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.

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.