An efficient and accurate lattice numerical model for options pricing on GPUs
File(s)
Author(s)
Omeru, Oghenevworhe Joan
Type
Thesis
Abstract
Option contracts are financial instruments that derive their value from the value of an underlying asset. There are options pricing problems which have no analytical solution, hence must be solved numerically, by discretising the problem into a grid, with an increasing grid resolution corresponding to both increased accuracy, but also an increase in computational time.
Following the 2008 financial crisis, the industry has faced real-time pricing demands to more effectively estimate/manage risk. Technological advances and availability of commodity parallel hardware such as GPUs, which provide exceptional compute power than traditional CPUs, taken together this has led to a need for faster numerical methods which retain accuracy and are also optimised for today's contemporary parallel hardware.
This thesis improves upon existing numerical options pricing methods in terms of both accuracy and computational time and thus presents novel lattice numerical algorithms, providing an improved accuracy-speed trade-off on GPUs compared to traditional algorithms.
The research objectives and original contributions are twofold: reducing overall compute operation count via reduced grid nodes density, that is, coarsening the grid without losing the solution accuracy achieved from existing methods, consequently, reducing the compute time needed to achieve this solution accuracy and ensuring that the computational cost in terms of both compute resources and compute time of this new approach can be realised in contemporary GPUs.
We present a novel options pricing numerical method, the Hybrid Mesh Model (HMM) with implementation on GPU achieving significantly faster solutions compared to existing methods. The HMM extends on the trinomial and explicit finite difference standard lattice methods initially with static grid refinement regions, then an extension to predict this refinement region boundaries based on the option pricing parameters. Finally, the HMM is extended to have a dynamic refinement zone adjustment, providing additional reduction in compute time over the static HMM.
Following the 2008 financial crisis, the industry has faced real-time pricing demands to more effectively estimate/manage risk. Technological advances and availability of commodity parallel hardware such as GPUs, which provide exceptional compute power than traditional CPUs, taken together this has led to a need for faster numerical methods which retain accuracy and are also optimised for today's contemporary parallel hardware.
This thesis improves upon existing numerical options pricing methods in terms of both accuracy and computational time and thus presents novel lattice numerical algorithms, providing an improved accuracy-speed trade-off on GPUs compared to traditional algorithms.
The research objectives and original contributions are twofold: reducing overall compute operation count via reduced grid nodes density, that is, coarsening the grid without losing the solution accuracy achieved from existing methods, consequently, reducing the compute time needed to achieve this solution accuracy and ensuring that the computational cost in terms of both compute resources and compute time of this new approach can be realised in contemporary GPUs.
We present a novel options pricing numerical method, the Hybrid Mesh Model (HMM) with implementation on GPU achieving significantly faster solutions compared to existing methods. The HMM extends on the trinomial and explicit finite difference standard lattice methods initially with static grid refinement regions, then an extension to predict this refinement region boundaries based on the option pricing parameters. Finally, the HMM is extended to have a dynamic refinement zone adjustment, providing additional reduction in compute time over the static HMM.
Version
Open Access
Date Issued
2024-04-01
Date Awarded
2026-04-01
Copyright Statement
Attribution-Non Commercial-No Derivatives 4.0 International Licence (CC BY-NC-ND)
Advisor
Imad, Jaimoukha
Publisher Department
Department of Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Master of Philosophy (MPhil)