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.

Antimicrobial activities and diversity of sponge derived microbes

In this study, marine sponges collected in Irish waters were analysed for their associated microbiota. Of the approximately 240 bacterial isolates obtained from two sponges several showed antimicrobial activity; among them members of genera which have rarely been shown to produce antimicrobial compounds. Differences observed from the sponge-derived groups of isolates in terms of bioactivity suggests that S. carnosus isolates may be a better source of antibacterial compounds, while Leucosolenia sp. isolates appear to be a better source of antifungal compounds. More than 60% of fungal isolates obtained from 12 sponge samples proved to be bioactive. One of the isolates, which was closely related to Fusarium oxysporum and showed activity against bacteria and fungi, was investigated for its secondary metabolite genes. At least 5 different NRPS genes, with a sequence similarity as low as 50 % to known genes, were identified highlighting the likelihood that this isolate may be capable of producing novel secondary metabolites. A Micromonospora sp. was isolated from a Haliclona simulans sample collected in Irish waters. The isolate inhibited the growth of Gram positive bacterial test strains in three different antimicrobial assays. Employing preparative layer chromatography the compound responsible for the bioactivity could be isolated. According to LC-MS andNMR data the bioactive compound could indeed be novel. Finally, two deep water sponges were shown to host a remarkably different bacterial and archaeal diversity by application of 454 Pyrosequencing. The L. diversichela –proteobacterial community was dominated by a single ƴ-proteobacterial bacterium whereas the S. normani sample hosted a largely sponge specific microbial community, even more diverse than has been previously reported for shallow water sponges. Organisms potentially involved in nitrification, sulphate reduction and secondary metabolite production were found to be spatially distributed in the sponge. Furthermore, a deep sea specific population was implied.

Chemical vapour deposition of complex ferroic oxide thin films

Herein is presented a novel chemical vapour deposition (CVD) route for the fabrication of oxide ferroelectrics. A versatile layer-by-layer growth mode was developed to prepare naturally super-latticed bismuth based materials belonging to the Aurivillius phase family, with which good control over composition and crystal structure was achieved. In chapter 3, the effect of epitaxial strain on one of the very simple oxide materials TiO2 was studied. It has been found that the ultra-thin TiO2 films demonstrate ferroelectric behaviour when grown on NdGaO3 substrates. TiO2 exists in various crystal phases, but none of them show ferroelectric behaviour. The epitaxial strain due to the substrate, changes the crystal structure from tetragonal to orthorhombic which in turn leads to ferroelectric behaviour. In chapter 4, a unique growth method for multiferroic BiFeO3 (BFO) thin films is shown, where a phase pure BFO thin films can be prepared even in the presence of excess bismuth precursor during the growth process. This type of growth is usually called adsorption controlled growth and can be used for growing various bismuth containing compounds, where the volatility of bismuth can create various types of defects. Chapter 5 describes the growth of Bi4Ti3O12 thin films in a layer-by-layer growth mode. In this section, the effect of Bi and Ti precursor flows on the growth of thin films is discussed and it is shown that how change in precursor flows leads to out-ofphase boundary defects during the layer-by-layer growth mode. In chapter 6, the growth of a compound Bi5Ti3FeO15, which is a 1:1 mixture of BiFeO3 and Bi4Ti3O12, is presented. The growth mechanism of Bi5Ti3FeO15 thin films is presented, where the Fe precursor flow was controlled from zero to the insertion of one full BiFeO3 perovskite unit cell into the Bi4Ti3O12 structure in addition, the effect of iron precursor flow on crystalline properties is demonstrated. The methods presented in this thesis can be adopted to grow ferroelectric and multiferroic films for industrial applications.