Optimising explicit finite difference option pricing for dynamic constant reconfiguration

Abstract

This paper demonstrates a novel optimisation methodology to adjust stencil based numerical procedures from the algorithm level, so as to reduce not only the amount of hardware resource consumption per kernel but also the amount of computation required to achieve desired result accuracy, when mapping the algorithm to reconfigurable hardware using dynamic constant reconfiguration. As a result, less area is needed to support run-time reconfiguration, and less computational steps are required in the numerical procedure to obtain a result with given error tolerance. We analyse one thousand fixed point implementations on a Virtex-6 XC6V-LX760 FPGA for randomly generated option pricing problems, which are representative of industrial computation. When comparing optimised implementations to the unoptimised ones, the reconfiguration area upper bound is reduced by 22%; the average number of computational steps is reduced by 23%; and the area-computation-time product is reduced by 40%; while the numerical errors of the results are kept below the error tolerant level used in industry.