Hot Topics Nanotechnology Biotechnology Computational Finance Astrophysics Green Chemistry Learning Goes Beyond Lectures Signs of Excellence Computing, Instrumentation, and the New Labs Why Choose Carnegie Mellon for Science?

Have a question? Try these links: Visits and Applications FAQ Parents Contact Us Site Map Home Carnegie Mellon Undergraduate Admissions

Mellon College of Science Carnegie Mellon

Computational Finance

Computational finance uses modern mathematics, most of which was developed in the twentieth century, to solve age-old problems of how to price and manage risk in financial markets. The importance of mathematics in finance became evident with the advent of the Black-Scholes formula for pricing stock options, a formula based on "stochastic calculus," a branch of mathematics which combines probability and calculus. This formula won for its creators the 1997 Nobel Prize in Economics.

Topics of current interest in computational finance at Carnegie Mellon include:

How to account for the risk of default of a corporate bond
How to measure and control risk in a portfolio of securities
How to compute option prices quickly and accurately
How to develop better mathematical models of financial markets
How to estimate parameters in current mathematical models

Revolutionizing Investment Banking

The Black-Scholes formula and its successors, such as the Heath-Jarrow-Morton model for pricing options on bonds, has revolutionized the practice of investment banking. These formulas are the basis for software used daily to trade billions of dollars of financial contracts. Department of Mathematical Sciences Professor David Heath was one of the creators of the Heath-Jarrow-Morton model.

Optimization Methods to Handle Risk

Reha Tütüncü's work on the application of optimization techniques focuses on financial and chemical engineering problems. His new methods allow fast and reliable computation of the optimal risky portfolios. He has also worked on a new algorithm for robust solution of asset allocation problems when the statistical input parameters are unreliable.

Strong mathematics involvement in Computational Finance Program

Carnegie Mellon has faculty in several departments with an interest and history of cooperation in computational finance. The university is unusual because so many of these faculty are in the Department of Mathematical Sciences. In addition to the ones mentioned above, Steven Shreve is well known for his books on mathematical finance and is the Director of the B.S. Program in Computational Finance. Dmitry Kramkov was Director of Research for Tokyo-Mitsubishi Bank before coming to Carnegie Mellon. Roy Nicolaides is another member of the Department of Mathematical Sciences who works on problems in finance.

Because of this large number of faculty, the Department boasts a rich offering of courses and undergraduate research opportunities related to mathematical models in finance.

Computational Finance links
B.S. in Computational Finance at Carnegie Mellon
Article in the July/August 2002 issue of The American Enterprise about mathematics professionals in the aggressive world of high-stakes investing
General undergraduate mathematics information, including the B.S. in Computational Finance program
Computational Finance suggested course sequence
Center for Computational Finance
Master of Science in Computational Finance