Electrical and Electronic Engineering, Imperial College London
Doi
Abstract
Monte Carlo simulation is one of the most widely used techniques for computationally
intensive simulations in a variety of applications including mathematical
analysis and modeling and statistical physics. A multivariate Gaussian
random number generator (MVGRNG) is one of the main building blocks of
such a system. Field Programmable Gate Arrays (FPGAs) are gaining increased
popularity as an alternative means to the traditional general purpose
processors targeting the acceleration of the computationally expensive random
number generator block due to their fine grain parallelism and reconfigurability
properties and lower power consumption.
As well as the ability to achieve hardware designs with high throughput it
is also desirable to produce designs with the flexibility to control the resource
usage in order to meet given resource constraints. This work proposes a novel
approach for mapping a MVGRNG onto an FPGA by optimizing the computational
path in terms of hardware resource usage subject to an acceptable
error in the approximation of the distribution of interest. An analysis on the
impact of the error due to truncation/rounding operation along the computational path is performed and an analytical expression of the error inserted into
the system is presented.
Extra dimensionality is added to the feature of the proposed algorithm by
introducing a novel methodology to map many multivariate Gaussian random
number generators onto a single FPGA. The effective resource sharing techniques
introduced in this thesis allows further reduction in hardware resource
usage.
The use of MVGNRG can be found in a wide range of application, especially
in financial applications which involve many correlated assets. In this
work it is demonstrated that the choice of the objective function employed
for the hardware optimization of the MVRNG core has a considerable impact
on the final performance of the application of interest. Two of the most important
financial applications, Value-at-Risk estimation and option pricing are
considered in this work