Analysis of parallel processor architectures for the solution of the Black-Scholes PDE

Common parallel computer microarchitectures offer a wide variety of solutions to implement numerical algorithms. The efficiency of different algorithms applied to the same problem vary with the underlying architecture which can be a multi-core CPU, many-core GPU, Intel´s MIC (Many Integrated Core) or FPGA architecture. Significant differences between these architectures exist in the ISA (Instruction Set Architecture) and the way the compute flow is executed. The way parallelism is expressed changes with the ISA, thread management and customization available on the device. These differences pose restrictions to the implementable algorithms. The aim of the work is to analyze the efficiency of the algorithms through the architectural differences. The problem at hand is the one-factor Black-Scholes option pricing equation which is a parabolic PDE solved with explicit and implicit time-marching algorithms. In the implicit solution a scalar tridiagonal system of equations needs to be solved. The possible CPU, GPU implementations along with novel FPGA solutions with HLS (High Level Synthesis) will be shown. Performance is also analyzed and remarks on efficiency are made.