricci a Ph.D. student in the Deparment of Statistics.
Office Hours:
I will hold office hours on Wednesday's from 2:00pm to 4:00pm in my office.