http://bura.brunel.ac.uk/handle/2438/235 2026-04-05T19:46:52Z 2026-04-05T19:46:52Z Penco, Vittorio http://bura.brunel.ac.uk/handle/2438/32341 2025-11-14T19:37:02Z 2025-01-01T00:00:00Z

Title: Application of factor models to risk premium estimation Authors: Penco, Vittorio Abstract: We provide a rigorous mathematical approach to the beta-pricing model, starting from the standard two-step cross-sectional regression, through Nonlinear Seemingly Unrelated Regression (NSUR) and Generalized Method of Moments (GMM), and finally compare the results with several linear approximation methods. The use of the linear approximation applied to a single-factor nonlinear system of equations is new in the literature and is one of the major contributions of this work. Our results show that, in the presence of heavy-tailed distributions, the L1-norm methods proposed in this study are more appropriate (exhibiting lower bias and variance) for risk price estimation than traditional L2-norm approaches. It is also the first time that the Capital Asset Pricing Model (CAPM) is applied systematically to compare the integration and segmentation between different markets and a given portfolio set. Our study, Penco and Lucas (2024), applies a two-factor integration model to the economies of Asia, Europe, Japan and North America, showing integration between the European and North American economies. We also extend the integration model to commodity markets. To capture more accurately the cross-sectional pricing of commodity risk we use the Cochrane factor mimicking approach and compare the results with alternative dependence-based integration measures using copulas. We show how the copula correlation between the Stochastic Discount Factor (SDF) and returns differentiates the contribution of joint dependence from the contribution of the risk prices. Finally, we introduce a penalised p-value Fama-MacBeth Generalized Least Squares (GLS) regularisation, which provides several advantages over other methods as it ensures that retained factors contribute not only to statistical fit but also to risk pricing. Unlike other approaches, this method regularises the pricing kernel directly. Factors that lack significance or explanatory power are penalised and removed, while priced and relevant sources of risk are preserved. Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London

2025-01-01T00:00:00Z Grublys, Mykolas http://bura.brunel.ac.uk/handle/2438/31718 2025-08-15T13:42:27Z 2024-01-01T00:00:00Z

Title: Echo state networks in forecasting chaotic dynamics and emergent universalities Authors: Grublys, Mykolas Abstract: Deep learning has become a popular way to accurately recognise, classify, generate and forecast data in various complex scenarios. It is commonly based on artificial neural networks, a type of machine learning architecture inspired by the human brain, that consist of multiple layers of neurons with non-linear activations. Their inside workings can be considered as a ‘black box’ because it is difficult, if not impossible, to truly understand “how” or “why” such networks work. Furthermore, the training relies on gradient decent methods which are inherently difficult and computationally expensive. Reservoir Computing has recently emerged as a new paradigm aimed to alleviate such difficulties. In this thesis, we study its particular realisation, known as Echo State Networks (ESNs), which show promise in many tasks, particularly in forecasting the dynamics of chaotic systems. The thesis will provide a detailed discussion of the ESN architecture, hyperparameters, and implementation. We introduce a new performance metric that highlights the networks maintaining small errors for the longest duration and use it in GridSearch to optimise ESN hyperparameters. We study the statistical properties of the correlation matrix that is formed during training, offering a novel approach not applied to ESNs or other types of recurrent networks. Our extensive numerical studies reveal universal results, consistent across tests and different chaotic training signals. Although analytical studies are limited, we introduce a simple ‘toy model’ to qualitatively describe some properties. We conclude our work with study of the statistics of trained output weights, which also exhibit universal characteristics. These universalities provide deeper insights into the inner workings and behaviour of ESNs, enhancing our understanding of how information spreads throughout the network. Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London

2024-01-01T00:00:00Z Jipreze, Kam http://bura.brunel.ac.uk/handle/2438/31502 2025-06-27T02:00:47Z 2024-01-01T00:00:00Z

Title: New control variates for pricing basket and Asian options Authors: Jipreze, Kam Abstract: In this thesis, we investigate new control variates for simulation-based pricing of options where the option price is a function of the sum of (or integral of) lognormal random variables. We use two different approaches: one is the use of Hermite polynomial approximation of the relevant function and another is the use of upper and lower bounds on the option prices obtained using the properties of Brownian motion. We provide detailed numerical experiments to illustrate the use of these approaches for accurate and low variance pricing basket and Asian options. First order Hermite polynomial approximation also gives a reasonable direct approximation to the basket or Asian option price for at the money and in-the-money options. Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London

