A domain specific language for accelerated multilevel Monte Carlo simulations

Abstract

Monte Carlo simulations are used to tackle a wide range of exciting and complex problems, such as option pricing and biophotonic modelling. Since Monte Carlo simulations are both computationally expensive and highly parallelizable, they are ideally suited for acceleration through GPUs and FPGAs. Alongside these accelerators, Multilevel Monte Carlo techniques can be harnessed to further hasten simulations. However, researchers and application developers must invest a great deal of effort to design, optimise and test such Monte Carlo simulations. Furthermore, these models often have to be rewritten from scratch to target new hardware accelerators. This paper presents Neb, a Domain Specific Language for describing and generating Multilevel Monte Carlo simulations for a variety of hardware architectures. Neb compiles equations written in LATEX to C++, OpenCL or Maxeler's MaxJ language, allowing acceleration through GPUs or FPGAs. Neb can be used to solve stochastic equations or to generate paths for analysis with other tools. To evaluate the performance of Neb, a variety of financial models are executed on CPUs, GPUs and FPGAs, demonstrating peak acceleration of 3.7 times with FPGAs in 40nm transistor technology, and 14.4 times with GPUs in 28nm transistor technology. Furthermore, the energy efficiency of these accelerators is compared, revealing FPGAs to be 8.73 times and GPUs 2.52 times more efficient than CPUs.