DEPARTAMENT ....... :
PROGRAM .................. :
COURSE....................... :
PROFESSOR ............... :
DAY/HOUR ................. :
Accounting and Finance (CFC)
CMCD
Continuous-Time Finance
Joao Amaro de Matos
Daily, 9 AM-1PM
Winter / 2014
SYLLABUS
OBJECTIVES AND CONTENTS
This courses aims at covering the fundamental principles of pricing and hedging derivative securities in a continuous-time framework.
The first part is more theoretical and discusses the probabilistic construction underlying the continuous-time formalism, introducing the
basic notions of stochastic processes, stochastic integration and stochastic calculus. The second part is more economically intuitive and
is devoted to modeling security markets and understanding how the continuous-time formalism applies to the pricing and hedging
principles. The third and final part is more about the applications and presents specific models for option pricing and for term-structure.
By the end of this course students are expected to be prepared to read and understand technical literature in various areas of Finance
that uses continuous-time language and techniques. Students are also expected to develop critical thinking and learn to make
presentations in a professional manner, which is fundamental to their careers as researchers.
FORMAT
The classes will be divided in two different parts. Roughly half of the classes will be lectures by the professor, and the other half
will be exercises and seminar-type, in order to prepare the students for the two exams.
The lectures will cover the basic topics of the course, as described in the course schedule below and will follow a standard textbook
in the area by Baxter and Rennie. A more advanced textbook by Lars Tyge Nielsen (LTN) for those interested is also reccomended.
There will be room for presentation of papers and discussion of exercises by the students. As the material is eminently technical,
the success of this course depends fundamentally on the effort and preparation of the students for the classes by studying intensively the
material and practicing the concepts by the doing exercises. Also very important is to participate actively in class.
Course readings will expose students to the theoretical methods and concepts being used in different papers. Seeing how the tools
are used by top researchers is often very useful in helping students understand the tools.
ASSESSMENT CRITERIA
Presentation / discussion of exercises:
Half-page handouts with exercises:
Participation during discussions:
Midterm exam:
Final Exam:
20%
10%
15%
20%
30%
REQUIRED BACKGROUND
- Topics in probability and measure theory (see Appendix A in LTN textbook);
- Topics in integration theory (see Appendix B in LTN textbook);
- Basic microeconomics.
COURSE SCHEDULE AND READING LIST
1) Each session will include a minimum of two hours of lecture and a minimum of one hour of exercises;
2) Students must present in each class a handout with a few original exercises based on the material of the former class with the
respective solutions. If there are enough students, this may be done in groups. Exercises are presented and discussed in class;
3) Each group will choose a paper from the list below to be presented and discussed in the last two classes. We expect a 30
minute PowerPoint presentation that discusses the paper, and each presentation will be followed by in-class discussion.
Participation discussing other groups’ presentations is heavily counted in the participation grade. The purpose of the
assignment is (1) to practice your academic presentation’s skills; (2) to assess your comprehension of key concepts and (3) to
expose you to well-crafted papers.
Guidelines for a good discussion (you do not have to strictly follow this order, but it may help you in preparing your
presentation):
- Briefly describe what the papers does and what it predicts;
- Make your point about the assumptions;
- Suggest improvements;
- Identify eventual gaps or defects. Be critical. You may use your own judgement or the following literature. In this case,
make explicit mention to the papers you are referring to.
Course schedule (tentative and subject to change)
Session
Date
Topics
Readings
1
21/Jul
Overview of the course
Expectation vs Arbitrage Pricing
Chapter 1, B&R
2
22/Jul
Discrete Process and Continuous models Chapter 2, B&R, Chapter 1, LTN
3
23/Jul
Stochastic Calculus
Chapter 3.1-3.4, B&R, Chapter 2, LTN
4
24/Jul
Construction Strategies and B-S Model
Chapter 3.5-3.8, B&R, Chapter 4, 4 & 6, LTN
5
25/Jul
Mid-term exam
6
28/Jul
Pricing Market Securities
Chapter 4, B&R
7
29/Jul
Interest Rates Models
Chapter 5, B&R, Chapter 7, LTN
8
30/Jul
Bigger Models
Chapter 6, B&R
9
31/Jul
Papers’ Presentations
10
01/Aug
Papers’ Presentations
11
Final Exam
Basic Textbook (to be used in class):
(B&R) Baxter and Rennie, Financial Calculus, an Introduction to Derivative Pricing, Cambridge University Press, 1996.
Advanced Textbook:
(LTN) Nielsen, L. T., Pricing and Hedging of Derivative Securities, Oxford University Press, 1999.
Papers for Presentations:

RC Merton, Optimum consumption and portfolio rules in
a continuous-time model, Journal of Ec. Th., Vol. 3, Issue 4, 373–413, 1971.










RC Merton, Theory of rational option pricing, The Bell
Journal of Economics and Management Science, Vol. 4, No. 1, 141-183, 1973.
F Black, M Scholes, The pricing of options and corporate
liabilities, The journal of political economy, Vol. 81, No. 3, 637-654, 1973.
JC Cox, SA Ross, The valuation of options for alternative
stochastic processes, Journal of financial economics, Vol. 3, Issues 1–2, 145–166, 1976.
Vasicek, An equilibrium characterization of the term
structure, Journal of financial economics, Vol. 5, Issue 2, 177–18, 1977.
JM Harrison, DM Kreps, Martingales and arbitrage in
multiperiod securities markets, Journal of Economic theory, Vol. 20, Issue 3, 381–408, 1979.
JM Harrison, SR Pliska, Martingales and stochastic
integrals in the theory of continuous trading, Stochastic processes and their applications, Vol. 11, Issue 3, 215–260, 1981.
HE Leland, Option pricing and replication with
transactions costs, The journal of finance, Vol. 40, Issue 5, 1283–1301, 1985.
John C. Cox, Jonathan E Ingersoll Jr, Stephen A. Ross,
An
Intertemporal
General
Equilibrium
Model
of
Asset
Prices,
Econometrica,
Vol. 53, No. 2, 363-384, 1985.
JC Cox, JE Ingersoll Jr, SA Ross, A theory of the term
structure of interest rates, Econometrica, Vol. 53, No. 2, 385-407, 1985.
J Hull, A White, The pricing of options on assets with
stochastic volatilities, The journal of finance, Vol. 42, Issue 2, 281–300, 1987.

I Karatzas, On the pricing of American options, Applied
Mathematics and Optimization, Vol. 17, No. 1, 37-60, 1988.



JC Cox, C Huang, Optimal consumption and portfolio
policies when asset prices follow a diffusion process, Journal of economic theory, Vol. 49, Issue 1, 33–83, 1989.
I Karatzas, JP Lehoczky, SE Shreve, GL Xu, Martingale
and duality methods for utility maximization in an incomplete market, SIAM J. Control Optim., Vol. 29, No. 3, 702–730, 1991.
David Heath, Robert Jarrow and Andrew Morton, Bond
Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation, Econometrica, Vol. 60, No. 1, 77-105,
1992