Energy-Efficient FPGA Implementation for Binomial Option Pricing Using OpenCL

International audienceEnergy efficiency of financial computations is a performance criterion that can no longer be dismissed, and is as crucial as raw acceleration and accuracy of the solution. In order to reduce the energy consumption of financial accelerators, FPGAs offer a good compromise with low power consumption and high parallelism. However, designing and prototyping an application on an FPGA-based platform are typically very time-consuming and requires significant skills in hardware design. This issue constitutes a major drawback with respect to software-centric acceleration platforms and approaches. A high-level approach has been chosen, using Altera’s implementation of the OpenCL standard, to answer this issue. We present two FPGA implementations of the binomial option pricing model on American options. The results obtained on a Terasic DE4 - Stratix IV board form a solid basis to hold all the constraints necessary for a real world application. The best implementation can evaluate more than 2000 options/s with an average power of less than 20W

Exploring Functional Acceleration of OpenCL on FPGAs and GPUs Through Platform-Independent Optimizations

OpenCL has been proposed as a means of accelerating functional computation using FPGA and GPU accelerators. Although it provides ease of programmability and code portability, questions remain about the performance portability and underlying vendor's compiler capabilities to generate efficient implementations without user-dened, platform specic optimizations. In this work, we systematically evaluate this by formalizing a design space exploration strategy using platform-independent micro-architectural and application-specic optimizations only. The optimizations are then applied across Altera FPGA, NVIDIA GPU and ARM Mali GPU platforms for three computing examples, namely matrix-matrix multiplication, binomial-tree option pricing and 3-dimensional nite difference time domain. Our strategy enables a fair comparison across platforms in terms of throughput and energy efficiency by using the same design effort. Our results indicate that FPGA provides better performance portability in terms of achieved percentage of device's peak performance (68%) compared to NVIDIA GPU (20%) and also achieves better energy efficiency (up to 1:4X) for some of the considered cases without requiring in-depth hardware design expertise

A parallel and pipelined implementation of a Pascal-simplex based two asset option pricer on FPGA using OpenCL

With the resurgence of hardware for financial technology, several methods for accelerating financial option pricing have been investigated. This paper presents the first architecture and implementation of a two-asset option pricer based on Pascal’s simplex, which takes advantage of the parallelism and pipelining offered by FPGA technology. The theory that this architecture is constructed from is based on a recombining multinomial tree approach which in turn is a generalization of the binomial tree model. Furthermore, we show that while a significant difficulty exists in efficiently maintaining the intermediate values required for the computation, a solution exists in the form of FIFOs. Our implementation, on an Intel Stratix 10 GX FPGA, is based on the OpenCL framework and can compute 6250 two asset option prices per second for a time step of 100 and the pipelining of the option value computation show a 25 times improvement when a 50-step pipeline is created

Accelerating Reconfigurable Financial Computing

This thesis proposes novel approaches to the design, optimisation, and management of reconfigurable computer accelerators for financial computing. There are three contributions. First, we propose novel reconfigurable designs for derivative pricing using both Monte-Carlo and quadrature methods. Such designs involve exploring techniques such as control variate optimisation for Monte-Carlo, and multi-dimensional analysis for quadrature methods. Significant speedups and energy savings are achieved using our Field-Programmable Gate Array (FPGA) designs over both Central Processing Unit (CPU) and Graphical Processing Unit (GPU) designs. Second, we propose a framework for distributing computing tasks on multi-accelerator heterogeneous clusters. In this framework, different computational devices including FPGAs, GPUs and CPUs work collaboratively on the same financial problem based on a dynamic scheduling policy. The trade-off in speed and in energy consumption of different accelerator allocations is investigated. Third, we propose a mixed precision methodology for optimising Monte-Carlo designs, and a reduced precision methodology for optimising quadrature designs. These methodologies enable us to optimise throughput of reconfigurable designs by using datapaths with minimised precision, while maintaining the same accuracy of the results as in the original designs

Automatic generation of high-throughput systolic tree-based solvers for modern FPGAs

Tree-based models are a class of numerical methods widely used in financial option pricing, which have a computational complexity that is quadratic with respect to the solution accuracy. Previous research has employed reconfigurable computing with small degrees of parallelism to provide faster hardware solutions compared with general-purpose processing software designs. However, due to the nature of their vector hardware architectures, they cannot scale their compute resources efficiently, leaving them with pricing latency figures which are quadratic with respect to the problem size, and hence to the solution accuracy. Also, their solutions are not productive as they require hardware engineering effort, and can only solve one type of tree problems, known as the standard American option. This thesis presents a novel methodology in the form of a high-level design framework which can capture any common tree-based problem, and automatically generates high-throughput field-programmable gate array (FPGA) solvers based on proposed scalable hardware architectures. The thesis has made three main contributions. First, systolic architectures were proposed for solving binomial and trinomial trees, which due to their custom systolic data-movement mechanisms, can scale their compute resources efficiently to provide linear latency scaling for medium-size trees and improved quadratic latency scaling for large trees. Using the proposed systolic architectures, throughput speed-ups of up to 5.6X and 12X were achieved for modern FPGAs, compared to previous vector designs, for medium and large trees, respectively. Second, a productive high-level design framework was proposed, that can capture any common binomial and trinomial tree problem, and a methodology was suggested to generate high-throughput systolic solvers with custom data precision, where the methodology requires no hardware design effort from the end user. Third, a fully-automated tool-chain methodology was proposed that, compared to previous tree-based solvers, improves user productivity by removing the manual engineering effort of applying the design framework to option pricing problems. Using the productive design framework, high-throughput systolic FPGA solvers have been automatically generated from simple end-user C descriptions for several tree problems, such as American, Bermudan, and barrier options.Open Acces

