CSI 779 / STAT 789

Topics in Computational Statistics:

Computational Finance

Spring, 2001

Wednesdays 4:30 to 7:10.

Instructor: James Gentle; email: jgentle@gmu.edu

This course will cover a variety of methods of computational statistics in the analysis of financial data. Many of the standard results in finance rely on simplifying assumptions about the distribution of random components. These results can be examined by Monte Carlo methods, and can be modified by bootstrapping. The course will address the use of Monte Carlo and the bootstrap in portfolio optimization and in the pricing of derivatives. The course will also cover the use of clustering, classification, and pattern recognition in studying classes of assets and asset prices.

The emphasis will be on the statistical methods and on the computations, rather than on topics in the domain of finance. While some background in finance would be useful, it will not be necessary. Some knowledge of statistical theory and methods (roughly equivalent to STAT 554 and STAT 652) and an introduction to computers are prerequisites.

Texts and References

The content of the course will be based primarily on two monographs: Fouque, Papanicolaou, and Sircar (2000), Derivatives in Financial Markets with Stochastic Volatility, and Michaud (1998) Efficient Asset Management . Some articles in the current literature will be used. Notes developed by the instructor will also be distributed. Links to some useful Web sites will also be provided.

Grading

Performance in the class will be evaluated based on

  • an in-class midterm (25%)
  • a final exam consisting of a take-home portion and an in-class portion (35%)
  • a project (30%)
  • a number of smaller assignments (10%)

    Students may discuss and otherwise collaborate on the project and the homework, but what is submitted for grading must be written by the individual students.

    Each student will prepare a Web page for presentation of the project and for some of the smaller assignments.

    Topics

    Schedule

    (subject to adjustment)

    January 17, 2001

    Statistical modeling of financial data.
    Methods of computational statistics (handout).
    The nature of financial data.
    Reference: Rydberg (2000), International Statistical Review 68, 233--258.
    Comparing two distributions; goodness-of-fit tests.

    January 24, 2001

    Structure in financial data.
    Smoothing data.
    Reference: Lo, Mamaysky, Wang (2000) Journal of Finance 55, 1705--1765.

    January 31, 2001

    Monte Carlo methods in analysis of financial data.

    February 7, 2001

    Models of Finacial Asset Prices and Portfolio Behavior

    February 14, 2001

    Discuss semester projects.
    Portfolio construction.
    Mean-variance optimization.
    Quadratic programming. Software.
    The efficient frontier and variations.
    Example in Michaud, page 13.

    February 21, 2001

    Review and summarize some basics of financial analysis.
    Reference: Sharpe, Alexander, and Bailey (1999) Investments

    February 28, 2001

    Discuss semester projects.
    More on technical patterns.
    More on portfolio optimization.
    Variations on classical mean-variance optimization; the efficient frontier under randomness (Michaud).
    Bootstrap methods.

    March 7, 2001

    No class --- Spring break

    March 14, 2001

    Midterm exam.

    March 21, 2001

    Review midterm.
    Discuss semester projects.

    March 28, 2001

    Brief descriptions of semester projects.
    Basics of derivatives.
    Classical Black-Scholes-Merton theory (Fouque, Papanicolaou, and Sircar, Chapter 1).
    Some basic results in the stochastic calculus (this will be expanded).
    Stochastic volatility and implied volatility (Fouque, Papanicolaou, and Sircar, Chapter 2).
    Assignment.

    April 4, 2001

    Longer descriptions of semester projects.
    Stochastic differential equations with two sources of randomness.
    Stochastic volatility and models for derivative pricing. (Fouque, Papanicolaou, and Sircar, Chapter 2.)

    April 11, 2001

    Stochastic volatility and derivative pricing.
    Clustering and mean-reverting stochastic volatility (Fouque, Papanicolaou, and Sircar, Chapter 3).
    Applications to pricing of financial derivatives.
    (Fouque, Papanicolaou, and Sircar, Chapters 4, 5, and 6).

    April 18, 2001

    Pricing of American derivatives and other topics (Fouque, Papanicolaou, and Sircar, Chapter 9).

    April 25, 2001

    Presentations of semester projects.
    Hand out take-home portion of final exam.

    May 2, 2001

    Take-home portion of final exam due.
    In-class portion of final exam.

    Students

    The students in the class all have homepages on which they put parts of their assignments and other interesting stuff.
    Ben Crain
    Yaru Li
    Phu Nguyen
    Paul Rowane
    Xun Wang