Risks, Values and Prices in Finance, Lecture Notes by S. Zhang.
Investment Science, by D.G.
Luenberger, Oxford University Press (recommended only)
The course aims to familiarize students with basic quantitative tools
used in modern finance. The student
intending to take the course should have a background in optimization
at the level
and elementary probability as well as familiarity with engineering
economics concepts. There will be homework
requiring use of XPRESS-MP optimization package, and of MATLAB.
no textbook. The instructor will provide hand-outs in class.
1. Cash flow
streams, present value, bonds (1 week)
2. Bond price
volatility, duration and convexity (2 weeks)
analysis, cash flow matching and dedication:
Nielsen's notes. (1 week)
4. Option basics
(2 weeks) Midterm examination
5. Arbitrage in option pricing (2
2 of Zhang)
6. Option pricing models (2 weeks)(chapter
4 of Zhang)
7. Modern portfolio theory, Risk
measures VaR and CVaR (2 weeks, reference: relevant parts of Tutuncu and Cornuejols' notes above and
and section 1 of review paper
by M. Steinbach)
Mortgage-backed securities (2 weeks)
Homework Assignment 1: Exercises 3.4.2, 3.5.2, 3.5.3 and 3.5.4,
Due date : 25.9.2008.
Homework Assignment 2: Exercises 4.1.2, 4.1.3, 4.2.1, 4.2.3, 4.2.7
Due date : 9.10.2008.
Homework Assignment 3: distributed in class,
Due date : 23.10.2008.
Homework Assignment 8: Due January 6, 2009. Select 20 stocks quoted at the
IMKB30 national index. You will receive by e-mail
a set of closing prices of these stocks corresponding to
the last quarter of 2006. Use the Excel data analysis tool
to compute the mean vector and covariance matrix for the data. Then 1. Compute and plot the MV
efficient frontier using the XPRESS-MP solver in MOSEL and any graphics
program of your choice. 2. Use the bank deposit for
the same period as a
risk free asset (find the average returnon bank deposits for the same
period). How does
the composition of the efficient portfolioschange? Report your observations along
with a discussion.
3. Assume you currently own the following portfolio:
x0(i)=0.20 for i=1,...,5 and x0(i) =0 for i=6,...,20. Reoptimize the
portfolio (without using the riskless asset)
considering transaction costs for buying and selling. Solve for a
fixed level of expected return and three different transaction
costs (0.2 %, 0.5 % and 2 %). Comment on your results.
examination (date to be announced, in class, closed notes):