Last updated: January 17, 2004
 
 

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.