FPGA-Based Reconfigurable Computing for Pricing Multi-asset Barrier Options

摘要

Multi-asset barrier contracts are path-dependent exotic options consisting of two or more underlying assets. As the dimensions of an option increase, so does the mathematical complexity of a closed form solution. Monte Carlo (MC) methods offer an attractive solution under such conditions. MC methods have an O(n-1/2) convergence rate irrespective of the dimension of the integral. However, such methods using conventional computing with CPUs are not scalable enough to enable banks to realize the potential that these exotic options promise. This paper presents an FPGA-based accelerated system architecture to price multi-asset barrier contracts. The architecture consists of a parallel set of Monte Carlo cores, each capable of simulating multiple Monte Carlo paths. Each MC core is designed to be customizable so that the core for the model (i.e., "model" core) can be easily replaced. In our current design, a Heston core based on the full truncation Euler discretization method is used as the model core. Similarly, we can use different payoff calculator kernels to compute various payoffs such as vanilla portfolios, barriers, look-backs, etc. The design leverages an early termination condition of "out" barrier options to efficiently schedule MC paths across multiple cores in a single FPGA and across multiple FPGAs. The target platform for our design is Novo-G, a reconfigurable supercomputer housed at the NSF Center for High-Performance Reconfigurable Computing (CHREC), University of Florida. Our design is validated for the single-asset configuration by comparing our output to option prices calculated analytically and achieves an average speedup of ranging from 123 to 350 on one FPGA as we vary the number of underlying assets from 32 down to 4. For a configuration with 16 underlying assets, the speedup achieved is 7134 when scaled to 48 FPGAs as compared to a single-threaded version of an SSE2-optimized C program running on a single Intel Sandy- Bridge E5-2687 core at 3.1 GHz with hyper-threading turned on. Finally, the techniques described in this paper can be applied to other exotic multi-asset option classes, such as look backs, rainbows, and Asian-style options.