CSI 779 / STAT 789

Topics in Computational Statistics:

Statistical Modeling of Financial Data

Fall, 2006

Mondays 4:30 to 7:10.

207 Innovation Hall

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

This course will cover a variety of methods of computational statistics in the analysis of financial data. The emphasis will be on the mathematical models, the statistical methods, and the computations, rather than on topics in the domain of finance.

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.


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) is a prerequisite. Knowledge of advanced calculus and differential equations is also required.


No particular software package will be required. The main software I use is R/S-Plus, but Matlab and other packages can also be used for the assignments and the project. However, students are encouraged to obtain and use R so that the exercises and discussions in class will be easier to follow.

There are a number of useful books on R. A list of books is available at the "Books" link on the main webpage for the R Project.

Frank Harrell has a very useful website on S/R resources. One of the links at that site is to a very useful introductory manual on S (and R).


Data, of course, are the raw materials of any statistical analyses. There is a wealth of easily accessible financial data. Traders need timely data. Persons studying fine structure of price movements require intraday data or even ticker data. For this course we need neither timely data nor intraday day. We will generally be interested in daily, weekly, or monthly closing prices and the volume corresponding to that period. An easy source of the kind of data we need is Yahoo.

Price and volume data can be obtained by entering the symbol. Symbols for indices begin with ^; for example, the symbol for the Dow Jones Industrial Average is ^DJI; for the S&P 500, it is ^SPX; for the Nasdaq Composite, it is ^IXIC; and for the CBOE Volatility Index, it is ^VIX.

The data can be downloaded in a spreadsheet format.

Prices and open interest in exchange-traded options can also be obtained at this Yahoo site.



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 to evaluate/compare derivative pricing models (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.

    Texts and References

    There are a number of useful books on various topics that together comprise "computational finance", or "financial engineering".

    Main text

    The text is Quantitative Methods in Derivatives Pricing: An Introduction to Computational Finance, by Domingo Tavella (2002).
    The general flow of the course follows this text.

    Models of derivative pricing

    Summary of derivative pricing formulas

    Probability theory, with an emphasis on stochastic processes

    Stochastic calculus

    Computational methods

    General reference on financial assets