Seeing Shapes in Clouds: On the Performance-Cost trade-off for Heterogeneous Infrastructure-as-a-Service

In the near future FPGAs will be available by the hour, however this new Infrastructure as a Service (IaaS) usage mode presents both an opportunity and a challenge: The opportunity is that programmers can potentially trade resources for performance on a much larger scale, for much shorter periods of time than before. The challenge is in finding and traversing the trade-off for heterogeneous IaaS that guarantees increased resources result in the greatest possible increased performance. Such a trade-off is Pareto optimal. The Pareto optimal trade-off for clusters of heterogeneous resources can be found by solving multiple, multi-objective optimisation problems, resulting in an optimal allocation of tasks to the available platforms. Solving these optimisation programs can be done using simple heuristic approaches or formal Mixed Integer Linear Programming (MILP) techniques. When pricing 128 financial options using a Monte Carlo algorithm upon a heterogeneous cluster of Multicore CPU, GPU and FPGA platforms, the MILP approach produces a trade-off that is up to 110% faster than a heuristic approach, and over 50% cheaper. These results suggest that high quality performance-resource trade-offs of heterogeneous IaaS are best realised through a formal optimisation approach.Comment: Presented at Second International Workshop on FPGAs for Software Programmers (FSP 2015) (arXiv:1508.06320

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.

The GPU vs Phi Debate: Risk Analytics Using Many-Core Computing

The risk of reinsurance portfolios covering globally occurring natural catastrophes, such as earthquakes and hurricanes, is quantified by employing simulations. These simulations are computationally intensive and require large amounts of data to be processed. The use of many-core hardware accelerators, such as the Intel Xeon Phi and the NVIDIA Graphics Processing Unit (GPU), are desirable for achieving high-performance risk analytics. In this paper, we set out to investigate how accelerators can be employed in risk analytics, focusing on developing parallel algorithms for Aggregate Risk Analysis, a simulation which computes the Probable Maximum Loss of a portfolio taking both primary and secondary uncertainties into account. The key result is that both hardware accelerators are useful in different contexts; without taking data transfer times into account the Phi had lowest execution times when used independently and the GPU along with a host in a hybrid platform yielded best performance.Comment: A modified version of this article is accepted to the Computers and Electrical Engineering Journal under the title - "The Hardware Accelerator Debate: A Financial Risk Case Study Using Many-Core Computing"; Blesson Varghese, "The Hardware Accelerator Debate: A Financial Risk Case Study Using Many-Core Computing," Computers and Electrical Engineering, 201

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

Massively Parallelized Monte Carlo Simulation and Its Applications in Finance

In this paper, we propose, develop and implement a tool that increases the computational speed of exotic derivatives pricing at a fraction of the cost of traditional methods. Our paper focuses on investigating the computing efficiencies of GPU systems. We utilize the GPU’s natural parallelization capabilities to price financial instruments. We outline our implementation, solutions to practical complications arising during implementation and how much faster GPU systems are. Each step that we explore has a significant impact on the efficiency and performance of GPU pricing. Rather than speaking in theoretical, abstract terms, we detail each step in an attempt to give the reader a clear sense of what’s going on. Efficiency is one of the pillars of financial calculations. With the volume of risk calculations mandated by prudent risk management practices, even moderate improvements in calculation efficiency can translate into material changes in trading limits or savings in regulatory capital. This can make the difference between a growing, successful trading operation or an also-ran. Unfortunately, a decent algorithm written in VBA cannot calculate option prices at the same speed as a farm of computers, particularly if we must price the trade in less than 150 milliseconds using 10 million simulation paths. Fast forward from one trade to a book of several hundred thousand trades, many of which are exotic products. Not only is it necessary to price each trade, but we must do so in each of thousands of different market scenarios in order to calculate even basic risk measures such as Greeks and Value-at-Risk (VaR). At the end of the paper, we discuss how GPUs are currently used in the industry and their various advantages, including cost, time, accuracy and calculation frequency. In addition, we discuss the implementation challenges of GPU systems and the attention to detail that is required for memory allocation

Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time

In recent years, the counterparty credit risk measure, namely the default risk in \emph{Over The Counter} (OTC) derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of \emph{Basel II} and \emph{Basel III.} More explicitly, to obtain the related risk figures, one has first obliged to compute intermediate output functionals related to the \emph{Mark-to-Market} (MtM) position at a given time $t \in [0, T],$ T being a positive, and finite, time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome latter issue, we propose a smart exploitation of the properties of the (local) time spent by the Brownian motion close to a given value