Dimension Reduction for the Black-Scholes Equation

In financial markets of today, where prices fluctuate by the minute, a common strategy is to use computational models to gain some insight into what the future holds. As the technology advances, more trust is invested in these models and the demands on accuracy and performance increase.

These pages present a study in which we investigated a numerical method for estimating the proper price of European basket options using a technique which is quite different from the standard stochastic methods. The pricing of basket options leads to high dimensional problems and these are difficult to solve numerically with discrete methods. Our approach is to reduce the dimensionality of the problem by taking advantage of the high correlation between the underlying stocks.

Here, you will find an overview of options and option pricing, then a description of the problem of high dimensionality
and the proposed solution that we have evaluated. Finally, the results of this evaluation is presented, followed by a discussion were possible improvements are also mentioned.

For more in depth information on this project, see the full report.