Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Investment incentives and valuation of power sector infrastructure assets with increasing interconnection, intermittency and decarbonisation

This dissertation applies a variety of quantitative methods to electricity and carbon market data, utility company accounts data, capital and operating costs to analyse some of the challenges associated with investment in energy assets. In particular, three distinct research topics are analysed within this general theme: the efficiency of interconnector trading, the optimal sizing of intermittent wind facilities and the impact of carbon pricing on the cost of capital for investors are researched in successive sections.

Exploring the relationship between social network sites and the consumption of cultural goods through the lens of affordances

This thesis presents research theorising the use of social network sites (SNS) for the consumption of cultural goods. SNS are Internet-based applications that enable people to connect, interact, discover, and share user-generated content. They have transformed communication practices and are facilitating users to present their identity online through the disclosure of information on a profile. SNS are especially effective for propagating content far and wide within a network of connections. Cultural goods constitute hedonic experiential goods with cultural, artistic, and entertainment value, such as music, books, films, and fashion. Their consumption is culturally dependant and they have unique characteristics that distinguish them from utilitarian products. The way in which users express their identity on SNS is through the sharing of cultural interests and tastes. This makes cultural good consumption vulnerable to the exchange of content and ideas that occurs across an expansive network of connections within these social systems. This study proposes the lens of affordances to theorise the use of social network sites for the consumption of cultural goods. Qualitative case study research using two phases of data collection is proposed in the application of affordances to the research topic. The interaction between task, technology, and user characteristics is investigated by examining each characteristic in detail, before investigating the actual interaction between the user and the artifact for a particular purpose. The study contributes to knowledge by (i) improving our understanding of the affordances of social network sites for the consumption of cultural goods, (ii) demonstrating the role of task, technology and user characteristics in mediating user behaviour for user-artifact interactions, (iii) explaining the technical features and user activities important to the process of consuming cultural goods using social network sites, and (iv) theorising the consumption of cultural goods using SNS by presenting a theoretical research model which identifies empirical indicators of model constructs and maps out affordance dependencies and hierarchies. The study also provides a systematic research process for applying the concept of affordances to the study of system use.

A study of the Hobson and Rogers volatility model

We firstly examine the model of Hobson and Rogers for the volatility of a financial asset such as a stock or share. The main feature of this model is the specification of volatility in terms of past price returns. The volatility process and the underlying price process share the same source of randomness and so the model is said to be complete. Complete models are advantageous as they allow a unique, preference independent price for options on the underlying price process. One of the main objectives of the model is to reproduce the `smiles' and `skews' seen in the market implied volatilities and this model produces the desired effect. In the first main piece of work we numerically calibrate the model of Hobson and Rogers for comparison with existing literature. We also develop parameter estimation methods based on the calibration of a GARCH model. We examine alternative specifications of the volatility and show an improvement of model fit to market data based on these specifications. We also show how to process market data in order to take account of inter-day movements in the volatility surface. In the second piece of work, we extend the Hobson and Rogers model in a way that better reflects market structure. We extend the model to take into account both first and second order effects. We derive and numerically solve the pde which describes the price of options under this extended model. We show that this extension allows for a better fit to the market data. Finally, we analyse the parameters of this extended model in order to understand intuitively the role of these parameters in the volatility surface.

Identifying novel molecular mechanisms of ghrelin receptor signalling underlying neural control of food intake: interaction with stress and impulsivity

The gut-hormone, ghrelin, activates the centrally expressed growth hormone secretagogue 1a (GHS-R1a) receptor, or ghrelin receptor. The ghrelin receptor is a G-protein coupled receptor (GPCR) expressed in several brain regions, including the arcuate nucleus (Arc), lateral hypothalamus (LH), ventral tegmental area (VTA), nucleus accumbens (NAcc) and amygdala. Activation of the GHS-R1a mediates a multitude of biological activities, including release of growth hormone and food intake. The ghrelin signalling system also plays a key role in the hedonic aspects of food intake and activates the dopaminergic mesolimbic circuit involved in reward signalling. Recently, ghrelin has been shown to be involved in mediating a stress response and to mediate stress-induced food reward behaviour via its interaction with the HPA-axis at the level of the anterior pituitary. Here, we focus on the role of the GHS-R1a receptor in reward behaviour, including the motivation to eat, its anxiogenic effects, and its role in impulsive behaviour. We investigate the functional selectivity and pharmacology of GHS-R1a receptor ligands as well as crosstalk of the GHS-R1a receptor with the serotonin 2C (5-HT2C) receptor, which represent another major target in the regulation of eating behaviour, stress-sensitivity and impulse control disorders. We demonstrate, to our knowledge for the first time, the direct impact of GHS-R1a signalling on impulsive responding in a 2-choice serial reaction time task (2CSRTT) and show a role for the 5-HT2C receptor in modulating amphetamine-associated impulsive action. Finally, we investigate differential gene expression patterns in the mesocorticolimbic pathway, specifically in the NAcc and PFC, between innate low- and high-impulsive rats. Together, these findings are poised to have important implications in the development of novel treatment strategies to combat eating disorders, including obesity and binge eating disorders as well as impulse control disorders, including, substance abuse and addiction, attention deficit hyperactivity disorder (ADHD) and mood disorders.