Course
Description
This
course will provide a systematic introduction to the development, analysis
and implementation of numerical methods for solving financial problems
and will focus on computational methods for the pricing and hedging equity
and fixed-income derivatives. We will cover three main areas: pricing
by formulas and approximations, pricing using lattices (one-, two-, and
n-dimensional) and finite differences, and pricing using Monte
Carlo simulation. We will cover the pricing of exotic derivatives (such
as barrier, Asian, lookback, and multi-asset options), pricing interest
rate derivatives in the Heath-Jarrow-Morton and Libor Market Models, and
also state-of-the-art topics such as low discrepancy sequences (quasi-Monte
Carlo) for financial computations and the pricing of American options
using simulation.
Course
Work
There will be approximately six homework assignments and
a course project. The project deliverables will be a written report and
a project presentation after the conclusion of the class. Students must
attend at least one project presentation, not including their own. Both
the homework and the project can be done in groups of three or less. Programming
experience with a high-level language, either C, C++, or Java, is essential
for this course.
Course
related books and papers
There will
not be a textbook for the course. Most of the reading for the course will
be in the form of journal articles that will be posted on this web site.
Additional reference material is given below. All of these
books are available from Amazon.com.
Three of the books are available for free on-line. Several of the books
mentioned below are available on reserve in the business school library.
- Seydel,
R., 2004, Tools for Computational Finance, 2nd edition, Springer-Verlag,
New York.
- Glasserman,
P., 2004, Monte Carlo Methods in Financial Engineering, Springer-Verlag,
New York.
- Press, W., S. Teukolsky,
W. Vetterling, and B. Flannery, 1997, Numerical Recipes in C: The
Art of Scientific Computing, Cambridge University Press, Cambridge,
UK available on-line at: http://www.nr.com/
- Lewis, A., 2000, Option
Valuation under Stochastic Volatility, Finance Press, Newport Beach,
California.
- Pelsser, A., 2000, Efficient
Methods for Valuing Interest Rate Derivatives, Springer-Verlag,
New York.
- Mathews,
J., and R. Howell, 2002, Complex Analysis: Mathematica 4.1 Notebooks,
available online at: http://math.fullerton.edu/mathews/c2002/content.html
Other
Derivatives Books
- Duffie,
D., 2001, Dynamic Asset Pricing Theory, 3rd edition, Princeton
University Press, Princeton, NJ.
- Baxter,
M., and A. Rennie, 1996, Financial Calculus: An Introduction to Derivative
Pricing, Cambridge University Press, Cambridge, UK.
- Hull, J.,
2003, Options, Futures, and other Derivatives, 5th edition, Prentice
Hall, NJ.
- Shaw, W., 1998, Modeling
Financial Derivatives with Mathematica, Cambridge University Press,
Cambridge, UK.
- Haug, E.G, 1998, The
Complete Guide to Option Pricing Formulas, McGraw-Hill, New York.
Other
Numerical Methods Books
- Morton,
K.W., and D.F. Mayers, 1994, Numerical Solutions of Partial Differential
Equations, Cambridge University Press.
- Tavella,
D., and C. Randall, 2000, Pricing Financial Instruments: The Finite
Difference Method, John Wiley and Sons, New York.
- Judd, K.,
1998, Numerical Methods in Economics, MIT Press, Cambridge, Massachusetts.
- Brown, J.,
and R.V. Churchill, 2003, Complex Variables and Applications,
7th edition, McGraw-Hill.
- Walker,
J., 1996, Fast Fourier Transforms, 2nd edition, CRC Press, Boca
Raton.
- Mathews,
J., and K. Fink, 2004, Numerical Methods: Using Matlab, 4th Edition,
Prentice-Hall, Upper Saddle River, NJ.
Other Programming Books
- Eckel, B.,
2003, Thinking in C++, available online at:
http://www.mindview.net/Books/TICPP/ThinkingInCPP2e.html
- Yang, D.,
2001, C++ and Object Oriented Numeric Computing for Scientists and
Engineers, 2001, Springer-Verlag, New York.
- James P.
Cohoon and Jack W. Davidson, 2002, C++ Program Design: An Introduction
to Programming and Object-Oriented Design. McGraw-Hill, 3rd edition.
- Wolfram, S., 1999,
The Mathematica Book, Cambridge University Press, Cambridge, UK.
- Hanselman, D., and B.
Littlefield, 1998, Mastering MATLAB 5, Prentice-Hall, Upper Saddle
River, NJ.
- Press, W., S. Teukolsky,
W. Vetterling, and B. Flannery, 1993, Numerical Recipes Example Book
(C), Cambridge University Press, Cambridge, UK.
- Learn Microsft Visual
C++ Now, 1999, Redmond, Washington.
- Microsoft Excel 97
Developer's Kit, Microsoft Press, 1997, Redmond, Washington.
- Visual J++ 6.0 Programmer's
Guide, Microsoft Press, 1998, Redmond, Washington.
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