MSI Weekly Bulletin - Week starting Monday 5 December, 2005

The performance gap between processing elements and memory has become the main obstacle in fast processing of large data sets. The von Neumann computing paradigm reinforces this problem by focusing on instruction rather than data processing. Graphics Processors Units (GPUs) have traditionally been optimised for high data throughput. They subscribe to a data-stream-based computing paradigm which maximises memory efficiency and exploits the parallelsim in situations when the same operation is applied to many data items. The presentationn gives an introduction to the GPU programming model and explains how to exploit the enormous computing power of up to 192 GFLOPS in scientific computations. Important topics are parallel GPU programming, matrix vector products, accuracy and discretisation schemes. The hardware acceleration is illustrated with solutions of different PDE and minimum problems in image processing and computer vision.

In the setting of a market where the stock price process is assumed to follow FATGBM, this paper presents a discrete approximation scheme and a possible pricing method for path dependent options. Based on the binomial model of Cox, Ross and Rubenstein (1979), a recombining tree is constructed so that the option price can be calculated as a conditional expectation. A proof of convergence of the scheme is outlined and an upper bound for the American option price is derived.