Lower Precision calculation for option pricing

The problem of options pricing is one of the most critical issues and fundamental building blocks in mathematical finance. The research includes deployment of lower precision type in two options pricing algorithms: Black-Scholes and Monte Carlo simulation. We make an assumption that the shorter the number used for calculations is (in bits), the more operations we are able to perform in the same time. The results are examined by a comparison to the outputs of single and double precision types. The major goal of the study is to indicate whether the lower precision types can be used in financial mathematics. The findings indicate that Black-Scholes provided more precise outputs than the basic implementation of Monte Carlo simulation. Modification of the Monte Carlo algorithm is also proposed. The research shows the limitations and opportunities of the lower precision type usage. In order to benefit from the application in terms of the time of calculation improved algorithms can be implemented on GPU or FPGA. We conclude that under particular restrictions the lower precision calculation can be used in mathematical finance.

Optimización del rendimiento y la eficiencia energética en sistemas masivamente paralelos

RESUMEN Los sistemas heterogéneos son cada vez más relevantes, debido a sus capacidades de rendimiento y eficiencia energética, estando presentes en todo tipo de plataformas de cómputo, desde dispositivos embebidos y servidores, hasta nodos HPC de grandes centros de datos. Su complejidad hace que sean habitualmente usados bajo el paradigma de tareas y el modelo de programación host-device. Esto penaliza fuertemente el aprovechamiento de los aceleradores y el consumo energético del sistema, además de dificultar la adaptación de las aplicaciones. La co-ejecución permite que todos los dispositivos cooperen para computar el mismo problema, consumiendo menos tiempo y energía. No obstante, los programadores deben encargarse de toda la gestión de los dispositivos, la distribución de la carga y la portabilidad del código entre sistemas, complicando notablemente su programación. Esta tesis ofrece contribuciones para mejorar el rendimiento y la eficiencia energética en estos sistemas masivamente paralelos. Se realizan propuestas que abordan objetivos generalmente contrapuestos: se mejora la usabilidad y la programabilidad, a la vez que se garantiza una mayor abstracción y extensibilidad del sistema, y al mismo tiempo se aumenta el rendimiento, la escalabilidad y la eficiencia energética. Para ello, se proponen dos motores de ejecución con enfoques completamente distintos. EngineCL, centrado en OpenCL y con una API de alto nivel, favorece la máxima compatibilidad entre todo tipo de dispositivos y proporciona un sistema modular extensible. Su versatilidad permite adaptarlo a entornos para los que no fue concebido, como aplicaciones con ejecuciones restringidas por tiempo o simuladores HPC de dinámica molecular, como el utilizado en un centro de investigación internacional. Considerando las tendencias industriales y enfatizando la aplicabilidad profesional, CoexecutorRuntime proporciona un sistema flexible centrado en C++/SYCL que dota de soporte a la co-ejecución a la tecnología oneAPI. Este runtime acerca a los programadores al dominio del problema, posibilitando la explotación de estrategias dinámicas adaptativas que mejoran la eficiencia en todo tipo de aplicaciones.ABSTRACT Heterogeneous systems are becoming increasingly relevant, due to their performance and energy efficiency capabilities, being present in all types of computing platforms, from embedded devices and servers to HPC nodes in large data centers. Their complexity implies that they are usually used under the task paradigm and the host-device programming model. This strongly penalizes accelerator utilization and system energy consumption, as well as making it difficult to adapt applications. Co-execution allows all devices to simultaneously compute the same problem, cooperating to consume less time and energy. However, programmers must handle all device management, workload distribution and code portability between systems, significantly complicating their programming. This thesis offers contributions to improve performance and energy efficiency in these massively parallel systems. The proposals address the following generally conflicting objectives: usability and programmability are improved, while ensuring enhanced system abstraction and extensibility, and at the same time performance, scalability and energy efficiency are increased. To achieve this, two runtime systems with completely different approaches are proposed. EngineCL, focused on OpenCL and with a high-level API, provides an extensible modular system and favors maximum compatibility between all types of devices. Its versatility allows it to be adapted to environments for which it was not originally designed, including applications with time-constrained executions or molecular dynamics HPC simulators, such as the one used in an international research center. Considering industrial trends and emphasizing professional applicability, CoexecutorRuntime provides a flexible C++/SYCL-based system that provides co-execution support for oneAPI technology. This runtime brings programmers closer to the problem domain, enabling the exploitation of dynamic adaptive strategies that improve efficiency in all types of applications.Funding: This PhD has been supported by the Spanish Ministry of Education (FPU16/03299 grant), the Spanish Science and Technology Commission under contracts TIN2016-76635-C2-2-R and PID2019-105660RB-C22. This work has also been partially supported by the Mont-Blanc 3: European Scalable and Power Efficient HPC Platform based on Low-Power Embedded Technology project (G.A. No. 671697) from the European Union’s Horizon 2020 Research and Innovation Programme (H2020 Programme). Some activities have also been funded by the Spanish Science and Technology Commission under contract TIN2016-81840-REDT (CAPAP-H6 network). The Integration II: Hybrid programming models of Chapter 4 has been partially performed under the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme. In particular, the author gratefully acknowledges the support of the SPMT Department of the High Performance Computing Center Stuttgart (HLRS)