970/ACC ACTSC 770:
Finance I Foundations of Finance
Tony S. Wirjanto
M3 -3013, x 35210
Email: twirjant at uwaterloo dot ca
Office Hours: Th, Fr: 4:00-5:00 pm (or by appointment)
Fall 2011
Course Syllabus
Objectives
This is a first graduate course in finance. It gives an introduction to theory of derivative security
(or option) pricing and proceeds in three stages. First, fundamental concepts of finance are
introduced, using a discrete-time binomial model. These concepts include financial markets,
derivative securities, arbitrage, hedging and replicating portfolios, risk-neutral probabilities, riskneutral pricing formula, and market completeness. Then basic ideas of probability and stochastic
processes are reviewed for finite probability spaces and discrete-time processes: conditional
expectation, martingales, and Markov processes. Lastly, the emphasis of the course is shifted
from a discrete-time to continuous-time framework to cover the main topics in the course. This
includes a summary of probability measure theory and conditional expectation, Brownian motion
and quadratic variation, martingales, Ito integral, stochastic calculus, replicating portfolios and
hedging, Black-Scholes-Merton formulae for a European-style call option price, change of
measure and Girsanov's Theorem, risk-neutral pricing theory, no-arbitrage and existence of riskneutral measure, and market completeness and uniqueness of risk-neutral measure.
Pre-requisites
There is no formal pre-requisite for this course. However students should be familiar with
concepts taught at undergraduate courses on ordinary differential equations, multivariable
calculus, linear algebra, and probability theory. In particular, a good understanding of probability
at the level of the textbook by Sheldon Ross, A First Course in Probability, would be a definite
asset. It would also be helpful (but not strictly necessary) if students are well acquainted with
concepts taught at undergraduate courses on real analysis and partial differential equations.
Required Textbooks
Steven E. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model.
Springer-Verlag, New York, 2004, ISBN 978-0-387-24968-1 (Henceforth SI) Chapters 1-3
Steven E. Shreve: Stochastic Calculus for Finance II: Continuous-Time Model. Springer-Verlag,
New York, 2004, ISBN 978-1-4419-2311-0 (Henceforth SII) Chapters 1-5
Supplementary Textbook
Hull, J. C, Options, Futures, and Other Derivatives, Eighth Edition, Pearson Prentice,
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2011, ISBN 0-13-277742-8 or ISBN 0-13-216494-9 (Henceforth H) Chapters 1, 2, 5 and 11
Both required and supplementary textbooks for this course can be purchased at the UW
bookstore: http://www.bookstore.uwaterloo.ca/home.html.
Some lecture notes as well as homework assignments and solutions, exam solutions,
supplementary articles, and computer programs are posted on the courses unofficial homepage
accessible by registered students.
Grading Scheme
Homework - 25%; midterm test - 25%; and final exam (to be scheduled by the university) - 50%.
Weekly Lecture Plans
Week 1
Lecture #1: Financial markets and derivative securities; No-arbitrage condition;One bond, onestock model; Forward contracts
Reading: H Chapters 1, 2, and 5
Lecture #2:No arbitrage pricing;No arbitrage price of an option for the binomial model.
