Quadrature based methods for numerical integration provide a means of quickly and accurately pricing financial products such as options. These methods can be applied to multi-dimensional products, such as options on multiple underlying assets, but suffer from an exponential increase in computational complexity as the dimension increases. This paper examines the theoretical complexity of quadrature methods for pricing multi-dimensional options, and then relates this to practical performance in contemporary hardware. An automated system for generating hardware architectures for quadrature is used to explore the performance of increasing dimensionality in FPGA implementations, and then compared them to GPU and CPU solutions. We find that a single-precision FPGA can provide 25 times speedup over software in three dimensions, and offers slightly improved performance over a GPU using comparable technology. The latest GPUs are 2.7 times faster than the older technology Virtex-4 FPGA, but the FPGA still provides over 9 times the energy efficiency.
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