Theory and application of the ornstein-uhlenbeck process: computational modelling and trading of the eur/gbp currency pair in an electronic market
File(s)
Author(s)
Scharpf, Benjamin
Type
Thesis
Abstract
The formulation of mathematical models which aptly represent the inherent complexity of financial data, while maintaining sufficient generality for diverse applications, is a prevalent challenge confronted by researchers and practitioners. This is particularly pertinent in the modelling of mean-reverting financial securities, regardless of whether the primary aim is to trade them or to engineer models capable of forecasting critical market parameters such as volatility or interest rates. This report delves into the stochastic differential equation of the Ornstein-Uhlenbeck (OU) process, subjecting it to rigorous mathematical analysis and computer simulation. Forward-modelling the process facilitates the retrieval of its parameters during inverse modelling via linear regression and maximum likelihood estimation, with the results being substantiated through Monte-Carlo simulation. Additionally, the Kalman filter is deployed to ascertain the true state of the OU process from noisy observations, thus offering an insight into the estimation of the OU process through an unsupervised online machine learning technique. A more intricate exploration of computational modelling leads to the formulation of an algorithm to compute the mean-stopping time for the OU process. This study also bridges the gap between continuous and discrete-time models, illustrating the variance characteristics of autoregressive time series versus Brownian motion, i.e. a diffusion-type process, as a limiting case in discrete time. Translating theory into practice, the EUR/GBP exchange rate process is meticulously examined through a case study, with data sourced from the European Central Bank spanning from 2009 to 2022. This is modelled to adhere to an OU process, providing a probabilistic outlook on potential future exchange rates in the EUR/GBP market for 2023 and beyond. Furthermore, significant attention is paid to the Kelly criterion, explored both theoretically and practically, emphasizing its critical role when actively trading the mentioned currency pair. In a frictionless market...
Version
Open Access
Date Issued
2023-02-28
Date Awarded
01/12/2023
Advisor
Parpas, Panos
Sponsor
London Interdisciplinary Social Science DTP
Publisher Department
Computing
Publisher Institution
Imperial College London
Qualification Level
Masters
Qualification Name
Master of Philosophy (MPhil)