Reading: H Chapters 11; SI Chapter 1
Homework #1 (Due date: 09/19/2011)
Week2
Lecture #3: First Fundamental Theorem of Asset Pricing for a one period, finite state model;
State-price vector
Lecture #4: State-price vectors and risk-neutral measure;Risk neutral pricing formula;
Examples
Reading: H Chapters 11; SI Chapter 1
Homework #2 (Due date: 09/26/2011)
Week3
Lecture #5: Binomial trees (continued); Probability theory and discrete-time stochastic
processes
Reading: SI Chapters 2 and 3
Lecture #6: Binomial trees Risk-neutral (continued): measure and option pricing
Reading: SI Chapters 2 and 3
Homework #3 (Due date: 10/03/2011)
Week4
Lecture #7:Binomial trees (continued)
Reading: SI Chapters 2 and 3
Lecture #8: Probability spaces
Reading: SI- Chapter 2; SII- Chapters 1.1, 12, 1.3
Homework #4 (Due date: 10/12/2011)
Week5
Lecture #9: Expectation, information, and -algebras
Reading: SI- Chapter 2.2; SII- Chapters 1.3, 1.5
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(October 10th: University holiday - Thanksgiving Day)
Week6
Lecture #10: Conditional expectation
Reading: SI- Chapters 2.3, 2.4, 2.5; SII- Chapter 2.1, 2.2, 2.3
Lecture #11: Brownian motion: Random walks and the central limit theorem
Reading: SII - Chapter 3.2
Homework #5 (Due date: 10/19/2011)
Week7
Lecture #13: Brownian motion: Markov property
Reading: SII - Chapter 3.3
Lecture #12: Brownian motion: Definition, martingale property, quadratic variation
Reading: SII Chapter 3.3
Homework #6 (Due date: 10/26/2011)
Week 8
Lecture #14: The It integral: An Introduction
Reading: SII - Chapters 4.2, 4.3, and 4.4
Lecture #15: The It formula
Reading: SII - Chapter 4.4
Homework #7 (Due date: 11/02/2011)
Week9
Lecture #16: The Black-Scholes-Merton PDE and its solution forEuropean-style call and put
option prices.
Reading: SII - Chapter 4.5
Lecture #17: The Black-Scholes-Merton formula, geometry of hedging,put-call parity
Reading: SII - Chapter 4.5
Homework #8 (Due date: 11/09/2011)
Week 10
Lecture #18: Multivariable stochastic calculus, Lvy's characterizationof Brownian motion,
Gaussian processes, Brownian bridge
Reading: SII - Chapters 4.6 and 4.7
Lecture #19: Change of measure, Radon-Nikodym derivative,Girsanov's theorem for single
Brownian motion
Reading: SII - Chapters 1.6, 5.1, and 5.2.1
Homework #9 (Due date: 11/16/2011)
Week 11
Lecture #20:Discounted stock and portfolio processes as martingales
Reading: SII - Chapters 5.2.2, 5.2.3, and 5.2.4
Lecture #21: Pricing under risk-neutral measure,derivation of Black-Scholes-Merton formula
Reading: SII - Chapters 5.2.4, and 5.2.5
Homework #10 (Due date: 11/23/2011)
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Week 12
Lecture #22: Martingale representation theorem, Multi-dimensional market model
Reading: SII - Chapters 5.3, 5.4.1 and 5.4.2
Lecture #23: Existence of risk-neutral measure, no arbitrage, and First fundamental theorem of
asset pricing
Reading: SII - Chapter 5.4.3
Homework #11 (Due date: 11/30/2011)
Week 13(December 5th: Lectures end)
Lecture #24: Uniqueness of risk-neutral measure, completeness, andSecond fundamental
theorem of asset pricing
Reading: SII - Chapter 5.4.4
Additional Textbooks
T. Bjrk, Arbitrage Theory in Continuous Time, Oxford, 2004 (Previously used in Finance II)
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1997
D. G. Luenberger, Investment science, Oxford, 1997
S. R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell, 1997
J. M. Steele, Stochastic calculus and financial applications, Springer, 2000
Software
Depending on the application, Excel/VBA or MATLAB will be used in the course.
Other Course Resources
Class slides and other reading materials as well as homework assignments, and solutions will be
posted on the unofficial website for the course maintained by me and accessible by registered
students. Information to get access to the website is given below:
On http://www.stats.uwaterloo.ca/, click Faculty Homepages on the 3rd row of the far right
side box
On Faculty in Statistics and Actuarial Science, click either "Statistics" or "Finance" or
"Professor"
Click "Wirjanto, Tony"
Click Personal Website: http://arts.uwaterloo.ca/~twirjant/
Click "Teaching"
Click "ACTSC970"
When prompted by Authentification Required, type in User Name and Password (This
information will be emailed to registered students)
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