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

  Home | Teaching | Research | Seminars | Consulting | Contact |

ACT 460 / STA 2502 – Stochastic Methods for Actuarial Science


For Sept 2012, the course will be held on Tuesday's from 2-5pm in SS2135

This page will be updated shortly


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

STA2502-Exam-2009.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
3 Price Sensitivity of Options, American Options


  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

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


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


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







Term Test

Oct 19





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:







Term Test

Oct 19






early Jan, 11


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.


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.