2024-01-01T00:00:00Z Roy, Gargi http://bura.brunel.ac.uk/handle/2438/31173 2025-05-07T02:01:02Z 2025-01-01T00:00:00Z

Title: Non-parametric probabilistic machine learning methodologies suited to real-world data Authors: Roy, Gargi Abstract: Recent years have seen a massive increase in the use of supervised learning for prediction tasks in various real-world applications. In supervised learning, the relationship between two variables - an input and an output - is sought. In spite of several existing learning models, the learning of this sought relation poses several challenges given real-world data due to different characteristics of this data, such as noise of the observations; non-stationarity in the data; inhomogeneities present in the correlations between different output pairs that are realised at inputs located differently in the space of the input variable. Moreover, real-world data can be high-dimensional, where both the input and the output can be tensor-valued in general. These challenges induce the following desirables in the prediction that is performed after such learning is undertaken: fast prediction that is accurate, uncertainty-included and reliable, as well as low in computational complexity, for easy implementation. Additionally, the prediction exercise - foreshadowed by the learning - needs to be scalable to high-dimensions. Although, some of the existing learning models address a subset of the challenges given non-stationary data, (towards reliable, uncertainty-included predictions), they typically require learning of a large number of hyperparameters, making these learning techniques computationally intensive. Also, they do not come with easy-to-implement algorithms, which makes these models infeasible for applications using medium sized real-world data. Furthermore, some of the existing models are designed for dedicated applications, using domain-specific model assumptions, generalisability of which outside the domains can be questioned. This thesis addresses challenges of real-world data, and presents applications of a generic, completely non-parametric learning model that is reliable, accurate, parsimonious, and works given non-stationary data that can be high-dimensional in general. Equipped with an easy-toimplement algorithm, such a learning technique overcomes the limitations of existing models. More precisely, this thesis attempts demonstration of reliable learning of a function (that represents the relation between a pair of random variables), by modelling this function as a sample function of a Gaussian Process. Such learning will be followed by fast prediction of the output that is realised at test inputs, where said prediction offers closed-form mean and variance of this output. In fact, in this approach, the predictions that follow the learning of the inter-variable relation, follows from the identification of the posterior predictive distribution of outputs realised at test inputs. The illustration of this approach has been performed for applications in various domains such as finance, energy consumption and astrophysics, were the data is inhomogeneously correlated and have diverse dimensions. From finance sector, real-world time-series data has been considered where both the input and output is scalar-variate. In the real-world energy consumption data, the input is vector-variate and the output is a scalar. The astrophysics application uses an astronomical simulation data where the input is a vector and the output is a matrix, yielding the sought function to be high-dimensional. Inference is undertaken throughout my doctoral work using Markov chain Monte Carlo (MCMC) sampling techniques. This thesis also highlights the sensitivity of predictions achieved with Deep Neural Networks (DNN), to the architecture of the DNNs. The chapter-wise distribution is as follows. The first chapter introduces the topic. The second chapter discusses various MCMC techniques and illustrations of these inference techniques to perform parametric learning with a small real-world data. The third chapter introduces the background of Gaussian Process (GP) based learning, application of GP-based supervised learning for efficient learning of uncertainty with an under-constraint MCMC for prediction. A probabilistic, non-parametric, non-stationary, parsimonious learning strategy is presented in the fourth chapter along with results on applying the model, and on comparison against existing models. This application is relevant to the case of both input and output is scalar-variate and the data is inhomogeneously-correlated. The fifth chapter includes the application of the learning strategy with a multivariate (with vector input and scalar output), inhomogeneously-correlated real-world data. This chapter also discusses some ideas about inhomogeneities in the correlation structure of the training data and the DNN exposition in both univariate and multivariate setups. An application of the learning of a high-dimensional function is discussed in the sixth chapter. In this application, the input is a vector and the output is a matrix. Prediction of the output at a test input vector is then presented. Finally the thesis has been concluded in chapter seven. The first appendix includes the application of the presented non-parametric learning strategy towards forecasting, along which a new strategy for designing of priors for performing forecasting with real-world inhomogeneously-correlated data. The second appendix includes some of the results of inference preformed with various MCMC techniques included in chapter two. Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London

2025-01-01T00:00:00Z