ACT 460 / STA 2502 – Stochastic Methods for Actuarial Science
Important:
You might be also interested in a Short Course on Commodity Models or Applied Probability for Mathematical Finance
Lecture 11 is now uploaded. see below. NOTE: the 2nd part of the lecture will NOT be tested in the exam, but I hope you watch it in anycase - it is interesting!
Problem Set #2 - PS2-Solutions
Last year's final exam: ACT460-Final-2008.pdf - ACT460-Final-2008-Sol.pdf
Last year's term test: ACT460-TermTest-2008.pdf - solutions
Time & Location
Time: Tuesday's 2pm - 5pm
Location: RW110
Class Notes / Lectures :
Class notes and videos will be uploaded regularly on completion of lectures.
| Lecture | Topic | Class Videos | Class Notes |
| 1 | Binomial model; arbitrage portfolio; numeraire probabilities; replication | ACT460-1.wmv | ACT460-1.pdf |
| 2 | Incomplete markets; CRR Tree; Continuous time limit; | ACT460-2.wmv | ACT460-2.pdf |
| SamplePathCRR.m | |||
| ProblemSet #1 - due Oct 6 at 2pm | Portfolio.xls | ||
| 3 | Price Sensitivity, Sample Path Generation, Monte Carlo Valuation | ACT460-3.wmv | ACT460-3.pdf |
| MonteCarloEuro.m | |||
| MonteCarloBarrier.m | |||
| 4 | Interest Rate Trees; BDT; Calibration | ACT460-4.wmv | ACT460-4.pdf |
| Calibration example | InterestRateTree.xls | ||
| 5 | Brownian motions; Total and Quadratic Variation; term test overview | ACT460-5.wmv | ACT460-5.pdf |
| 6 | Term Test | ||
| 7 | More on Brownian Motions; short talk on GMWB; Correlated Brownian Motions | ACT460-7.wmv | ACT460-7.pdf |
| Simulate two correlated Brownian motions | CorrBMotion.m | ||
| 8 | Computations with Brownian motions, The Ito Integral | ACT460-8.wmv | ACT460-8.pdf |
| Problem Set#2 - due Nov 17 | |||
| Solve the SDE int_0^t W_s dW_s | SDEintro.m | ||
| 9 | Ito's isometry and Ito's Lemma | ACT460-9.wmv | ACT460-9.pdf |
| 10 | Dynamics Hedging, Black-Scholes PDE, Feynman-Kac Thm. 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 | Delta-Gamma Hedging | ACT460-11.wmv | ACT460-11.pdf |
| Excel sheet for Delta-Gamma hedging | HedgeSim.xls |
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
Problem Sets :
I will hand out 4 problem sets throughout the term; however, only one or two questions in each set will be graded. You are strongly encouraged to carry out the exercises in Hull as preparation for the problem sets which will be more involved than those in the texts.
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 will be based on an exam ( 55% ), a term test ( 35% ), quizzes ( 5% ) and problem sets ( 10% )
|
Date |
Mark |
TBA |
50% |
|
Term Test |
Oct 20, 09 |
35% |
Quizzes |
weekly |
5% |
| Problem Sets | biweekly | 10% |
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 will be based on an exam ( 35% ), a term test ( 35% ), quizzes (5%), problem sets (10%) and a final project (20%):
|
Date |
Mark |
TBA |
35% |
|
Term Test |
Oct 20, 09 |
30% |
| Quizzes | weekly |
5% |
| Problem Sets | biweekly | 10% |
| Project | TBA |
20% |
Tutorials:
Your TA is Adrian Yang. He will hold Stat Aid Centre hours on Thursday's from 2 to 3pm.
Office Hours:
I will hold office hours on Tuesday's before class from 12:30pm to 2:00pm in my office (SS6005).