S. Jaimungal
Department of Statistics and Mathematical Finance Program, University of Toronto

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ACT 460 / STA 2502 – Stochastic Methods for Actuarial Science

For 2010 archive go here.

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:

  1. Review of Arbitrage in Discrete Time and Tree models
  2. Interest rate trees
  3. Defaultable Securities
  4. Continuous time limit of binomial model
  5. Monte-Carlo option valuation
  6. Control Variates
  7. Options on Correlated Assets
  8. Brownian Motions
  9. Stochastic Differential Equations
  10. Ito's Lemma
  11. Simulating SDEs
  12. Black-Scholes dynamic hedging and PDEs
  13. 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

STA2502-TermTest-2010-sol.pdf

STA2502-TermTest-2012-sol.pdf

Here are some additional problems & partial solutions:

ACT460-2009-Exam

ACT460-2008-Exam

PS3.pdf PS3-partial-sol.pdf

PS2.pdf PS2-partial-sol.pdf

PS1.pdf PS1-sol.pdf

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 stream
download

ACT460-2012-1.pdf
2 Multiple steps, CRR Model, Limiting log-normal distribution, European & American Options

ACT460-2012-2 stream
download

SimCRRdriver.m
SimCRR.m
American.m

ACT460-2012-2.pdf
3 Alternate Discret Models, Measures and Drifts, Forward-Starting Options, Monte Carlo Simulation

 

ACT460-2012-3 stream
download

SimForwardStart.m
SimBarrier.m

ACT460-2012-3.pdf
4 Barrier Options, Interest Rate Trees, Ho-Lee Model, Calibration to Bond Prices

ACT460-2012-4 stream
download

KnockInBinary.xlsx

BondCalibration.xlsx

 

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 stream
download

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.