Monte-Carlo Simulation-Based Financial Computing on the Maxwell FPGA Parallel Machine [chapter]

Xiang Tian, Khaled Benkrid
2013 High-Performance Computing Using FPGAs  
Efficient computational solutions for scientific and engineering problems are a priority for many governments around the world, as they can offer major economic comparative advantages. Financial computing problems are a prime example of such problems where even the slightest improvements in execution times and latency can generate large amounts of extra profits. However, financial computing has not benefited relatively greatly from early developments in high performance computing, as the latter
more » ... aimed mainly at engineering and weapon design applications. Besides, financial experts were initially focusing on developing mathematical models and computer simulations in order to comprehend the behavior of financial markets and develop risk-management tools. As this effort progressed, the complexity of financial computing applications grew up rapidly. Hence, high performance computing turned out to be very important in the field of finance. Many financial models do not have a practical closed-form solution in which case numerical methods are the only alternative. Monte-Carlo simulation is one of the most commonly used numerical methods, in financial modeling and scientific computing in general, with huge computation benefits in solving problems where closed-form solutions are impossible to derive. As the Monte-Carlo method relies on the average result of thousands of independent stochastic paths, massive parallelism can be harnessed to accelerate the computation. For this, high performance computers, increasingly with off-the-shelf accelerator hardware, are being proposed as an economic high performance implementation platform for Monte-Carlo-based simulations. Field programmable gate arrays (FPGAs) in particular have been recently proposed as a high performance and relatively low power acceleration platform for such applications. In light of the above, the project presented in this chapter develops novel FPGA hardware architectures for Monte-Carlo simulations of different types of financial option pricing models, namely European, Asian, and American options, the stochastic volatility model (GARCH model), and Quasi-Monte Carlo simulation. These architectures have been implemented on an FPGA-based supercomputer, called Maxwell, developed at the University of Edinburgh, which is one of the few openly available FPGA parallel machines in the world. Maxwell is a 32-CPU cluster augmented with 64 Virtex-4 Xilinx FPGAs connected in a 2D torus. Our hardware implementations all show significant computing efficiency compared to traditional software-based implementations, which in turn shows that reconfigurable computing technology can be an efficacious and efficient platform for high performance computing applications, particularly financial computing. One widely used computational technique in financial computing is Monte-Carlo simulation. The latter is a numerical computational algorithm which is often used in simulating physical and mathematical systems. It relies on repeated random sampling to compute their result. This method is often used when it is impossible or impractical to get an analytical solution, or closed-form result, to system equations. The Monte-Carlo method is particularly important in physical chemistry, computational physics, and related applied fields. These are characterized by systems with a large number of coupled degrees of freedom, such as liquids, disordered materials, strongly coupled solids, and cellular structures. Monte-Carlo simulations are also used to forecast a wide range of events and scenarios, such as the weather, sales, and consumer demands. In financial computing, the Monte-Carlo technique is used to simulate the various sources of uncertainty that affect the value of the underlying instrument, portfolio, or investment in question. Many financial computing applications have no closed form solutions, as they depend on three or more stochastic variables. Here, Monte-Carlo simulation tends to be numerically more efficient than other procedures [4] . This is because the computational time of Monte-Carlo simulations increases approximately linearly with the number of variables, whereas in most other methods, computational time increases exponentially with the number of variables. One of the important characteristics of Monte-Carlo simulation is parallelism as multiple independent paths need to be computed. This makes it attractive to parallel implementation using multi-threading and/or multiprocessing. When evaluating a high performance computing platform, we have to consider several aspects. The cost of cluster computers and supercomputers can be prohibitive. Area and power consumption can also be a major problem with these computing platforms. For these reasons, various acceleration technologies are being considered. Field programmable gate arrays (FPGAs), for instance, offer the high performance of a dedicated hardware solution of a particular algorithm, with a fraction of the area and power consumption of equivalent microprocessor-based solutions. Moreover, the continuous developments in transistor integration levels mean that it is now possible to implement a considerable number of floating-point arithmetic units on modern FPGAs. If this trend is to continue, FPGA use is set to conquer new application domains, including financial computing. The work presented in this chapter is mainly targeted on an FPGA parallel machine, called Maxwell. Maxwell was one of the first publicly accessible FPGA parallel machines and was built in Edinburgh, Scotland, by the FPGA High Performance Computing Alliance (FHPCA). Established in 2004, the FHPCA's aim was to explore the computing capability of a heterogeneous high performance computing platform, which combines general purpose processors (GPPs) and Xilinx FPGAs. Led by Edinburgh Parallel Computing Centre (EPCC) at The University of Edinburgh, the FHPCA was funded by Scottish Enterprise and built on the skills
doi:10.1007/978-1-4614-1791-0_2 fatcat:tz34xzedmvdulkbwnwxy7numme