ACT 460 / STA 2502 – Stochastic Methods for Actuarial Science
Important:
Problem Sets and Solutions:
| Problem Set |
| PS1 |
| PS2 |
| PS3 |
| PS4 |
Location and TiMe:
Time: Tuesdays 2 - 5pm
Location : Ramsey Wright Building, room 110
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
- Deafultabl Securities
- Continuous time limit of binomial model
- Monte-Carlo option valuation
- Introduction to Jump-diffusion models
- Control Variates
- Options on Correlated Assets
- Brownian Motions
- Stochastic Differential Equations
- Ito's Lemma
- Simulating SDEs
- Black-Scholes dynamic hedging and PDEs
- Foreign Exchange Options
- Foreign Stock Options
- Continuous time short rate models
Class Notes / Lectures :
Class notes and videos will be uploaded regularly on completion of lectures.
For last year's notes and videos please click here.
| Date | Topic | Class Videos | Class Notes |
| Sept 11,07 | Binomial Model, Arbitrage Portfolios, CRR model, Lognormal limit | STA2502-1a.wmv | STA2502-1a |
| Explicit Two Period Model Example | STA2502-1b.wmv | STA2502-1b.pdf | |
| CRR limit re-recorded | STA2502-1c.wmv | STA2502-1c.pdf | |
| Sept 18, 07 | Black-Scholes pricing equation; 1st look at generating PnLs via Monte Carlo; IR Tree basics | STA2502-2.wmv | STA2502-2.pdf |
| Basic Option Portfolio Excel Sheet | Portfolios.xls | ||
| Sept 25, 07 | Black-Derman-Toy model and calibration; Monte Carlo basics | STA2502-3.wmv | STA2502-3.pdf |
| Calibration Spread Sheet [ updated - I posted the wrong file before sorry] | BDT-Calib-Updated.xls | ||
| Oct 2, 07 | More on Interest Rate Trees; Monte Carlo pricing | Video unavailable | STA2502-4.pdf |
| Simple Monte Carlo Pricer | MonteCarlo.xls | ||
| IR Tree - complex options | IRTree.xls | ||
| Oct 9, 07 | Correlated Asset Trees; Exchange Options; Monte Carlo for two assets | STA2502-5.wmv | STA2502-5.pdf |
| Simple Exchange option Monte Carlo Pricer | Exchange.xls | ||
| Oct 30, 07 | Brownian motion; Introduction to Stochastic Calculus | STA2502-6.wmv | STA2502-6.pdf |
| Nov 13, 07 | More on Stochastic Calculus; Correlated Brownian Motions; Integration by Parts | STA2502-7.pdf | |
| Nov 20, 07 | Ito's Lemma for Ito Processes; Black-Scholes Dynamic Hedging argument; Feynmac-Kac probabilistic representation of PDE solution | STA2502-8.wmv | STA2502-8.pdf |
| Nov 27, 07 | Delta calculations; Delta hedging in discrete time; PnL simulations | STA2502-9.wmv | STA2502-9.pdf |
| Discrete hedging simulation - one and two rebalances | SimDeltaSimple.xls | ||
| Discrete hedging simulation - multiple rebalances | HedgeSim.xls | ||
| Dec 4, 07 | Gamma; Delta-Gamma Hedging; intro to continuos time interest rate models | STA2502-10.wmv | STA2502-10.pdf |
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 Mc Donald or 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
- 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 ( 55% ), a term test ( 35% ), and problem sets ( 10% ):
|
Date |
Mark |
TBA |
55% |
|
Term Test |
OCt 16 |
35% |
Problem Sets |
total of 4 |
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% ), problem sets (10% ) and a final project ( 20% ):
|
Date |
Mark |
TBA |
35% |
|
Term Test |
Oct 16 |
35% |
Problem Sets |
total of 4 |
10% |
| Project | TBA | 20% |
Tutorials:
Your TA is Andreaa Cojocaru - an M.Sc. student in the Department of Statistics. There are no regularly scheduled tutorials for this course. Instead, the TA will hold Stat Aid Center hours before problem sets are due and the term test.
Office Hours:
I will hold office hours on Tuesday's after class from 5:00pm to 6:30pm.